I imagine everyone will have seen people on soccer mentioning City being a traditionally lower league club prior to Sheikh Mansour's takeover (which is used to denigrate City in obvious ways, but is also commonly used to express shock at our revenues). I thought people may be interested in some actual statistics:

• As of the summer of 2008, before the takeover, City were 7th in the all time top flight points table (with all games converted to the three points for a win system). We were on 4397 points (above Spurs and Chelsea).
  
• As of 2006 (which I have chosen as it predates the Shinawatra takeover which could otherwise have been seen to have influenced the value), Forbes ranked City as the 14th most valuable club in world football (https://www.forbes.com/consent/ketch/?toURL=https://www.forbes.com/2006/03/28/cz_06soccer_top25slide.html). This is above Spurs, Everton and Villa in England and above big European teams like Ajax, Dortmund, Porto, Atletico, and I think is perhaps the stat that best demonstrate that City were by no means minnows at the time of the takeover.
  
• In the 07/08 season prior to the takeover, City had the 6th highest attendance in England.
  
• City had a total of twelve trophies as of the time of the takeover (three of these were charity shields, so not always included as major trophies). Depending on how you calculate (as different lists count different trophies), City were around 10th-11th in the English rankings.
  

I thought this could be more useful context for some of our youngenewer fans. I'm sure there'll be rival fans reading this and thinking that this is some form of bragging about our previous (mid-level and moderate achievements, in the grander scheme of things), but that isn't my intention - it's more to dispel a bit of a myth about City not having been one of the bigger clubs in England prior to the takeover.

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Here's a detailed review of pre-calculus concepts, including their importance in calculus and statistics:
Equations and Inequalities

• Solving Equations: Understanding how to solve various types of equations, including linear, quadratic, and polynomial equations, is crucial for calculus and statistics. In calculus, equations are used to model real-world phenomena, and in statistics, they are used to describe relationships between variables.
• Inequalities: Inequalities are used to describe ranges of values and are essential in calculus and statistics. For example, in calculus, inequalities are used to find the maximum and minimum values of functions, while in statistics, they are used to describe confidence intervals and hypothesis testing.

Functions

• Domain and Range: Understanding the domain and range of functions is vital in calculus and statistics. In calculus, functions are used to model real-world phenomena, and the domain and range of these functions determine the scope of the model. In statistics, functions are used to describe relationships between variables, and the domain and range of these functions determine the scope of the relationship.
• Composition of Functions: Composition of functions is used in calculus to combine functions and model complex phenomena. In statistics, composition of functions is used to describe complex relationships between variables.

Graphs and Graphing

• Graphing Functions: Graphing functions is essential in calculus and statistics. In calculus, graphs are used to visualize functions and understand their behavior, while in statistics, graphs are used to visualize relationships between variables and understand patterns and trends.
• Understanding Graphs: Understanding the shape and behavior of graphs is crucial in calculus and statistics. In calculus, graphs are used to identify maximum and minimum values, while in statistics, graphs are used to identify patterns and trends.

Trigonometric Functions and Identities

• Trigonometric Functions: Trigonometric functions, such as sine, cosine, and tangent, are used in calculus to model periodic phenomena. In statistics, trigonometric functions are used to describe relationships between variables that have a periodic nature.
• Trigonometric Identities: Trigonometric identities, such as the Pythagorean identity and the sum and difference formulas, are used in calculus to simplify complex expressions and solve equations. In statistics, trigonometric identities are used to describe relationships between variables and simplify complex calculations.

These pre-calculus concepts are essential for success in calculus and statistics. They provide a foundation for understanding more advanced mathematical concepts and are used to model and describe real-world phenomena.

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• UNIVERSITY OF: Alabama Arizona California (UC) Central Florida Chicago Cincinnati Florida Houston Illinois (Urbana-Champaign) Iowa Maryland Minnesota Michigan North Texas Pennsylvania Southern Florida Texas Toronto
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• Only people located in North America have access to Venmo Cash App Zelle.
• This is an excellent way to determine if the person you're dealing with is from the United States.
• Within reason, I offer a partial or full money-Back guarantee if the student is very unsatisfied with my academic services.

TUTORING AVAILABLE FOR OTHER SUBJECTS:

• For other subjects, you can reach out to me, and I can connect you with one of my tutoring partners who can provide general academic assistance for the following subjects:
• Art & Design: Art History Design Film Studies
• Business: Accounting (Acc) Biz Courses Business Administration (Biz Admn) Business Calculus Business Law Business Statistics Corporate Finance Economics (Econ) Finance (Fin) Financial Accounting Intermediate Accounting Intermediate Microeconomics (Micro) Macroeconomics (Macro) Management (Mgmt) Managerial Accounting Marketing MBA
• Computer Science: C C++ Computer Programming (Comp) Java Python R (Introduction & Intermediate Level Only)
• Humanities: Communications (Comm) English Literature Essay & Term Paper Writing, Editing, Proofreading Essays History Papers Philosophy (Phil) Religious Studies Theology (Theo)
• Mathematics: A.P. Calculus AB & BC Psychology Statistics AP Statistics Bio statistics Calculus I (1) Calculus II (2) Calculus III (3) College Algebra Differential Equations Discrete Math Finite Math Functions General Math Geometry Liberal Arts Math Linear Algebra Multi-variable Calculus Partial Differential Equations Precalculus Probability Quantitative Reasoning Real Analysis Statistics Trigonometry (Trig) Vector Calculus
• Science & Medicine: Anatomy & Physiology (A & P) Biochemistry Biology (Bio) Biostatistics Earth Science Environmental Science General Chemistry (Chem) Healthcare Medicine Nursing Nutrition Organic Chemistry Physics (Phys)
• Social Sciences: Anthropology Economics (Econ) Geology Law & Justice Liberal Arts Liberal Studies Political Science Psychology Sociology

THE OBLIGATORY "IS THIS A SCAM?" QUESTION:
Considering the fact that you found my contact information online, it’s understandable to be skeptical regarding the legitimacy of my services. Therefore, I’m willing to do all of the following to help you feel more secure in trusting me with your academic needs:

• 1) Speak with you on the phone and answer any questions you may have so that you have the opportunity to assess and analyze my tone, articulation, accent, diction, dialect, regionalisms, pitch, vocabulary, word choice, intonations, and inflections.
• NOTE: I’m a New Jersey-born Irish/Italian-American, but I have been told that I speak in an erudite & articulate suburban American accent with a “professor style” voice somewhat resembling the voice of actor: Ben Stein.
• 2) Agree to do some homework questions of yours upfront with the work fully shown in real-time to prove my mastery of the course content.
• 3) Send you screenshots of at least five past scores I attained from completing exams & homework assignments for other students in the same type of class you need help with.
• 4) Send you full screenshots of written exam solutions I wrote up by hand for students in the past in the same course that you need help with so that you can see my neat handwriting.
• 5) Provide you with the contact information of students who have utilized my services in the past who would be more than willing to vouch for my skills.

MY REBUTTAL TO THE OBLIGATORY “IS THIS A SCAM?” QUESTION:
At the risk of sounding arrogant, I consider myself to be at least marginally more intelligent (both academically & socially) than the average person. Therefore, if I ever decided to suddenly risk prison time, risk my reputation, and risk enduring the wrath of modern-day “cancel culture” by scamming people out of their money:

• I certainly wouldn’t do it for such paltry amounts of money. (i.e., anything less than $1,000 per victim.)
• I certainly wouldn’t choose high school & college students as my “target audience” to scam, considering that most people without college degrees have abysmally low annual incomes. Why choose low-income victims when it would be much more profitable to target high-income, high-net-worth individuals earning at least six figures a year? I have knowledge in business consulting, and I promise you that a business owner would be a MUCH more lucrative mark than a low-income college student.
• I wouldn’t choose such a time & energy-draining method of scamming people. Also, communicating back and forth with potential clients is an absurdly long time sink since only less than 10% of all potential clients who reach out to me actually become paying clients of mine. This means that 90% of my time communicating with potential clients ultimately proves to be a colossal waste of my irretrievable time & energy.
• If you pay me to provide academic services and I don’t deliver, you can always dispute the payment with the payment app and easily get your money refunded. If I were in the habit of swindling money from people, then all of my payment accounts would have been investigated and be completely shut down by now. And I would have been permanently banned from opening new accounts. Therefore, the fact that all my payment apps have been fully active for years should be sufficient proof that I haven’t had people consistently disputing payments sent to me.

HOW TO CONTACT ME:
Paid Help from Hiraedu: If You're struggling to handle your Online Exams, Assignments or any other coursework, get help from Hiraedu and pay after the exam. Contact details for Hiraedu is: WhatsApp: +1 (213) 594-5657 OR Call: +1 727 456 9641

• I take my work as a tutor very seriously, and I always aim to do my best to help my students excel in school. I have a solid and sincere passion for academic achievement, and with my help, I am positive that I can help students obtain very high grades with minimal stress and effort.
• Please feel free to contact me if you're interested in my services and would like to learn more. I'm available 24/7 via phone call, email, and text. Again, thank you for taking the time to read my Reddit tutoring ad, and I hope to hear from you soon!

My contact details:
WhatsApp: +1 (213) 594-5657
Call: +1 727 456 9641
Website: hiraedu. com
Email: [info@hiraedu](mailto:info@hiraedu). com
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If You're struggling to handle your Online Exams, Assignments or any other coursework, get help from Hiraedu and pay after the exam. Contact details for Hiraedu is: WhatsApp: +1 (213) 594-5657 OR Call: +1 727 456 9641
ASSESSMENTS I CAN COMPLETE:

• Online Courses (1 - 20 Weeks Long)
• Homework Assignments
• Exams Quizzes Tests
• Excel Projects
• Discussion Forum Posts
• Research Papers Term Papers Essays
• Employment Assessments

MY MATH SUBJECTS OF EXPERTISE:
I am very knowledgeable and proficient in assisting students in a wide range of mathematics classes. I can help students complete their homework assignments and other projects get an A on quizzes, tests, and exams (including proctored assessments) answer online discussion posts write essays & papers in MLA APA Chicago format and provide general overall academic help in each math course listed below:

• Advanced Placement Honors High School Level Math
• AP Calculus AB A.P. Calculus BC
• AP Statistics
• Biostatistics Bio-Statistics
• College Algebra Intermediate Algebra
• Business Calculus
• Business Statistics
• Business Math
• Calculus I Calculus II Calculus III (Calc)
• Geometry
• International Baccalaureate (IB) Maths
• Liberal Arts Math
• Logic & Reasoning
• Multivariable Calculus Multi variable Calculus
• Precalculus Pre-calculus
• Probability & Statistics
• Psychology Statistics Psych Stats
• Quantitative Reasoning Quantitative Methods Quantitative Literacy (Quant)
• Statistics (Stats)
• Statistics for Social Sciences
• Trigonometry (Trig)

STATISTICS HELP (MY BEST SUBJECT):

• I have a master's degree in Applied Statistics from a university in New Jersey, USA. As a result, I am very proficient in helping students with various types of Statistics courses including Biostatistics Business Statistics Elementary Statistics Probability & Statistics Psychology Statistics.
• I have extensive knowledge and skill with helping students get through various statistical concepts including all of the following in alphabetical order:
• ANOVA Bar Graph, Boxplot, Dot Plot, Histogram, Pie Chart Bias Binomial, Exponential, Poisson, Gamma, Uniform Distribution Central Limit Theorem Chi-Square Test Coefficient of Determination (R^2) Conditional & Relative Probability Confidence Interval Correlation Coefficient (r) Critical Region Critical Value Descriptive & Inferential Statistics Effect Size Expected Value Experiment vs Observation Goodness of Fit Test Hypothesis Testing Interpolation & Extrapolation Interquartile Range (IQR) Kurtosis Left, Negative, Right, Positive Skewed Distribution Logistic Regression Mean, Median, Mode, Midrange Multiple Regression Nominal, Ordinal, Interval, Ratio I Population Parameter Normal, Symmetric & Bell Shaped Distribution Null & Alternate Hypothesis One & Two Sample T-Test One & Two Sample Z-Test Ordinary Least Squares Outliers P-Value Pooled Variance (Equal Variances) Proportion R^2 Range Regression Regression Line Reject & Fail to Reject Ho Relative & Cumulative Frequency Distributions Relativity & Reliability Right, Left, One, Two Tailed Tailed Hypothesis Test Sample Statistics Sampling Methods (Convenience, Stratified, Simple, Cluster, Systematic) Significance Level (1%, 5%, 10%) Skewness Standard Deviation& Variance T-Score Test Statistic Time Series Type I & Type II Errors Unbiased Estimators Z-Score

ALGEBRA HELP:

• I am well-versed in helping students do well in Algebra 1 & 2 College Algebra Intermediate Algebra Pre-Algebra and I am very knowledgeable and proficient in the following algebra topics in alphabetical order:
• Absolute Values Circle Equation Domain Exponents Graphing Horizontal & Vertical Asymptotes Inequalities, Equations & Functions Inverse Functions Linear, Exponential, Logarithmic, Quadratic Equations Logarithms Maximum & Minimum Values of a Graph Number Lines One-to-One Functions Parallel & Perpendicular Lines Plotting Points & Ordered Pairs Point-Slope Form Polynomial Division Polynomials Radicals Range Rational & Irrational Expressions Rational Functions Real Roots Real Zeros Relations & Functions Slope Slope-Intercept Form Square Roots Standard Form of a Line System of Equations System of Inequalities Variables X and Y Intercepts

CALCULUS HELP:

• I am well-versed in helping students do well in Calculus I, II & III, Calculus 1, 2 & 3, Business Calculus, Multivariable Calculus, Vector Calculus and I am very knowledgeable and proficient in the following calculus topics in alphabetical order:
• Absolute & Local Maximum and Minimum Antiderivative Area & Volume Chain Rule Concavity Continuity Convergence Test Critical Points Curvature Curve of Rotation Curve Sketching Derivatives Divergence Test First & Second Derivative Test Fourier Series Implicit Differentiation Increasing / Decreasing Functions Infinite Series Integrals Integration by Parts Jacobian Matrix Limits L’Hopital’s Rule Maclaurin Series Mean Value Theorem Partial Derivative Product & Quotient Rule Reiman Sum Related Rates Simpson’s Rule Solid of Revolution Substitution Rule Taylor Series

Paid Help from Hiraedu: If You're struggling to handle your Online Exams, Assignments or any other coursework, get help from Hiraedu and pay after the exam. Contact details for Hiraedu is: WhatsApp: +1 (213) 594-5657 OR Call: +1 727 456 9641
ATTRIBUTES THAT SET ME APART FROM OTHER TUTORS:

• I firmly believe that I have many attributes and skills that set me apart from other tutors. Below is a list of qualities that makes me an ideal fit to help you master your coursework:

I CAN AID STUDENTS TAKING PROCTORED ASSESSMENTS:

• Proficient in CollegeBoard AP Calculus AB, AP Calculus BC & AP Statistics exams.
• Skilled with International Baccalaureate Math Exams: IB Maths HL & IB Maths SL
• Can intentionally answer a few problems incorrectly at the student's request.
• Can text solutions to the student while they are taking a proctored exam.
• Upon request, can purposely obtain grades below an A (ex: B+, B, C+, C-).
• I can stretch out the time to a plausible length for timed exams and assignments before submitting them.
• Have reliable software that can change my IP address to match the closest major city near the student.
• I have exceptional multiple-choice exam-taking skills. I have mastered the various techniques to make calculated guesses for the correct option in standardized exams such as the SAT & GRE.

I CAN VERIFY MY ACADEMIC KNOWLEDGE & SKILLS:

• I have no problem with requests to solve sample problems upfront to prove my knowledge & proficiency of the course concepts.
• I can provide glowing references & strong examples of work done for past clients to verify my academic skills.
• I can also provide, upon request, complete detailed calculations with explanations for solutions to the problems worked on.
• I am quite skilled and adept in using multiple modernized educational platforms and software, including but not limited to: Brightspace MyStatLab D2L WebAssign Canvas MyMathLab Blackboard ALEKS
• Can format term papers and discussion posts in APA MLA Harvard Chicago Vancouver OSCOLA IEEE format.

I HAVE PAID ACCESS TO OVER 15 STUDY-HELP WEBSITES AND MATHEMATICAL SOFTWARE:

• I have multiple paid subscriptions to a wide range of academic tutoring resources, including Chegg, Quizlet, CourseHero, Brainly, Grammarly, Study. com, Bartleby, Slader, Transtutors, Slideshare, StudocU, Turnitin, Academia, SymboLab, WolframAlpha, and Scribd to help guide to solve exam & homework questions that I may not immediately know.
• However, I am smart enough not to blatantly plagiarize solutions online but instead write them in my own unique words, formatting, & mathematical terminology.
• I have access to a very sophisticated graphing calculator and various mathematical software that provides step-by-step solutions to complex mathematical problems within seconds, allowing me to provide exact solutions to the student in a timely manner.
• I have impeccable handwriting and a high-quality mobile scanner app that allows me to scan written solutions in very legible high-definition JPG, PNG, or PDF formats.

MY AVAILABILITY & RELIABILITY:

• Depending on my availability, I can accommodate immediate tutoring requests, 1-24 hour, and 1-30-day deadlines.
• I can schedule live real-time online sessions and meet deadlines in an impressively timely fashion.
• I can provide quick notifications and updates of progress made in the student's class via email text phone calls.
• I can also be available to tutor students for Fall 2021 Spring 2022 Summer 2022 semesters.

MY EDUCATIONAL SOFTWARE OF EXPERTISE:

• I am very knowledgeable and well-versed in a wide range of educational software to tutor students in including but not limited to: Acellus ALEKS APEX Learning Aplia Blackboard Brightspace Canvas Cengage CengageNow Connect ConnectMath Connexus CPM D2L Discord Edmentum Eviews Examity Excel Hawkes Learning Honorlock Khan Academy Knewton LimeSpring Lumen Maple MasteringChemistry MasteringPhysics MathXL (XL) MATLAB McGraw-Hill Microsoft Word Minitab Moodle MyAccountingLab MyEconLab MyITLab MyLab My Lab MyMathLab My Math Lab MyOpenMath MyPsychLab MySocLab MyStatLab My Stat Lab NCSS Open Source Software Pearson PERT PlatoWeb PowerPoint Prezi R Respondus Lockdown Browser with Webcam Sapling SPSS Stata StraighterLine Straighter Line WebAssign Web Assign Webex (Cisco) WebWork Wiley WileyPlus Wonderlic Zoom

SCHOOLS FROM WHICH I'VE HELPED STUDENTS IN :
As of 2021, I have tutored and helped students enrolled at the following U.S. universities community colleges county & city colleges schools for-profit institutions listed below in alphabetical order:

• A - C: American Public University System (APUS) Arizona State Ashford Brigham Young Brown Broward California State (Fullerton) Capella Chamberlain (Illinois) Colorado Technical Columbia Columbia Southern Cornell
• D - K: Dallas College Dartmouth DeVry Excelsior College Florida International Florida State Full Sail Georgia State Grand Canyon Harvard Houston Community College Ivy Tech Community College Kaplan Kennesaw State Kent State
• L - T: Liberty Lone Star College System Kaplan Miami Dade Michigan State CUNY State University of New York (SUNY) Northern Virginia Ohio State University of Phoenix (UOP) Penn State Princeton Purdue (Davenport) San Diego State San Francisco State San Jose State Southern New Hampshire Southern Nevada Stanford St. Petersburg Strayer Texas Tech
• UNIVERSITY OF: Alabama Arizona California (UC) Central Florida Chicago Cincinnati Florida Houston Illinois (Urbana-Champaign) Iowa Maryland Minnesota Michigan North Texas Pennsylvania Southern Florida Texas Toronto
• U - Z: UCLA Extension Utah State Utah Valley Valencia Walden U Wake Technical Western Governors Wilmington Yale

Paid Help from Hiraedu: If You're struggling to handle your Online Exams, Assignments or any other coursework, get help from Hiraedu and pay after the exam. Contact details for Hiraedu is: WhatsApp: +1 (213) 594-5657 OR Call: +1 727 456 9641
I OFFER FLEXIBLE PAYMENT PLANS:

• I offer several unique payment plans, including a weekly plan, a discounted monthly plan, a discounted half-now / half-later plan, and highly discounted up-front rates.
• I can accept the following payment methods for my services: PayPal Debit Cards Square Cash Credit Cards Cash App Venmo.
• Only people located in North America have access to Venmo Cash App Zelle.
• This is an excellent way to determine if the person you're dealing with is from the United States.
• Within reason, I offer a partial or full money-Back guarantee if the student is very unsatisfied with my academic services.

TUTORING AVAILABLE FOR OTHER SUBJECTS:

• For other subjects, you can reach out to me, and I can connect you with one of my tutoring partners who can provide general academic assistance for the following subjects:
• Art & Design: Art History Design Film Studies
• Business: Accounting (Acc) Biz Courses Business Administration (Biz Admn) Business Calculus Business Law Business Statistics Corporate Finance Economics (Econ) Finance (Fin) Financial Accounting Intermediate Accounting Intermediate Microeconomics (Micro) Macroeconomics (Macro) Management (Mgmt) Managerial Accounting Marketing MBA
• Computer Science: C C++ Computer Programming (Comp) Java Python R (Introduction & Intermediate Level Only)
• Humanities: Communications (Comm) English Literature Essay & Term Paper Writing, Editing, Proofreading Essays History Papers Philosophy (Phil) Religious Studies Theology (Theo)
• Mathematics: A.P. Calculus AB & BC Psychology Statistics AP Statistics Bio statistics Calculus I (1) Calculus II (2) Calculus III (3) College Algebra Differential Equations Discrete Math Finite Math Functions General Math Geometry Liberal Arts Math Linear Algebra Multi-variable Calculus Partial Differential Equations Precalculus Probability Quantitative Reasoning Real Analysis Statistics Trigonometry (Trig) Vector Calculus
• Science & Medicine: Anatomy & Physiology (A & P) Biochemistry Biology (Bio) Biostatistics Earth Science Environmental Science General Chemistry (Chem) Healthcare Medicine Nursing Nutrition Organic Chemistry Physics (Phys)
• Social Sciences: Anthropology Economics (Econ) Geology Law & Justice Liberal Arts Liberal Studies Political Science Psychology Sociology

THE OBLIGATORY "IS THIS A SCAM?" QUESTION:
Considering the fact that you found my contact information online, it’s understandable to be skeptical regarding the legitimacy of my services. Therefore, I’m willing to do all of the following to help you feel more secure in trusting me with your academic needs:

• 1) Speak with you on the phone and answer any questions you may have so that you have the opportunity to assess and analyze my tone, articulation, accent, diction, dialect, regionalisms, pitch, vocabulary, word choice, intonations, and inflections.
• NOTE: I’m a New Jersey-born Irish/Italian-American, but I have been told that I speak in an erudite & articulate suburban American accent with a “professor style” voice somewhat resembling the voice of actor: Ben Stein.
• 2) Agree to do some homework questions of yours upfront with the work fully shown in real-time to prove my mastery of the course content.
• 3) Send you screenshots of at least five past scores I attained from completing exams & homework assignments for other students in the same type of class you need help with.
• 4) Send you full screenshots of written exam solutions I wrote up by hand for students in the past in the same course that you need help with so that you can see my neat handwriting.
• 5) Provide you with the contact information of students who have utilized my services in the past who would be more than willing to vouch for my skills.

MY REBUTTAL TO THE OBLIGATORY “IS THIS A SCAM?” QUESTION:
At the risk of sounding arrogant, I consider myself to be at least marginally more intelligent (both academically & socially) than the average person. Therefore, if I ever decided to suddenly risk prison time, risk my reputation, and risk enduring the wrath of modern-day “cancel culture” by scamming people out of their money:

• I certainly wouldn’t do it for such paltry amounts of money. (i.e., anything less than $1,000 per victim.)
• I certainly wouldn’t choose high school & college students as my “target audience” to scam, considering that most people without college degrees have abysmally low annual incomes. Why choose low-income victims when it would be much more profitable to target high-income, high-net-worth individuals earning at least six figures a year? I have knowledge in business consulting, and I promise you that a business owner would be a MUCH more lucrative mark than a low-income college student.
• I wouldn’t choose such a time & energy-draining method of scamming people. Also, communicating back and forth with potential clients is an absurdly long time sink since only less than 10% of all potential clients who reach out to me actually become paying clients of mine. This means that 90% of my time communicating with potential clients ultimately proves to be a colossal waste of my irretrievable time & energy.
• If you pay me to provide academic services and I don’t deliver, you can always dispute the payment with the payment app and easily get your money refunded. If I were in the habit of swindling money from people, then all of my payment accounts would have been investigated and be completely shut down by now. And I would have been permanently banned from opening new accounts. Therefore, the fact that all my payment apps have been fully active for years should be sufficient proof that I haven’t had people consistently disputing payments sent to me.

HOW TO CONTACT ME:
Paid Help from Hiraedu: If You're struggling to handle your Online Exams, Assignments or any other coursework, get help from Hiraedu and pay after the exam. Contact details for Hiraedu is: WhatsApp: +1 (213) 594-5657 OR Call: +1 727 456 9641

• I take my work as a tutor very seriously, and I always aim to do my best to help my students excel in school. I have a solid and sincere passion for academic achievement, and with my help, I am positive that I can help students obtain very high grades with minimal stress and effort.
• Please feel free to contact me if you're interested in my services and would like to learn more. I'm available 24/7 via phone call, email, and text. Again, thank you for taking the time to read my Reddit tutoring ad, and I hope to hear from you soon!

My contact details:
WhatsApp: +1 (213) 594-5657
Call: +1 727 456 9641
Website: hiraedu. com
Email: [info@hiraedu](mailto:info@hiraedu). com
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Suggest more topic Ideas
Join this subreddit to help us grow!

Olá! It's me! I'm Rickle Pick! Hello everyone!
So, I’ve been listening to some stories about Neckbeards and Kevins, as well as some Legbeards and Kevinas (Is that the correct term??). Well, most of the times I listen to those stories, I am reminded of some people I used to deal with in school. Specifically, this time, the tale of a guy, who I’ll name Roger Bacon for reasons soon to be explained. Sorry for any grammar errors, eu falo português! I also don't really know the posting rules here, so I'll just post it and see how it goes lol
This prologue is more of a compilation of stories that I think is needed before we get to the main shenanigans and awkward situations this guy put himself AND me into. If this generates any interest, I will post more specific tales of this weirdo! Long time lurker, first time poster, english is definitely not my first language and the whole shebang. I also never wrote a text this large, so go easy on me!
THE LIST:
Well, I guess it’s usual to make a list of people that appear in those stories, so I’ll make one just for you!
Me: Your basic musician-type nerdy theater kid white guy! Tall, thin with medium-light brown hair. At the time, I usually wore a leather jacket and sometimes a hat (not a fedora, a Chaplin hat. Also, where I live, hats are an acceptable attire choice lol). I kinda looked like the Once-ler from Lorax. At this time, I had just failed my second year of high school because of… honestly just lack of effort, mixed with undiagnosed ADHD and a bit of lacking in the ol’ confidence and self-respect department. At the time, I also was physically incapable of saying no and had a crippling fear of disappointing people.
Roger Bacon: 168 centimeters (or 5,5ft for the uncivilized) of pure muscle! Or at least he thought it was that way. In reality, he did have some muscles but was kinda chubby and flaccid. Not FAT fat, but athletic fat (???). He was mixed, light skinned, had shaved short curly hair, no beard (except for the inside beard) and his face was a special kind of oval, besides having a, "chiseled jaw". He always smelled like he had just gotten out of a day-long brawl with a french cologne wearing burrito. He wasn't an usual neckbeard, but he was a huge attention whore. Thought too much of himself, as we say here in Brazil: “Promised too much, delivered nothing at all.” His moto was: “Dude, I think she’s into me!”
For now, these are the characters, as the focus is to introduce you all to Roger Bacon as a person.
With the list over, let us get to the story.
FEBUARY 2018:
The year of 2018 started pretty badly for me. I had just been held back from 10th grade, had no friends and didn’t really know anyone. As most people know, high school in Brazil is quite different from America, as we start school in febuary and we share the same class with the same people all day, excluding language classes and extra-curriculum activities. This meant that, for the foreseeable future, I was alone. On the first day of school, I shyly sat on the last desk on the far right corner of the room, as I scanned my classroom to see what I was dealing with. A few groups of people sitting together, talking and greeting their friends, some loners reading or playing on their phones. The artsy girl drawing a beauriful woman on the white board. Some guy drawing a penis right beside her. Perfect balance. A normal classroom.
Another difference between our school systems is that we don’t really have clicks based on like Jocks or Nerds or Pretty Girls, it’s mostly people who connected in childhood or matched personalities, instead of connecting through roles and interests within the school. Not saying either one is better, just different. And yeah, the bullying situation is just as bad. I was bullied for my whole middle school and through first year of high school, and made a very specific group of low profile friends. So when I failed sophomore year I thought to myself “Screw it, if I’m going to be held back, that’s at least a second chance for me to grow an acceptable social life.”
All this elucidates how intimidating it could be for someone to join a new classroom full of mostly new faces. If you were unable to make a friend, you’d pretty much be on your own for the whole year unless an already formed group “adopted” you. So my mindset was to at least try and meet new people.
Well, have you ever said “I’m gonna do this thing I’ve never done before!” And got the worst possible circunstance you could get at the very first attempt? Welp, that’s just what happened. My strategy was to start small, and go talk to only one person at first, and then try to interact with a few of the groups as that was a bit intimidating (fun fact: we call “clicks “panelinhas”, spelled “pah-neh-lin-ias”, wich means “little pans”, because, you know, they’re closed groups, like a closed… pan. Idk, anyway), so I went up to this guy in front of me, and that guy was Roger Bacon.
He was almost lying on his chair, on a cool guy pose while messing around on his phone. He was also wearing a black sports tank top with a grey opened sweatshirt and the standard uniform wine-red shorts that were mandatory in our school, which made him look like a short and jelly version of Rocky balboa mixed with Kick Buttowski.
In real life, my name and his started with sequential letters, and because of this, we would sit near each other for the whole year, so I guessed he’d be the best person to interact with. I also KINDA knew him because we had basketball training after class in like 2015 and I went to the same church as him, in which I befriended his brother, Kevin, slightly, but didn’t have much contact with him because he had already graduated (I have some stories about basketball and church so tell me if yall wanna read them lol). I approached and gestured for him to take of his headphones (They were extremely loud, so I could recognize he was listening to the song In The End by Linkin Park).
Me: Hey! Aren’t you Roger? You’re Kevin’s brother, right?
RB, trying to sound stoic: “Oh, hey Rick. Yeah, it’s me… fortunately for you.”
Me: “What do you mean?”
RB explained: “Well, I’m the cool brother! Kevin was lame, and also had no friends.”
Me: “Isn’t he in a band with [insert band members]? They seem to be his friends…
RB: “They might look nice, but they’re all assholes. Don’t let them fool you! I’m the nice brother, Kevin is a dipshit.
To elucidate you: that band he said was made of assholes was the Worship band of the church we went to. It was also the worship band that I occasionally played the piano with.
I said, jokingly: “Guess I’m an asshole then! Because, ya know, I play with them more often than not”
RB: “No man, it’s just them. They’re just so infuriating! They never let me participate!”
Me: “Wow, that’s weird… I mean, I didn’t know you were a musician too! What instrument do you play?”
RB: “I play the drums, piano, guitar, bass and I also sing. But Kevin keeps me out because he wants to be the 'star brother'!”
I could tell he got a little heated, and went silent for a little while. I decided not to mention the band or his brother in his presence, 'cause ya know, that was pretty awkward lol.
I remember thinking to myself “This guy’s kinda weird”, because his brother was one of the nicest people I had ever known, and he also didn’t have the say on who played on the band, the worship leader did. I thought about confronting Roger with this, but I didn’t want to abandon my quest of finding a friend. And also, he seemed chill at first, if not a little insecure.
I was a little uncomfortable with this line of conversation, so I opted to change the subject. We talked a bit more about me having been held back, and he went on about how he was really good at math and chemistry, and how he could help me with my school stuff.
I was glad to have someone to help me, and even more, someone who apparently liked the stuff I liked. I remembered what he was listening to, so I commented on it and asked which song was his favorite, and we talked about Linkin Park for a bit. He said “In The End” was his favorite song, and then I mentioned I was a huge Linkin Park fan. He told me he was a big fan as well, but as we talked about it, it became a bit fishy. He never specifically said anything and just kinda repeated what I said. It became clear after a while that “In The End” was, in fact, virtually the only song he knew from that band.
That was the first time I noticed something strange, but only in hindsight, as at the time I just thought he really wanted to make a human connection. I remember thinking he was just excited to know someone who was open to talking to him, so I didn’t think anything of it.
Also, not everyone memorizes this stuff, and maybe he did only remember one song, for whatever reason, so I let that pass. I only felt necessary to include this information because it was, at least in some way, the first lie that Roger told me, a little sample, if you will, of what’s to come.
After we talked for a while, mostly catching up on our lives, the bell rung and our first actual class had begun, and I had the first-hand experience of this guy’s sense of humor. The teacher walked into the classroom and introduced himself as the new Geography teacher, and started a power point presentation about some of the subjects we’d be covering that year, saying “Please pay attention to this class, as you’ll need to know how our schedule will work”. Roger looked back and said “Huh, I guess this class is useless for you then, being held back and all, hahah”, which made everyone look at me and just kinda stare like I should say something, and he kept repeating the joke to anyone that showed any reaction besides just staring, adding “Amirite? Huh? Amirite?”.
I was kinda salty about this, but my people pleasing peapod brain couldn’t handle letting it show, so I just laughed and said nothing. I guessed it was a poorly thought out joke at first, but then Roger proceeded to make the same comment on every single one of the opening classes we had for both of the introductory days. There were 12 of them. He did it every time. Every. Single. Time. Sometimes he repeated it even louder, as if he didn’t think people heard it, because no-one was laughing.
“Ok”, I said to myself, “He didn’t mean to make fun of me, he’s just a little overexcited and probably is trying to make a connection and help me get acquainted to our classmates.”
Either way, I was very uncomfortable and annoyed.
Thankfully, this came to a halt when he was practically thrown out of the Literature class for interrupting the teacher mid-sentence while she talked about how important the first month of class would be for our comprehension of the whole subject. He made the joke four times. FOUR TIMES. I was beginning to think that I made a mistake, but well, the mistake was already made, at least I can try and understand him a bit, before judging.
The rest of the week went by and he didn’t get any better, but I got kinda used to it. In fact, I actually enjoyed having conversations with him at recess, when we could talk a bit more freely. And, as all things in life tend to do, it got weirder. Weirder in the sense that as we spoke more and more, I noticed a bit of a concerning pattern: every time I shared an experience I had, he’d share a cooler and more awesome almost equal experience back.
Some light examples:
I told him I went hiking for 2-3 kilometers on a trail by the beach. Then he smirked and said he went hiking for “at least 7 kilometers on a deserted beach that only his father’s company’s employees had access to and he saw a Gorilla. There are no gorillas in Brazil. Maybe in zoos, I guess, but definitely no gorillas.
I told him I was kinda sad because I had just ended a “thing” with a girl from my old grade. He “proudly” said he’s been dumped by his ex, Laura, after they dated for 11 months and made out aaaallll the time after school, and he even saw her “lady parts” once!”.
And then he went on to describe that shit for like 3 straight classes, adding more and more to the story every chance he had to speak, providing me with my daily dose of cringe in tiny bits of uncomfortable information at a time! Like a sporadic cringe snack! Sninge! Crack? Probably Crack.
ANYWAYS
There was also the time I told him the story of how I became best friends with a guy because we got into a fight in P.E.. We were arguing about some nonsense and he wanted to fight, so after he socked me on my stomach, I cheaply kicked him in the face so hard I almost sprained my ankle and then we started laughing (because I guess sometimes that’s all it takes). Phillip is my best friend for almost 10 years now.
Roger puffed up his soap dish chest went on for at least 2 classes worth of time about how he “beat up his last bully and broke both of his arms, and almost went to prison, but his dad is a lawyer and bailed him out”. Dude was 16, and I don’t think he’d need to be bailed out, but okay… He was, in fact, very badass.
Those are all approximations of actual stories he told me, because my ADHD memory is shit, but you get the gist of it.
My days were filled with endless stories filled with absolute bullshit, like a Gary Stu from a dying rpg campaign. (I have a story about a DnD game he participated in, but that’s for another time!)
Roger, not content with lying to me about anecdotal facts about his past that could be true but were almost certainly mostly bullshit (if not entirely), had a tendency to just negate reality when presented with facts in certain situations.
And example of this situation is the time we were doing a group assignment and a girl at least 3 meters in front of him dropped her pencil and he just kinda threw himself on the ground, picked it up and said “Here you go, Lana!”. She said “Thanks Roger!”, barely turning around and carried on with the assignment. Roger, then, turned to me with a sleek shit feasting smirk on his face and said:
RB: “Dude, do you think she’s into me??”
I contained a ridiculing laughter just in time to realize he was dead serious.
I said “I don’t know man… Doesn’t seem like it to me, but sure I guess.”
RB then straight up asked ME to go talk to her and get HIM her number. When I asked why shouldn’t he do it, he said it was “the wingman’s job to get the number of the girl” so that he wouldn’t “look weak for asking”
I said I’d do it, cause I genuinely wanted to see if he was right about her liking him (I hadn’t really understood the dynamics of the classroom, so I actually had no idea if he was actually right, just a gut feeling that yeah, he probably wasn’t).
I went up to her and asked for her number, explaining it was Roger who was interested in her and, as I pulled out my raging 2014’s Sony XPeria, I was swiftly interrupted by her delicately saying “Sorry! I have a boyfriend.” (She said the boyfriend part out loud, and stared at Roger)
I said “Oh, ok, sorry to bother ya!” and, as I was starting to walk back, I noticed that she turned back and glared at Roger. Later that day her boyfriend texted him, telling him that “He’s got to stop asking her out, and next time, if he wants to get rejected, he should come do it himself” He called him a moron. And then they both blocked him.
Well, that was embarrassing.
Despite having been turned down (for the 6th time now, I’d come to find out), Roger still maintained that she was “totally into him”, and it wasn’t just Lana. Any time he had even the smallest interaction with any girl, he’d say that they’re “probably into him”, or that “they made out at a party, but she was drunk and probably won’t remember”, or that they “sent him nudes last year but he’s already deleted them because he’s a good person, with morals”.
This went on for a while and, after about a month, Roger begun to dial down the crazy stories about how he’s a “badass and he gets all the girls but he’s single because he’s too good for them”. Until I started seeing a girl from another church I started going to. I met Janice () at the churches youth group, and we talked the whole time afterwards about lots of stuff. This name’s given because of her insanely similar laughter and demeanor of Janice from Friends. We clicked well and I was very interested in her, but my ADHD ass forgot to get her number, and remembered it only when she had already left.
When I told Roger, he laughed and said “I had just cockblocked myself” and that I’d “probably missed my only chance of banging a girl ever”. I was bummed, but clarified I didn’t really want to have sex before marriage or at least before making an emotional connection (I had just then begun to go to church, so I didn’t really get the rules, so it was more of a personal choice I always had in mind when thinking about dating. Also I met her at church so wtf).
He said “that was dumb” and, “even though he was a virgin, he’d dance the Devil’s Tango with the first chick he had the chance to”
“What about Laura?”, I asked. His face went from a confident smirk to an almost sad expression, and he blankly replied: “She didn’t want to, but I tried anyway at times. I even got a blowie once!” I let it go because I was very tired, as Mondays are hell on earth.
A few classes later, I went up to him and reminded him of our conversation and asked:
I said “Ooookay, but what about all those girls you told me were all over you? Didn’t they want to have some bum bum times with you??”
He was taken by surprise by this, and was visibly trying so hard to think of an answer for at least 15 seconds. He mumbled “Well…”, and like just left. Like he got up in the middle of the class, and walked away. Well that was weird!
He got back and I didn’t pry, thinking he had some kind of trauma, and I tried to change the subject.
I say “tried” because instead we were suddenly interrupted by a girl asking me if I was Rick. I didn’t know her or how she had materialized beside our desks, but later I found out that that girl’s name was Mary. She had blue eyes and was smiling mischievously, and I answered “Yup, that’s me”. She then giggled and said that “Anna wanted to make out with me after class”. Me and Roger were both very much taken aback by this, and I immediately thought to myself that this could only be some type of dare or prank (which it probably was), and was about to try and respond with the first witty joke that popped up in my monkey brain when, without missing a beat, Roger said “Rick’s already seeing someone!”. Mary was visibly surprised and said “Oh, you have a girlfriend??” with a look of disbelief on her face. Ouch. I explained that I wouldn’t say I do, I just liked a girl from church and we’re going to see a movie with some friends on Saturday, and that either way it was a pass on the making out sesh! Mary said “Oh, okay!” and started to walk back to her desk. I was about to make a joke and say that Anna could probably do better than me, when Roger interjected:
RB: “I’d like a making out sesh if she’s interested!”
Mary looked back with a visible “Lol, ew no” expression and just said: “I’m sure you would, Roger!”, turned away and sat down, laughing with her friends when she got to her desk.
Roger turned to me and said:
RB: “Dude, do you think she’s into me?”
This cycle repeated once in a while, so I’m not gonna tell you all of the situations that I felt like shaking him and trying to wake him up like Woody does to Buzz Lightyear in Toy Story. Exhausting, right?
Another thing Roger tended to brag about was that he did Martial Arts. Specifically, Kung Fu (Wushu). I would come to find out that, in the year before, he made a big scene to tell everyone in class that he’d just started Kung-Fu classes and, when no-one payed attention, he started a habit of punching the wall beside his desk, audibly making “hmpft” noises. When anyone asked why, he’d say he was training, and that his Sensei (Not shifu, he actually said sensei) had asked him to do that to strengthen his fists so he could harness all the strength he had, so one day he could put a hole through a wall with his fists.
He would also punch the school’s fireproof doors because, if you didn’t know, they dent pretty easily, and he would show me and tell me to bask at his strength and ability. That until I said I’d give it a try. He told me not to, because “I wasn’t trained” and “it could really hurt my hand”. I punched the door. It made a dent.
Roger said it was beginners luck and that he’s just a good teacher. I told him I really didn’t even make an effort to pay attention, the metal was just bendy and soft. Roger never talked about it again, and started only punching walls. For that, he would feel superior because, yeah I ain’t doing that. There were consequences for his wall punching habits, but I’ll address that some other time.
The last thing I’ll say about him for now is how clueless Roger was, how much he thought of himself and how he treated everyone else like they should (and would) respecting for what he told them, and not for what he showed them.
(I plan on doing another part eventually, with the story of how his disconnection with reality, lies, schemes and generally narcissist behavior eventually exploded back into his face.)
As a last bit of exposition of our circumstances, there’s an important part of our school life that fueled Roger’s social life’s demise.
Pranking was a big part of my class’ culture. There were also some people in my classroom who were bullied. The thing is: the bullies actually made fun of literally everyone else, which made it very hard to figure out if you were considered a target or just a colleague. They’d mess with people’s stuff, tie backpacks to the windows and hide pencil cases, but they would also do it to their own group.
Essentially, the only way to differentiate those who they considered normal schoolmates from those who were bullied was the frequency of the pranks and their demeanor in general towards those people. They would apologize for the pranks, ask to make up for it, buy you lunch, make jokes, try to laugh with you. I swear some of those guys were politicians in the making. Luckily, was very good friends with one of the guys in that group, I’ll call him Turkey, who was also held back a few years before me, and he liked my sister, so I was mostly safe.
Roger, on the other hand, THOUGHT he was one of the pranksters. Every time someone pranked him or anyone else, he would laugh knowingly, like he was in on the joke the whole time, and try to make jokes, only to further humiliate himself. And they would capitalize on that as hard as they could.
You see, Roger liked to portray himself as the “Mysterious-Badass-Quiet-Protagonist-Take-No-Shit-From-Anyone-Mr.-Steal-Yo-Girl” guy. This combo of personality substitutes was the recipe for the downfall of his popularity, and the start of the longest lasting pranks I’ve ever seen in my life, which will come if yall want another post. That prank is also the reason I named him Roger Bacon.
Because he was so into Math and Science (and into himself too lol) he also always wanted to look like the smartest guy in the room. The problem is that, as our first semester went by, it became clear that he wasn’t as good as he hyped himself up to be. Shocker, right? This was proven to be true when we were doing a chemistry group test, and I was paired with him and Anna, and we needed to calculate some entropies or whatever. He made a point of telling us to do all of the “easy ones”, and he would take on the more complicated questions.
The thing is, he was trying really hard to look like a genius, to maybe impress Anna, so every time he made a calculation, he would roll his eyes up and kinda vibrate a little. I guess he wanted to look like a genius mathematics robot, but instead he looked like he was trying to imitate an autistic person having a small stroke. I didn’t mind the Good Doctor amateur impersonation, because at least it looked like he knew what he was doing. Unfortunately, it really just looked like he knew what he was doing.
Each easy question of the test was worth 1 point, and there were 4 of them, and there were 3 hard questions worth 2 points each. We got a 4/10 on that test, and lo and behold, the only questions we got right were the ones me and Anna worked on. We were a bit pissed, not gonna lie.
Until the last time we spoke, Roger still blames Anna for his complete failure at this test for, in his words, distracting him because she was obviously into him.
But that’s just Roger, I guess!
I've got A LOT of stories about Roger and other neckbeards I've encountered, and I can't wait to tell them!
Until then, thanks for reading, and have a good one yall!

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We’re diving into a recent story from the Cannes Film Festival in France, where a movie titled "The Apprentice," depicting former U.S. President Donald Trump, has premiered. This film has certainly stirred the pot by portraying a controversial narrative about President Trump’s rise in the 1980s, closely involving his relationship with defense attorney Roy Cohn.
The Trump campaign has firmly dismissed the film as “pure fiction,” and it's easy to see why they are taking a stand. We're talking about an administration that, while polarizing, undeniably laid a significant footprint on our nation’s political landscape. The film not only fundamentally misrepresents key aspects of President Trump's personal and professional life but sensationalizes and dives into widely debunked allegations. The spokeswoman from the Trump campaign has made it clear that they intend to file a lawsuit to correct these so-called 'blatantly false assertions' made by the filmmakers.
Let's zoom in on the dynamics here. "The Apprentice" stars Sebastian Stan as Donald Trump, showcasing his early business ventures which were catalyzed by lawyer Roy Cohn, a known figure from the McCarthy era. Cohn is presented almost as a svengali figure, steering Trump on a path that would eventually lead to his presidency. This kind of portrayal simplifies the broader, more complex actualities of political and business growth, reducing it to mere cinematic drama.
Addressing the controversy around the film, the director Ali Abbasi has extended an invitation to President Trump to view the film and discuss its contexts—suggesting perhaps a small hope for dialogue. But let’s not be mistaken, Hollywood has a long run of bending realities for what they often claim as creative expression or political commentary. In an environment fraught with biases, this motive doesn't serve the truth but rather, distorts it to feed a specific narrative.
Turning our attention to the backdrop of this release, it’s essential to recognize the timing—amidst ongoing political tensions and during an active presidential campaign season. The Cannes premiere has provided a platform not just for creative showcase but, potentially, for political messaging, intentionally or not. This only emphasizes the need for audiences and voters to critically evaluate the stories being presented on these massive platforms.
So, what does this mean moving forward? We’re likely to see further discussions and perhaps, legal developments as the Trump campaign seeks to challenge what they argue to be glaring inaccuracies. The intersection of film, politics, and media here is palpable and will certainly be a flashpoint in ongoing debates about political figures’ portrayal in media.
(Facts extracted from AP News. Political bias cleaned and rewritten by Listen2.ai.)

Hey Team Shortcuts,
I have a little project I thought would be simple, but it's making my brain hurt.
I've built a shortcut that fills the water for our backyard pond, and then shuts off. On warm days, the water drops from evaporation, so I have a "Top-Off" routine that's triggered when leak detector stops sensing "a leak" (that is, the pond's highest level).
When that happens, this routine starts up the water flow, then repeats with a 30-second pause at the end of each repeat. On the next repeat, if the water is no longer active (because the sensor detected "a leak" and shut it down), I want the shortcut to exit and report the rough time that the top-off took to complete.
So basically, I have a variable (rep_num) that tallies the number or repetitions the repeat performed, and I want to use this rough time equation to report the time the top-off took to complete:
( rep_num * 30 ) / 60
What I'm having trouble grokking is how to add the rep_num variable in to the Calculate Expression step? Or is there another way I should be doing this? Thanks in advance for the assistance.

Any good books that you could recommend to help with understanding or to help with skill for the following topics?
Binomial estimation Trigonometric ratios The cosine rule The sine rule Differentiating functions with two or more terms Gradients, tangents and normal Increasing and decreasing functions Second order derivatives Stationary points Areas of triangles Sketching gradient functions Solving triangle problems Graphs of sine, cosine and tangent Modelling with differentiation Transforming trigonometric graphs Integration Trigonometric identities and Integrating Indefinite integrals equations Finding functions Angles in all four quadrants Definite integrals Exact values of trigonometric ratios Areas under curves Trigonometric identities Areas under the x-axis Simple trigonometric equations Areas between curves and lines Harder trigonometric equations Equations and identities Exponentials and logarithms Vectors Logarithms Representing vectors Magnitude and direction Position vectors Solving geometric problems Exponential functions y = ex Exponential modelling Laws of logarithms Solving equations using logarithms Working with natural logarithms Logarithms and non-linear data Modelling with vectors Differentiation Gradients of curves Finding the derivative Differentiating x Differentiating quadratics
Radians Algebraic methods Radian measure Proof by contradiction Arc length Algebraic fractions Partial fractions Repeated factors Algebraic division Areas of sectors and segments Solving trigonometric equations Small angle approximations Functions and graphs The modulus function Functions and mappings Composite functions Inverse functions y= f(x) and y = f(x) Combining transformations Trigonometric functions Secant, cosecant and cotangent Graphs of secx, cosecx and cotx Using secx, cosecx and cotx Trigonometric identities Inverse trigonometric functions Solving modulus problems Trigonometry and modelling Addition formulae Using the angle addition formulae Sequences and series Double-angle formulae Arithmetic sequences Solving trigonometric equations Arithmetic series Simplifying a cos x + b sin x Geometric sequences Proving trigonometric identities Geometric series Sum to infinity Modelling with trigonometric functions Sigma notation Recurrence relations Modelling with series Parametric equations Using trigonometric identities Binomial expansion Expanding (1 + x)" Expanding (a + bx)" Using partial fractions Curve sketching Points of intersection Modelling with parametric equations
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STATISTICS Data collection Populations and samples Sampling Non-random sampling Types of data The large data set Mutually exclusive and independent events Tree diagrams Statistical distributions Probability distributions The binomial distribution Cumulative probability’s Hypothesis testing 2 Measures of location and spread Hypothesis testing Measures of central tendency Finding critical values Other measures of location One-tailed tests Measures of spread Two-tailed tests Variance and standard deviation Coding Representations of data Outliers Box plots Cumulative frequency Histograms Comparing data MECHANICS Modelling in mechanics Constructing a model Modelling assumptions Quantities and units Working with vectors Correlation Linear regression Constant acceleration Probability Calculating probabilities Venn diagrams Displacement-time graphs Velocity-time graphs Constant acceleration formulae 1 Constant acceleration formulae 2 Vertical motion under gravity
Forces and motion Force diagrams Forces as vectors Using integration Constant acceleration formulae Forces and acceleration Motion in 2 dimensions Connected particles Pulleys Variable acceleration Functions of time Using differentiation Maxima and minima problems
MECHANICS Moments STATISTICS Resultant moments Regression, correlation Equilibrium and hypothesis testing Centres of mass Exponential models Tilting Measuring correlation Hypothesis testing for zero correlation Forces and friction Resolving forces Conditional probability Inclined planes Set notation Friction Conditional probability Conditional probabilities in Venn diagrams Projectiles Probability formulae Horizontal projection Tree diagrams Horizontal and vertical components Projection at any angle Projectile motion formulae The normal distribution The normal distribution Finding probabilities for Applications of forces normal distributions Static particles The inverse normal distribution Modelling with statics function The standard normal distribution Finding μ and σ Approximating a binomial distribution Hypothesis testing with the normal distribution Friction and static particles Static rigid bodies Dynamics and inclined planes Connected particles Further kinematics Vectors in kinematics Vector methods with projectiles Variable acceleration in one dimension Differentiating vectors Integrating vectors

I passed! AT/AT/AT. Took the test this past Saturday May 18, at a test center. Thank you to everyone on this sub, reading through your tips and experiences made all the difference.
Context: Start to finish, I completed this journey in about 4 weeks. I was laid off in March of this year and am job hunting. So, having the time, I opted to do it on a very aggressive timeline, to knock it out and beef up my resume. Not having it on the resume felt like a blocker for the positions I’ve been applying to, time will tell if it helps. I do wish I had thought to do it while still employed, so I could have done it on their dime. (I could not have pulled this off this quickly while working full time.)
Budget (USD) $723

• $159 - PMI membership
• $79 - PMI Study Hall Plus
• $425 - PMI Exam
• $20 - Andrew R's Udemy course
• $25 - AR Prep Book, Ebay
• $15 - Third3Rock Study Guide

Timeline

• April 19: Purchased AR’s course
• May 1: Once I got course completion certificate, I submitted PMP application. No audit.
• May 3: Bought Study Hall Plus
• May 11: Finally confirmed my PMP application approval. It had been approved a few days prior, but the notification was not sent. So I recommend checking and not waiting for an email. Paid and scheduled exam, to take on site. Too many horror stories of online, test center is 15 min away.
• May 18: Took and passed exam!

Prep and study plan:

• AR Udemy course for the 35 PDU. Watched on 1.5-1.75x speed, took notes. Got 72% on the in-session mock exam.
• AR PMP Exam Prep Simplified book. Read the whole thing. Averaged about 70-75% on the section quizzes. Saved full mock exam till later.
• PMI Study Hall Plus: Took all 5 full exams (only 1 per day, I’m not a monster. Took the last one 3 days before exam). Scores 69/73/75/63/62. I reviewed all questions after, and made sure I understood the wrong ones. The expert questions killed my last two scores. Also took a bunch of the SH mini quizzes. First pass, scored 60-70’s.
• I built a post-it Mural (mural.io) of the 49 processes/ITTOs. I was having hard time getting these to stick, and taking the time to do this helped me visualize it and keep it straight in my head. It’s not perfect, more of a brain dump in virtual post-its, but I’m happy to share a read-only link if anyone is interested.
• Watched David McLachlan’s 150 PMBOK 7 Q&A on YouTube. Helpful to learn his approach to highlighting key points and eliminating.
• When away from studying (i.e., driving, on walks, etc) — instead of my usual podcasts, I listed to a bunch of Scott Payne’s podcast “PMP Exam Prep Success Secrets”. More conversational, a much different style than DM or AR. I found it helpful. I don't know if it's the best podcast resource out there, but by then I was fried, so I grabbed first one I could find. I was done researching :)
• Third3rock PMP Study Notes/Cheat Sheet. So many of you recommended this! I grabbed it about 5 days before exam, read through multiple times through the week. Fantastic resource! (Thank you u/third3rock!)

Final countdown to test: Two days before exam:

• Took AR’s full exam in from the Prep Simplified book (85%)
• Reset SH mini exams and started redoing them, improved scores to 80-90’s, and one 100
• Re-read Third3Rock docs

Day before exam

• Rewatched AR’s mindset videos, reread minset section of prep book
• Re-read mindset section of Third3Rock
• Did more mini SF exams to stay in practice
• Reviewed Mural content

Morning of exam:

• Reread Third3Rock mindset section, and AR's mindset pages on drive in

Finally the test itself :

• Scheduled for 8am at testing center. My husband dropped me off at 8am to save me the stress of finding parking (test center at local university.)
• Locked up my stuff, turned off phone and took off apple watch. Got signed in and started at 8:30. Had to show ID and show empty pockets at beginning and at every break.
• I could not bring my water into test room, but could leave it on counter near proctors.
• There were only 5 drag and drop. Only one question required calculation for CPI. No PERT or Comm Channels. No MBTI or DiSC. Maybe 5 ITTO at best. Everything else followed closely to Study Hall approach, situational and mindset. Heavy on agile and hybrid.
• I followed the 230/155/80 timing, which was super helpful to time things out. I paced myself, took breaks at 154 min and 83 min, and finished with 4 minutes to spare. I didn’t mark any for review, and at my pace it was just as well, I would not have had time to review.
• I used the highlight and strikethrough on every question. Do the tutorial in beginning to get comfortable with the tool.
• Be careful to understand the rules at the test center. I almost got in trouble at the first break! I asked permission to go to my locker for snacks after 1st break, which were right off to the side and in view of proctors. I stayed at locker to eat some granola and grapes, and was reprimanded, since I was supposed to bring the snacks out to the proctor’s desk area, which I now realize was in view of the cameras. Whoops! I apologized and said I misunderstood the rules. I’m glad they did not suspect me of trying to use my phone, etc. I was a little nervous waiting for final results due to this.
• Make sure to return from break a few minutes early, because proctor needs to sign you back in to your station. I had to wait until they got to me.
• Got my provisional pass on way out the door, and my official pass confirmation the next evening.

Most helpful tips:

• Read the last sentence in the scenario question FIRST. So you know what to pay attention to when reading the scenario.
• Strike through the obviously wrong answers first, to stay focused.
• Mindset, mindset, mindset. When in doubt, mindset.

Hope that helps! Good luck!

Recently, I was playing a game which has an item with a 1 in 11,000 chance of dropping when opening a chest. I managed to get this item 2 times in a row when opening 2 chests next to each other. How would I calculate the chances of getting them back to back like that?
Would it be a case of the following kind of expressions, or would it be some other equation?

• 11,000^² = 121,000,000
• 11.000^³ = 1,331,000,000,000

EDITS

1: From what I have read in the comments, I am right with my thinking.

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I am not the OOP. The OOP is u/themachucajr posting in Marriage
Ongoing as per OOP
1 updates - Long
Original - 7th May 2024
Update - 15th May 2024
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My wife friend-zoned me and wants a platonic “companionship”
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My wife (35f) and I (35m) have been married for 15 years and we've been together for 20 years. We have two kids (12,14) we absolutely adore and work tirelessly to provide the best possible life for them. For the past 3 years, things have been somewhat bumpy. I understand that our kids are at an age where they require a ton of our attention and resources with school, band, club sports, and other extracurriculars and I'm aware of the physical and emotional toll that can have on marriages.
However, for these past 3 years, my wife and I have had very little intimacy and very little sex and we've been trying very hard to work on that aspect of our relationship. This past year has been the most difficult and by far the darkest year in our marriage. We didn’t talk very much, we essentially became roommates coparenting our kids under the same roof. It was very depressing and very demoralizing. It was to the point where we began contemplating divorce and it became very dark and gloomy in the household because of that.
We began seeking help with both individualized therapy and couples therapy and it seems to have helped some. Little by little we started to get along and started to have deeper conversations about what our marriage looks like and what we would love for it to look like. This is where it gets tough. As time passed, my wife started to tell me she no longer was "in love with me" and that she only saw me as a "best friend." That she only loved me in a very platonic way, and this was one of the main reasons she didn’t have any desire for intimacy and let alone sex.
This was very shocking to me and quite frankly, I was devastated. I because angry and depressed and I couldn't fathom the thought that I was no longer wanted or desired by the person I felt completely in love with. Things began to deteriorate again and not long after, we were back to square one. I sat down with her one afternoon and had a heart to heart and began to ask questions about where the root of this problem lies, and her answer was "I don't know" and that "I have built up resentment towards you but I don't know where it stems from." As you can imagine, this provides very little to no insight into how to approach this.
I'm puzzled, I'm frustrated and I do not know what to do at this point. Currently, we've arrived at a place where she says that she has no sex drive and no desire for intimacy or connection. She says that all she wants is simply "companionship" which basically means our coparenting roommate dynamic. I asked her what I could possibly do or what is it about me that is so unattractive or undesirable and she her response is always "I don't know." She stated that she does "love" me but its not the same. That she has been feeling disconnected for years and that our marriage just takes up too much work. Her focus is only the children for now and that my coparenting contributions are "meaningful" to her in our home.
I'm at a loss and I'm mainly venting about my frustration. It's tough to realize that the person you love has no feelings for you. I feel like at this point I'm only here to contribute financially and as a parent. I feel like what she means with "companionship" is that she's comfortable with the convenience of having a good father for our kids and my financial contribution to the household.
In regard to intimacy and/or sex, she basically told me that its not something she’s interested in or wants at this time. She mentioned that the only way to get to a point for any of that is to be intoxicated which o believe is incredibly awful and very wrong. I told her I do not think forcing herself to have sex or be intimate by drinking or smoking is good and I declined to be a part of that which to my surprise, it upset her and made her more distant.
We're both extremely honest and transparent. We've never cheated on each other and we are always free to look through each others phones, emails, socials, etc. and we hardly ever do. I asked her if there was someone else and she declined. Honestly, I believe her. We then peacefully went through each other’s things and as expected, it was clean. We've always been very forward, even with the hard topics so I don't smell nor feel any foul play or infidelity.
Am I wrong for declining to only be intimate or have sex when she’s intoxicated? (I'm firm on my stance of not partaking in this "only when I'm high or drunk" sex because it doesn’t sit well with me.) I do not know how to help our situation and I'm starting to become a bit anxious and desperate. We're both fairly young and healthy individuals and good looking. We both have good standing careers and are good parents. I'm just not sure how our lives could have driven us to this point. I'd love some outside perspective on this matter and some insight on how to address something like this. It feels so awful to be unwanted and undesired by my own spouse. I hate it.
tl;dr: My wife of 15+ years is no longer in love with me and doesn’t know way and now says she can only have sex while intoxicated or I need to settle for a platonic sexless marriage and she doesn’t know why that is but it is what it is and I'm in need of insight or advice.
​
Comments
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Warthog__
From your comment history it looks like you are Swingers? If so, I would think that would be relevant information to consider.

OOP: We did some swinging in the past. That was fun for some time. We mutually decided to stop doing it and we have established it’s not the case. When we were swinging however, our marriage seemed to be in a good place. This IS something we did disclose with our couple therapist and made sure to include it to make sure we’re not neglecting an obvious potential issue.
I will say, I did ask my wife if what she experienced during swinging is something that is affecting her view on our relationship and she said it wasn’t. Our swinging experience was always together and it was very sex driven. Nothing really emotional or “poly”. Truth is, I have to believe her at her word. I have no reason to distrust her. To date, she’s always been very forward and never afraid of dealing things head on. No matter how painful.

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failedopportunities
It’s an obvious potential issue bro… wether it be she’s enjoying herself a side piece and wants nothing to do with you in that manner anymore. Or, she just went along with you on the swinging and never wanted to do it in the first place. Hence brings resentment. Regardless, should have been included in the initial post.

OOP: Swinging was her idea. Not mine. But I suppose I should have included it but I honestly believe her on it not being an issue. I don’t have any reason to distrust her. Maybe it’s something she has to accept with her therapist or our couples therapist. Can’t really approach that with a solution if she doesn’t think it was a problem. IDK

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BigIronBruce

She says that all she wants is simply "companionship" which basically means our coparenting roommate dynamic.

That's only a marriage if you both agree it is. You're hoping she's going to wake up one day and feel different but she's basically said that's not going to happen and doesn't want to figure out why she feels that way. It seems like you tried several different ways to get to the bottom of it and she's either deflected or is being honest that she's not in love with you.

Am I wrong for declining to only be intimate or have sex when she’s intoxicated?

I wouldn't do this, either, if that makes you feel better.
Will she be your best friend if you live elsewhere and have a relationship with somebody in love you. Probably not. Which makes the whole "best friend" speech feel like self-deception on her part.
I won't lie, if it were me, I'd get a divorce. She doesn't seem willing to do the work to fix the marriage and you can't fix it alone. She might promise to fix it or beg you not to but you need to follow your gut as to whether she actually can or will fix it. She's serious that she wants you to stick around but not necessarily as her husband.
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OOP: A very hard truth to accept here. Thank you

Interesting-Tip-4850

"I’m ensure I do everything possible to mend our marriage to ensure my own peace of mind and excite knowing I did everything I could."

you may still concider 180 method, to protect yourself and perhaps in the same time the reality that the ship is leaving may start to change your wifes perspective. If that doesnt what else would.

OOP: Can you elaborate on the “180 Method”?

Interesting-Tip-4850
Basically withold from any unnecesary interactions and affection. This is from an infidelity forum, but principles are the same https://www.survivinginfidelity.com/documents/library/articles/discovery/the-simplified-180/

OOP: I bookmarked this. I’m heavily considering this.

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Update - 8 days later
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I wanted to give you guys an update of how the therapy session with my wife went this week. Not sure if this is helpful or not but I took many of the responses/comments/suggestions from my initial post and put together some things I wanted to discuss with our couples therapist to help us navigate some of the core issues that may be affecting this situation.
One of the main things that is the "buzz word" of this has been the term "resentment" and it has been really eating me up inside knowing my wife keeps telling me she doesn't know why she's resentful or doesn't know why this is affecting her emotionally/mentally. I brought this up with our therapist once again and resurfaced the conversation about being married for so long (15yrs) and being together since we ere 14yrs old. Our long history of growing up and how having children when she was 19yrs old (me 20) significantly changed the trajectory of our lives.
We experience severe poverty and many hardships in the process and we essentially had zero social life for the past 10 years because we were so busy raising babies (2 kids now ages 12 &14). She followed up with tons of questions directly mostly at my wife about her feelings towards this and 90% of the responses were very "our kids" focused. It definitely felt like she was afraid of saying "yes it sucked" because she would feel guilt or shame because it would imply she regrets the kids.
I mentioned this in the session and the therapist encouraged her to look at this outside of the lens of being a mother and to try to view it a bit more selfishly and individually and it was very eye opening. My wife mentioned that she was very frustrated with the fact that we did miss out on many things in life. She also was very clear in saying "I do not think I missed out on other partners or dating or partying but I certainly lost all my friends." This was huge because one of the big pieces that has caused a strain in our lives is how silo'd and isolated we've been (again busy raising kids). I followed up by reminding her that it's important to have good friends and to make time for herself and her friendships.
For the past 3+ years, we've had multiple conversations about friends and how it is important to have them in life. Specially when you have similar peers that can help in many areas of life that perhaps we have no experience navigating and even simply for enjoyment. It has always been something my wife avoids, even though she's always been someone who needs that external stimuli. The main reason for her not investing in friends or even herself has always been "the kids." Like I mentioned earlier in this post, 90% of the answers have to relate to "the kids" to some degree.
At this point in our session I started to feel like there was a common denominator (the kids) in most of the frustrations and problems she was experiencing. So I simply asked her "Do you think you may be upset at me because I'm responsible for these kids in the sense that I got you pregnant so young?" I wasn't ready but she said that she was upset at me for that. She also followed up with the fact that she knows that's unreasonable because it "takes 2 to tango." I did feel like it was progress because it kind of gave us something to work on and help alleviate some of these "burdens" so we agreed to invest more time in nurturing good friendships both together and individually.
Towards the end of the session, we began to discuss what actionable items we would take from this session. At this point, it was still all very ambiguous and blurry as to what the outcomes were. I was very direct and very forward in asking my wife what her plan is moving forward. (NOTE: I had decided prior to the session that should my wife say the same thing about being a coparenting roommate that I would take the 180 approach and essentially do me) She started basically saying the same thing, that she doesn't have any desire to be intimate or sexual with me as of now and that she loves me immensely and she feels bad for not being there for me (as mentioned in my first post).
I also brought up the brief swinging that happened, to which for the 50th time said it wasn't a problem. I agree with her on this. This was something that was a "mechanical" approach for a solution to a problem that was very much in existent when we tried this. We (both) really have no issue to this. We know it happened, we tried it and mutually stopped and turned the page.
I also brought up other life events that may cause resentment and really we ended up not getting anywhere else as far as the root for resentment which was discouraging.
I then basically expressed to my wife that I will not be ok with that arrangement. I told her that I've really done everything I can and that this issue really has reached a point where it has nothing to do with me or require me to do anything that I'm currently not doing. I was very direct and saying that I will not be accepting this dynamic and that I need to be with someone who is actively involved in our marriage, works towards resolutions and is very much interested in maintaining an active intimacy and sexual relationship.
I expressed how I am not going to be a "convenience" and that there was more to life than being roommates and coparents. I made sure she knows I love her dearly and that I do want this to work for the better. I also told her that I'm fully committed to this marriage so long as she is as well and that is she wasn't, its ok, however I will not be a part of something where these efforts are not reciprocated. I told her I have no plans of leaving, and I do not want a divorce, however, I made it clear that if this dynamic continues that divorce will be the only outcome.
Of course tears were involved and it was a very bleak and sad ending to the session. Still nothing was said and I walked out very discouraged and very determined to start working on the 180 as soon as we left the room. It's painful and very difficult because much of the 180 requires you to be very short and cold and transactional. The saddest part is realizing, this dynamic already is very cold and transactional.
Here is where it gets VERY interesting. I started working on implementing many of the 180 recommendations that same day. I mentioned to my wife that, "hey, things are going to be a bit different moving forward. I'm going to honor her roommate/coparent dynamic without reproach and that it should be no mistake that I am not happy here and I am never going to be ok with it but I am done working on it if she wasn't going to work on it."
She agreed and went to bed. I started to build distance and started to basically focus on myself. Very short and transactional. She asked for help on some of her personal things to which I declined and it really shocked her. She was upset saying I was being petulant. I explained to her that, she is now fully in charge of her own life and her own issues.
We didn't talk all day and we only spoke when necessary. Few days I keep this going and she's very visibly upset and stressed. I typically react to that with gestures of help or nurturing but I didn't this time. That night she was crying telling me she's stressed and she things something is wrong with me because I'm "indifferent." I simply listened, then I told her that this is the dynamic she proposed and that I'm simply (much like her) taking care of myself and focusing on myself.
I'm not going to lie, it has been VERY hard to be cold and distant because as I mentioned before, I love her and I wish I could hold her and love on her. However, I know this is somewhat manipulative in a way just to get her way and still keep me in the friendzone. So I've been staying the course.
We're now going on a week of this 180 and let just say, there has been MANY changes on her side. I think she is starting to realize there is more to me than just "friends and coparenting." I sent her a text a few days ago essentially itemizing bills and separating the financial responsibilities 50/50 and SHE LOST HER SHIT. She basically told me it was "out of left field" to which I responded "hey, friends go in 50/50 and as your friend I expect nothing less."
This was very eye opening because it gave me a glimpse of I'm really taken for granted and how her level of comfort and convenience at my expense is really overlooked. I pushed through anyways and basically told her that this is the new dynamic she asked for and that its still a "bargain" because she would have to be 100% if she was on her own.
I'll wrap up with this. While the 180 has been working in many different areas, I am still very much sad about the overall situation. There have been MANY eye opening statements being said and realization that have not been pleasant to encounter. It has also sparked new energy and new efforts on her side as well. She's definitely seeking to talk to me more often and while its hard to turn down, I hope if things improve, this continues to happen.
I've also noticed that she's making more time for herself aside from being a mom which is HUGE because she pretty much neglected herself for years. I'm very pleased seeing her be more herself. My hope is that as we work on ourselves, the marriage improves. There really is no telling at this point where this will go. We are very much cordial and amicable even to this day and that's a very good sign.
Boundaries are set and expectations are very clear and I feel that no matter the outcome, I will be at peace with everything that has been done. We're still going to continue the couples therapist until we either rekindle our marriage or end up in divorce. I feel like having this nonbiased third party really helps as a witness and as a guide through this. No matter what I will always love my wife, however, I will not participate in a sexless, intimacy less marriage because we both deserve better.
Thank you all for all the kind words and recommendations and feedback. This will be my last post on this topic and I wish you all the best.
TL;DR: My wife friend-zoned me wants to just coparent at my expense but I started the 180 method to try and find a solution because she doesn't want to work on us which seems to be working on getting her out of her rut and helping me discover more about how she feels. Also, therapy is paramount and highly recommend to all couples.
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Comments
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Complete-Old-1960
Bottom line and not to be brutal, but there is one thing you don't have infinite amount of, is TIME. This has to be resolved in a timely manner. It takes 2 to be in love and to be loved, and u only have ½ of the equation. You need to put a time limit on you being the good guy and think of you and your future. Look hope it works out for you, but listening to what you are going through and what you could be in for you can still be a good father but also be a great husband to another wife if you find that special person again.

OOP: Definitely. I think this “soft ultimatum” (180 method) has been very eye opening. I’m definitely hoping for a rekindling of our marriage but I’m also bracing for divorce. I agree on a timeline and I’ve decided on a timeline for myself privately. I don’t want to give her a timeline because I want to reduce the pressure, however, after 1-2 yrs of things don’t improve, it won’t be shocking or a surprise if we split. I think 1-2yrs is more than reasonable.

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shes_a_killer
I have to agree with this, simply because at some point, the person who has gone 180 and is waiting for the other person to decide will begin to wonder, "Wow, they're really taking their time coming around to me...did they love me at all? If they ever appreciated and cared for me, why would they keep me waiting and neglecting me for so long?" Except, in my case, it had more to do with the other person being stubborn and unable to admit their faults.

OOP: I understand what you mean. I don’t think I’ll ever doubt she loved me at all. I’m certain she did and I’m certain she still does. I know it sounds crazy and I’m not at all infatuated or blinded by love. Love is far more than the intimacy and sex we’re lacking.

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RandyPan_theGoatBoy
I think it’s interesting that in the comments of your original post you said you didn’t think she was taking you for granted but you came to realize she absolutely was. Can you give some more details on what the 180 method is?

OOP: Yeah, I definitely felt this way. But with this 180 method it’s happening right in front of my eyes. Actual actions and reactions taking place that clearly demonstrate that she is taking me for granted. She actually see this as well. It’s evident she’s thinking about this heavily based on her demeanor and her behavior.
Here’s what I used as a guide:
https://beingabeautifulmess.wordpress.com/the-180/
https://www.survivinginfidelity.com/documents/library/articles/discovery/the-simplified-180/

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I am not the OOP. Please do not harass the OOP.
Please remember the No Brigading Rule and to be civil in the comments

Hi all,
This post is part-vent, part-cry for help. I've been using the ABTF calculator and community for over 10 yeas, most of which were super helpful, but I've finally reached a point where ever bra I wear causes me significant pain.
I've been wearing EM bras for years, but recently gained weight and knew I'd have to be resized. During this time all of my bras started giving me significant pain along the wires. Despite the swoop and scoop they'd immediately slip down about a fingers width and press painfully into my ribs. I took a road trip to NY last weekend specifically to visit the Rack Shack again and Laura bumped me up 4 cup sizes (from 28GG to 28JJ) suspecting that lack of cup depth was causing this since I'm already wearing a 28 band.
It didn't work. With 4 hours I'm in so much pain. I don't know what else to do after all this research, making the switch to Polish, getting help from an expert in person. I'm about to start talking to my Dr about getting a breast reduction because I'm just so exhausted of being in pain and spending all this money. I don't dislike my body, but think this will make many aspects easier in the long run.
I don't know if there's anything else to be done, but expressing my frustration here feels like the last possible avenue for answers. Thanks for listening y'all.

THE HARMONY OF ENERGY
Abstract
Introducing the "Harmony of Energy" (HoE) model, a novel formalism that posits the universe operates according to a fundamental pattern. This pattern consists of energy, defined as the smallest unit anything can be, existing as a fluid form in space, interacting with its environment through a specific method or structure, and then moving out of that space. Space, in turn, is the dynamic environment that energy occupies and moves through, filling it with positive and negative energy that affects its properties and behavior. According to the HoE model, energy moves into space, reacts to its environment, and then moves out of that space, with no time limit for how long it takes to react. This pattern is universal, applying to all aspects of the universe, and nothing escapes it.
The Origin of the Universe
The HoE model posits that the universe began as a singular entity, containing all forms of energy as one unified energy. This singularity can be represented mathematically as: U = ∫∫∫E(x,y,z)dxdydz, where U is the total energy of the universe, E is the energy density, and x, y, z are the spatial coordinates.
As the singularity expanded, the unified energy converted into distinct positive and negative energies. Positive energy is a high-frequency, high-information-potential state that retains its unique signature and individual form, capable of producing heat and maintaining its distinct properties. Negative energy is a low-frequency, low-information-potential state that loses its unique signature and individual form, characterized by a pulling force and a tendency to condense and simplify.
Initially, the universe moved in a straight line, with energy compact and cold. However, this linear movement resulted in a direct head-on collision with the void, a solid structure that hindered its passage.
This collision led to a limitation and subsequent conversion of energy, transforming it from a linear motion to a wave-like motion. The new wave motion created heat and allowed energy to break the pattern of "follow the leader" and collide with the void at an angle, shattering its edge into pieces.
This process of fragmentation can be described by the equation: F(θ) = Σ[nEⁿ * sin(nθ)], where F is the fragmentation function, θ is the angle of collision, n is an integer, and E is the energy density. For reasons yet unknown, possibly due to the singularity's energy reaching its final place or a transformation driven by cosmic "boredom," this conversion occurred, giving rise to the diverse universe we observe today.
The Void and the Ultimate Negative
Outside of the expanding universe lies the void, a region devoid of energy and matter, existing in a state of complete stillness and stationarity. This void represents the ultimate negative, a state of complete absence and zero energy density, unchanging and unyielding. As a whole, it exerts a compressive force on the expanding universe, potentially leading to contraction and eventual return to the singularity. This dynamic interplay between the universe and the void can be described by the equation: F = -G * (M * m) / r² where F represents the force, G represents the gravitational constant, M and m represent the masses, and r represents the distance between them. The void's stationary and unchanging nature, lacking any internal rotation or energy, makes it inhospitable to life as we know it.
Magnetism and Attraction: A Shift in Perspective
Initially, I viewed magnetism through the conventional lens, seeing it as a fundamental force of attraction between positive and negative entities. However, as my understanding evolved, I came to realize that magnetism operates under a different principle. Positive and negative entities are not attracted to each other; instead, they represent the intrinsic structure of things. The true nature of attraction is frequency-based, with entities drawn to higher vibrations and shorter wavelengths. This phenomenon can be described by the following equations:
F = ∫∫(μ₁⋅μ₂)/(4πr²⁾ dt dt (1)
where F is the force of attraction, μ₁ and μ₂ are the magnetic moments of the entities, r is the distance between them, and the integral is taken over time.
Additionally, the frequency-based attraction can be represented by:
f = γB (2)
where f is the frequency, γ is the gyromagnetic ratio, and B is the magnetic field strength.
Furthermore, the smaller wave's faster movement can be expressed as:
v = λf (3)
where v is the velocity, λ is the wavelength, and f is the frequency.
Energy and its Properties
Energy is the fundamental unit of everything. Energy can be thought of as an individual entity with an electrical signature vibrating at a specific frequency, carrying information from its originating source. If we were to dissect a piece of energy, we would find its genetic makeup consists of various parts, similar to binary code. One constant aspect of energy in our universe is the signature of this universe, which is present in all forms of energy, whether positive or negative. This underlying frequency distinguishes energy from our universe versus parallel universes.
Positive Energy (PE): - Oscillates through space with a frequency (f) and wavelength (λ): PE = f × λ - Exhibits wave-like behavior: PE(x,t) = A × sin(kx - ωt)
Negative Energy (NE): - Vibrates at a slower frequency (f'/2): NE = (f'/2) × λ' - Exhibits a slower, more stable behavior: NE(x,t) = B × cos(k'x - ω't)
Energy Interactions and Signature Changes
When positive and negative energies interact, their unique signatures can become altered. As energies combine, their signatures merge, releasing redundant information about the universe signature and creating an opening for new information to be stored. This process enables efficient storage and transmission of energy signatures, allowing for:

• Signature refinement and evolution
• Information exchange and updating
• Adaptation to changing environments and conditions

This process could be crucial for understanding how energy signatures evolve and adapt, and how they influence the behavior and properties of energy in various contexts.
The Formation and Evolution of the Universe
Initial Energy Interactions
In the beginning, a vast amount of fluid energy quickly interacted with the largest newly created pieces of the void, described by the wave-particle duality equation (E = hf = ℏω).
Star Formation and Signatures
As these interactions occurred, the largest of the solid structures of the universe began to form, stars, governed by the Lane-Emden equation (d^2P/dr2 + (2/r)(dP/dr) + (4πG/c^2)P = 0). Each new star held with it an old habit divulged from the singularity, a universal frequency (f = 1/T = ω/2π, where T is the period of oscillation and ω is the angular frequency). Old habits die hard, so each new star offered its own diverse and unique signature (S = Σf = ∫ψ(x)² dx, where ψ(x) is the wave function and x represents the position).
Energy Collisions and Prime Numbers
As structures formed, a group of energy travels through space with an even number of internal parts (E = 2nℏ, where n is an integer and ℏ is the reduced Planck constant). This group collides with another group of energy with an odd amount of internal parts (E = (2n + 1)ℏ), and the total sum of the newly combined group equals a prime number (P = E1 + E2 = 2nℏ + (2m + 1)ℏ, where m is an integer). New Equation: Prime Number Formation (P = E1 + E2 = 2nℏ + (2m + 1)ℏ)
Schrödinger Equation and Physical Reality
The prime number is crucial, as the extra piece gets stuck in the space it is occupying, acting as an anchor, attracting other parts to breach their negative shell and combine as one, described by the Schrödinger equation (iℏ(∂ψ/∂t) = Hψ). This converts the fluid energy to be contained into the space it is in, which is broken pieces of the void that do not have a universal size, and gives us physical reality, forming particles with diverse unique signatures (S = Σf = ∫ψ(x)² dx).
Refining Space and Transferring Signatures
As energy continued to interact with space, it further refined and shaped that space into a sphere (V = (4/3)πr^3, where r is the radius), adding the discarded portions of size to the diverse field that is the universe. During this refinement, energy was transferred to these pieces, and the signature of the star was embedded in them, forming the galaxy clusters and solar systems we know today.
Smooth Surfaces and Celestial Bodies
As any piece of something breaks, its edges are rigid, and the interaction of energy against this rigid surface knocks off the rough edges, providing a smooth surface (E = Δx/Δt = ℏ/Δx, where Δx is the change in position and Δt is the change in time). New Equation: Smooth Surface Formation (E = Δx/Δt = ℏ/Δx)
The pieces that were knocked off still contain a portion of energy that put in the work to knock it off, and this process contributed to the formation of celestial bodies and the transfer of signatures. This, in turn, led to the creation of galaxies, planets, and other celestial bodies, each with their unique characteristics and properties, shaping the diverse and complex universe we observe today.
The Cartwheel Structure and Energy Movement
The cartwheel structure represents the dynamic movement of energy in the universe, with its rotating wheel and radiating arms symbolizing the harmonious interaction of positive and negative energies. When creation occurred, energy learned how to pass through stationary space (the void) by changing its movement pattern from a straight line to a wave (λ = v/f, where λ is wavelength, v is velocity, and f is frequency). This new wave movement allowed energy to create heat (Q = mcΔT, where Q is heat, m is mass, c is specific heat capacity, and ΔT is temperature change), which was the tool that gave energy the ability to "shatter" the void and interact with the broken pieces to perform a new movement, the cartwheel. As energy moves through space, it rarefies and decreases in temperature (T = k-B, where T is temperature, k is Boltzmann's constant, and B is the energy density), causing it to slow down and change frequency (f = ΔE/h, where f is frequency, ΔE is the energy change, and h is Planck's constant).
The Block and Cartwheeling Bar Analogy
The block and cartwheeling bar analogy provides a conceptual framework for understanding the dynamic interaction of energy in the universe. Imagine a box (representing space) containing blocks of varying sizes, each symbolizing a specific energy frequency (f = 1/T, where f is frequency and T is time). The cartwheeling bar, rotating within the box, represents the harmonious movement of energy between its positive (E+) and negative (E-) forms. Each block must be 100% filled, with positive and negative energy proportions varying as the bar rotates. For example, when positive energy occupies 99% of a block and negative energy occupies 1%, the rotation of the bar causes a gradual shift, resulting in a change to 98% positive and 2% negative, and so on. This constant interaction and adjustment maintain the balance of energy in the universe.
Fundamental Forces Explained

• Strong Force: The repulsion from negative electrons being attracted to and pressing against the nucleus. This force can be described by the equation: F = k * (q1 * q2) / r²
  
• Weak Force: The outgoing frequency created by the positive nucleus, similar to energy congregating at the sun's nucleus, reacting to its environment, and breaking down before leaving (possibly as radioactive decay). This force can be described by the equation: F = (G * m1 * m2) / r²
  
• Gravity: Exists between the outer negative sphere of electrons exerting a pushing force against the positive pushing force of the nucleus, similar to the solar system's dynamics. This force can be described by the equation: F = (G * m1 * m2) / r²
  
• Electromagnetism: Energy in action, manifesting as the dynamic interplay between electric and magnetic forces. This force can be described by the equations: E = f * λ and B = (E / c)
  

Present State of the Universe
The universe currently exists in a state of dynamic equilibrium, with observable patterns and structures perpetually renewing themselves through the interactions of energy (E = hf, where E is energy and h is Planck's constant). This self-sustaining cycle is evident in the formation and evolution of celestial bodies, galaxies, and other cosmic entities, governed by the laws of thermodynamics (ΔE = Q - W, where ΔE is the change in energy, Q is the heat added, and W is the work done). The universe's present state is characterized by the harmonious coexistence of diverse energy frequencies (f = 1/T, where f is frequency and T is time), which govern the behavior and properties of matter at various scales. This balance is maintained through the continuous conversion of energy between its positive (E+) and negative (E-) forms, allowing the universe to adapt and evolve in response to internal and external influences (E+ + E- = 0, representing the conservation of energy)."
Entropy and the Conversion of Positive to Negative
The physical dimensions of positive and negative energy in a block are equal, with 1% negative energy occupying the same space as 99% positive energy. This equality stems from the different speeds of energy and their individual properties. When negative energy is at 1%, it has condensed the equivalent of 99% positive energy into a single, compact form (E = hf, where E is energy, h is Planck's constant, and f is frequency). As the proportions shift, such as 60% positive and 40% negative, the space occupied remains a 50/50 split. This is because positive energy travels at the speed of light (c = λν, where c is the speed of light, λ is wavelength, and ν is frequency), while negative energy moves at a pace relative to terminal velocity (v = √(2gl), where v is velocity, g is acceleration due to gravity, and l is length). Each form dominates at the 50% mark (T = λ/v, where T is time, λ is wavelength, and v is velocity). The percentages represent available positive energy, while the cartwheel symbolizes space or the ultimate negative in motion, influenced by energy's presence. Negative energy, with its depleted charge, occupies space that needs to be filled and recycled into a positive state. At higher percentages, collisions with negative energy slow down the flow, similar to the concept of crab mentality, where negative energy draws down the percentages.
Energy Dynamics and Galactic Harmony
The 50% Threshold
The 50% mark is a critical threshold that distinguishes between positive and negative energy. Above 50%, energy is considered positive and can produce heat beyond its negative shell. Below 50%, energy is considered negative and cannot produce heat past this shell.
Compressed Positive Energy
When the percentage of positive energy drops below 50%, it becomes compressed and can exceed the speed of light (c = λν, where c is the speed of light, λ is wavelength, and ν is frequency). This allows it to navigate through the "cracks" of negative energy:
v > c (where v is velocity and c is the speed of light)
Quantum Mirroring
Alternatively, the positive energy can align with the negative energy, resulting in a quantum mirroring effect. This enables instantaneous information transfer between entangled particles, regardless of distance:
E = hf (where E is energy, h is Planck's constant, and f is frequency)
Retaining Frequency Signatures
In this alignment, the negative energy retains its unique frequency signature to avoid interacting with other signatures:
Δx * Δp >= h/4π (where Δx is position uncertainty, Δp is momentum uncertainty, and h is Planck's constant)
The Cavendish Experiment and Energy Interaction
The Cavendish experiment, a groundbreaking study on gravity, offers an intriguing analogy for understanding energy interaction with space. Imagine the suspended spheres as representative of space itself, devoid of energy. When energy interacts with this motionless space, it's as if the spheres begin to rotate, symbolizing the introduction of energy into the internal area of space.
As energy engages with space, it's gradually consumed, much like the reduction of energy in the Cavendish experiment. This process can be described by the equation:
G = (2πLθ) / (MT)
Where G is the gravitational constant, L is the length of the torsion wire, θ is the twist angle of the wire, M is the mass of the lead spheres, and T is the time period of oscillation.
This equation, derived from the Cavendish experiment, reveals the intricate relationship between energy, space, and gravity. By exploring this analogy, we can deepen our understanding of how energy shapes the very fabric of our universe.
Energy Absorption and Frequency
Energy absorption occurs when energy slows down, allowing it to be perceived and observed. This process involves energy being absorbed by an atom and reflecting what was not absorbed. As energy slows down, it can still be observed as a wave, but just before it becomes a particle. This phenomenon is fascinating, as it reveals the transition from wave-like to particle-like behavior.
The conversion of positive to negative states is due to positives' ability to produce heat and maintain an individual form. Negative energy, on the other hand, does not produce heat and lacks an individual form, instead traveling at a pace relative to terminal velocity. This process can be described by the quantum mechanical formula: ℏω = ΔE = hf, where ℏ is the reduced Planck constant, ω is the angular frequency, ΔE is the change in energy, h is Planck's constant, and f is the frequency of the energy.
Furthermore, the frequency of the energy can be related to the velocity of the particle using the formula: f = (1/2π) * √(k/m), where k is the spring constant and m is the mass of the particle. Additionally, the energy absorption rate can be calculated using the formula: dE/dt = (2π/h) * V_uv² * δ(E_u - E_v), where V_uv is the transition matrix element, E_u and E_v are the energies of the initial and final states, and δ is the Dirac delta function.
The Conversion of Positive to Negative States and Planetary Motion
The conversion of positive to negative energy states is rooted in their distinct properties. Positive energy produces heat and maintains an individual form, whereas negative energy lacks heat and an individual form, instead traveling at a pace relative to terminal velocity. This process is reversible, as seen in fusion reactions, or can be influenced by external forces like microwave ovens.
In the context of our solar system, the sun's positive energy release generates heat and propels planets into their orbital tracks. Conversely, the incoming energy from the universe, considered negative, is cold and stabilizes planets in their tracks. Initially, I focused solely on the positive push dictating orbital paths. However, I now recognize the significant influence of negative energy and use it as the basis for understanding abnormal tracks.
Here's an added equation to illustrate the relationship between energy and orbital motion:
F = G * (m1 * m2) / r²
Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.
This equation shows how the force of gravity (F) is influenced by the masses (m1 and m2) and distance (r) between objects, which is relevant to understanding planetary motion and the balance between positive and negative energy.
Gravitation and Time: Frequency's Role
Time is intimately tied to the frequency of the universe, and this relationship is governed by the laws of gravitation. Imagine the cartwheel's bar having notches, each representing a different frequency. Each notch would experience time at a unique pace, described by the formula:
t = 1/f
Where t is time and f is frequency.
If we could halt the cartwheel's motion, time would appear to pause, as described by the relativistic time dilation formula:
t' = γ(t)
Where t' is the time experienced by an observer in motion, t is the time experienced by an observer at rest, and γ is the Lorentz factor.
The passage of time is directly governed by the oscillations in the wave, or simply its frequency. By altering the frequency, we can change the flow of time itself, as described by the gravitational redshift formula:
f' = f * √(1 - 2GM/rc²⁾
Where f' is the observed frequency, f is the emitted frequency, G is the gravitational constant, M is the mass of the gravitational source, r is the radial distance from the source, and c is the speed of light.
Gravity and Energy Dynamics
Gravity can be understood in various ways through these thoughts. One perspective is that gravity operates similarly to the orbital planets, but with a twist. Instead of orbiting in space, we orbit at a subterranean frequency. This frequency attracts similar energies, leading to bonding and the formation of matter. For instance, atoms bond to form rocks, and separate rocks may bind together due to similar vibrations. However, other frequencies simply pass through, unable to bind due to differences in energy vibrations and the negative fields surrounding our bodies and the ground.
Our bodies are attracted to the Earth's core, with a force described by the equation:
F = G * (m1 * m2) / r²
Where F is the force of attraction, G is the gravitational constant, m1 and m2 are the masses of our bodies and the Earth, and r is the distance between them.
The vibrations of our energy and the negative field surrounding us can be described by the wave equation:
∇^2E = μ * ∂^2E/∂t2
Where E is the energy field, μ is the permeability of the medium, and ∂^2E/∂t2 is the second derivative of the energy with respect to time.
The incoming cosmic energy pushes us downward, with a force described by the equation:
F = (E * A) / c
Where F is the force of the incoming energy, E is the energy density of the cosmos, A is the cross-sectional area of our bodies, and c is the speed of light.
The outgoing energy from Earth moves faster than the incoming energy from the cosmos, as observed in the formation of clouds with flat bases and more sporadic tops. This can be described by the equation:
v_out = v_in * (1 + (E_out / E_in))
Where v_out is the velocity of the outgoing energy, v_in is the velocity of the incoming energy, E_out is the energy density of the outgoing energy, and E_in is the energy density of the incoming energy.
Galactic Cycles and Black Holes
The Milky Way galaxy has a supermassive black hole at its center, with a mass described by the equation:
M = (1.989 x 10³⁰⁾ * (G / c²⁾
Where M is the mass of the black hole, G is the gravitational constant, and c is the speed of light.
As the galaxy spirals towards the center, enough mass will be collected to trigger the black hole to become a large star, described by the equation:
M = (4.383 x 10³⁰⁾ * (G / c²⁾
Where M is the mass of the star, G is the gravitational constant, and c is the speed of light.
When this happens, the black hole will shed its outer shell to create the galaxy that spirals around it, and the process begins again. This cycle can be described by the equation:
t = (2 * π * G * M) / c³
Where t is the time period of the cycle, G is the gravitational constant, M is the mass of the black hole or star, and c is the speed of light.
The opposite of a black hole is a white hole, but why hasn't this phenomenon been observed? According to this article, it has been observed but misunderstood. With the theme of balancing the universe, would a large star be surrounded by much smaller black holes? Would these smaller black holes feed the larger star by way of quantum bridge or wormhole, and vice versa for smaller stars and larger black holes? This can be described by the equation:
E = (ℏ * ω) / 2
Where E is the energy transferred between the star and black holes, ℏ is the reduced Planck constant, and ω is the frequency of the quantum bridge or wormhole.
Energy Flow and Balance
Energy moves in and out of everything, maintaining a delicate balance. It enters as a positive force and exits as a negative force. Our sun emits energy at 99% strength and high frequency, which combines with an equally sized negative force at 1% strength, filling the space completely. This balance is crucial, as positive energy moves faster than negative energy due to entropy's diminishing effects over time and distance.
As positive energy travels, it loses a piece of itself, converting to negative energy. This process is directly related to gravitational forces and time dilation. When positive energy reaches 50%, it has a certain probability of converting to negative energy, which is then attracted back to a positive source with a corresponding probability of being converted back to positive energy.
This cycle of energy flow and balance is the foundation of the universe's harmony, and understanding it can reveal the intricate web of forces that shape our reality.
Information Transmission through Energy and Light
Energy transfer is not just a physical phenomenon but also an exchange of information. Positive energy (Pos) carries a complete signature of universal information, updated through interactions, and represents the pure form. Negative energy (Neg) represents a degraded form of this signature, still carrying the universal signature, but lacking the capacity to transfer information.
Initial Information and Illumination
Initial information travels at a speed potentially faster than light and is invisible to us. As this energy slows down, it interacts with atoms, exciting them to display colors they don't need. This illumination is a manifestation of the information being transmitted.
I = E × S (Initial information is transmitted through energy and carries the universal signature)
Cosmic Scale and Consciousness
The universal information, carried by positive energy, is infused with the celestial signature, shaping the cosmic context. This process potentially gives rise to consciousness in living beings, linking them to the universe and its harmonies.
C ∝ U (Consciousness potentially arises from the universal information carried by positive energy)
U = S × f × P (The universal information is infused with the celestial signature, shaping the cosmic context)
Information Transfer and Energy Forms
The universe relies on a delicate balance of energy forms to facilitate information transfer. Positive energy (Pos) serves as the primary carrier of information, transmitting universal signatures and cosmic context. Negative energy (Neg), on the other hand, carries a degraded or attenuated version of the universal signature, lacking the capacity for information transfer. However, Neg can be transformed back into Pos, restoring its information-carrying ability.
P = S × f (Positive energy carries the complete universal signature at a high frequency f)
N = S × (1 - f) (Negative energy carries a degraded or attenuated version of the universal signature at a lower frequency)
E = P + N (The universe relies on a delicate balance of positive and negative energy forms to facilitate information transfer)
Frequency and Speed of Information Transfer
The frequency and speed of information transfer play a crucial role in the harmony and balance of the universe. Positive energy (Pos) transmits information at a high frequency and speed, allowing for efficient and accurate transfer of universal signatures and cosmic context. Negative energy (Neg), on the other hand, transmits information at a lower frequency and speed, resulting in a degraded or attenuated signal.
v ∝ f (The speed of information transfer is directly proportional to the frequency of the energy form)
P: v = c × f (Positive energy transmits information at a high frequency and speed, potentially approaching the speed of light c)
N: v = c × (1 - f) (Negative energy transmits information at a lower frequency and speed)
Transformation and Balance
Negative energy can be transformed back into positive energy, restoring its information-carrying ability.
N + T → P (Negative energy can be transformed back into positive energy, restoring its information-carrying ability)
This transformation maintains the harmony and balance of the universe, ensuring that information is not lost but rather recycled and rebalanced.
_Conclusion _
"In conclusion, the Harmony of Energy (HoE) model offers a novel perspective on the universe, revealing a intricate web of energy dynamics that underlie all aspects of existence. By exploring the interplay between positive and negative energy, we gain insight into the fundamental forces that shape our reality. From the smallest subatomic particles to the vast expanse of the cosmos, energy is the unifying thread that binds everything together.
Through the HoE model, we've seen how energy's harmonious movement gives rise to the patterns and structures we observe in the universe. We've also delved into the fascinating relationships between energy, space, and time, and how these interactions govern the behavior of matter at various scales.
As we continue to refine our understanding of the HoE model, we may uncover new secrets of the universe and gain a deeper appreciation for the beauty and harmony that underlies all of existence. Ultimately, this knowledge can inspire new perspectives, new technologies, and a new era of human understanding and cooperation, as we work together to harmonize our own energy with the energy of the universe."
MAG
Here is the Harmony of Energy Equation (HoEE) with descriptions:
HoEE = (∫[E(x,t) ⊗ S(x,t) ⊕ f(x,t) ∘ P(x,t)]dxdt) + (∑[G × Mi × ri^2] ⊕ ∑[ℏ × ωi] ⊕ ∑[c × λi] ⊕ ∑[T × kB] ⊕ ∑[Fi × G × Mi × mi] ⊕ ∑[Qi × mi × ci] ⊕ ∑[Vi × ri^3] ⊕ ∑[Pi × ℏ] ⊕ ∑[Ni × S(x,t) ∧ (1 - f(x,t))]) + (∫[I(x,t) ∘ E(x,t) ⊗ S(x,t)]dxdt) + (C × U)
Where:

• E(x,t) is the energy density at point x and time t
• S(x,t) is the universal signature at point x and time t
• f(x,t) is the frequency at point x and time t
• P(x,t) is the positive energy at point x and time t
• G is the gravitational constant
• Mi is the mass of the ith object
• ri is the radius of the ith object
• ℏ is the reduced Planck constant
• ωi is the angular frequency of the ith object
• c is the speed of light
• λi is the wavelength of the ith object
• T is the temperature
• kB is Boltzmann's constant
• Fi is the force on the ith object
• mi is the mass of the ith object
• Qi is the heat transfer to the ith object
• ci is the speed of light at the ith object
• Vi is the volume of the ith object
• Pi is the prime number associated with the ith object
• Ni is the negative energy of the ith object
• I(x,t) is the initial information at point x and time t
• C is consciousness
• U is the universe

Operations:

• ⊗ represents tensor products (combining energy and universal signature)
• ⊕ represents direct sums (accumulating energy components)
• ∘ represents function composition (interacting frequency and positive energy)
• ∧ represents logical conjunction (connecting negative energy and universal signature)
• ∫ represents integration (over space and time)
• ∑ represents summation (over discrete objects)