Dedicated to helping math, physics, and engineer majors understand math and physics.
The Daily Upset “Willy Wonka’s Garden of Eve and The Old Ladies that Support Not Supporting”
In this episode I discuss different outlooks on personal beliefs in the form of hypocrisy. Order a signed novel The Daily Upset "Willy Wonka's Garden of Eve and The Old Ladies that Support Not Supporting" Ah, all right, you little freaks. It's, it's that time again, the obsessive compulsive disorder issue of should I do this? Or should I do that?
4.5 Billion Years BCE [edited] – Anunnaki Origins – Audiobook Chapter 1
Purchase this title within the TIMEWAVES Collection Just outside the edge of Earth’s solar system, a large spherical vessel cuts through the fabric of space like a knitting needle slipping through a bubble. After a quick lightspeed jump, it becomes stationary, floating near Neptune. It then rotates slowly, adjusting its trajectory to align with the Sun. Once the object's course is set, the metallic…
eBook with Audiobook | Capitol Murders: The Madison Ripper
Audiobook – Capitol Murders: The Madison Ripper
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PDFeBook – Capitol Murders: The Madison Ripper
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How to Solve a Linear Algebra Problem using the Textbook: Column Space and Nullspace | Construct a matrix whose column space contains (1,1,1) and whose nullspace is the line of multiples of (1,1,1,1)
Strang, G. (2006). Linear algebra and its applications (4th ed.). Brooks/Cole. Full Original Lesson Quick Recap Lesson Written Lesson Title: Construct a Matrix with Given Column Space and Nullspace (Step-by-Step Proof) In this walkthrough, we show how to construct a matrix…
Chapter 1 “A Shoot to Remember” | Capitol Murders: The Madison Ripper
Chapter 1: A Shoot to Remember Dead Man Thawing “You know, you can tell everything about a woman’s vagina by the shape of her nose.” “Thanks. Now, I’ll never picture anything else when I talk to a girl.” “Or your mom.” “God – damn-it, man!” “And you get the whole aerial view when she puckers up for a kiss.” “Jesus, dude.
Matrix Determinants- 2×2, 3×3, and Higher Order Cofactor Expansion.png
Matrix Determinants: 2x2, 3x3, and Higher Order Cofactor Expansion This sheet from the Ultimate Algebra Crash Course walks you through how to calculate the determinant of a matrix—an essential concept in linear algebra, systems of equations, and transformations in multivariable calculus and physics. From solving 2x2 systems to expanding cofactors in 4x4 matrices, understanding determinants gives you…
Matrix Systems and Rank- A Visual Guide to Solving Linear Equations
Absolutely! Here's the revised version of your post using ( ) parentheses instead of [ ] brackets, fully optimized and ready to paste into your WordPress site: Matrix Systems and Rank: A Visual Guide to Solving Linear Equations This page from the Ultimate Algebra Crash Course presents the foundation of solving systems using matrix operations and introduces the concept of…
Geometry, Volume, and Business Math Formulas- The Ultimate Reference for STEM Students
Geometry, Volume, and Business Math Formulas: The Ultimate Reference for STEM Students This final cheat sheet page brings your algebra toolkit full circle—applying what you've learned to geometry, volume, and business functions. Whether you're in engineering, finance, economics, physics, or data science, these are the formulas that appear everywhere from standardized tests to…
Equations of Conic Sections and Lines- Complete Reference Sheet for Algebra and Precalculus
Equations of Conic Sections and Lines: Complete Reference Sheet for Algebra and Precalculus This final visual and symbolic reference page brings together the standard forms of all major graphable equations in algebra: lines, parabolas, circles, ellipses, and hyperbolas. These are known as conic sections, and they form the geometric backbone of analytic geometry, trigonometry,…
Conic Sections and Their Graphs- Circles, Hyperbolas, and Advanced Algebraic Curves
Conic Sections and Their Graphs: Circles, Hyperbolas, and Advanced Algebraic Curves This final visual reference extends your algebraic understanding into a powerful realm of mathematics: conic sections. These equations and their graphs aren’t just curve sketches—they’re foundational in geometry, trigonometry, calculus, and even physics. If you can read these graphs and recognize their…
Common Graphs and Formulas in Algebra: Your Visual Library of Functions
Common Graphs and Formulas in Algebra: Your Visual Library of Functions Every algebra student needs a visual library of basic functions and how they appear on a graph. These aren’t just important for exams—they form the foundation for transformations, modeling, and calculus. This final reference page summarizes six of the most common parent functions: quadratic, cubic, square root, reciprocal,…
Algebra in Action- Inequalities, Interest Formulas, Symmetry, and Proportionality
Algebra in Action: Inequalities, Interest Formulas, Symmetry, and Proportionality This final installment of the Ultimate Algebra Cheat Sheet bridges the gap between abstract algebra and real-world application. It includes how to solve absolute value inequalities, use exponential interest and loan formulas, understand symmetry in graphs, and model proportional relationships. These are the…
Graphing Rational Functions- Holes, Asymptotes, and Behavior at Infinity
Graphing Rational Functions: Holes, Asymptotes, and Behavior at Infinity This final page brings together everything you've learned about domain restrictions, graphing, and asymptotes into a single topic: how rational functions behave across different parts of their domain. You’ll learn to identify holes, horizontal asymptotes, vertical asymptotes, and even oblique (slant) asymptotes—the full…
Domain Restrictions, Inverse Functions, and Asymptotes: Precision Rules in Algebra and Graphing
Domain Restrictions, Inverse Functions, and Asymptotes: Precision Rules in Algebra and Graphing The deeper you go into algebra and calculus, the more important it becomes to understand the boundaries and structure of functions. Not all functions are defined everywhere, and not all functions are reversible. This page—the final capstone of the Ultimate Algebra Cheat…
A small lead sphere with a mass of 8.00 g has excess electrons added so its net charge is -3.20 × 10⁻⁹ C.(a) How many extra electrons are on the sphere?(b) How many of these excess electrons are there per lead atom, given that lead has an atomic number of 82 and an atomic mass of 207 g/mol?
How to Calculate Excess Electrons and Charge Per Atom on a Lead Sphere This problem is from University Physics with Modern PhysicsLink to textbook: University Physics with Modern…
Mastering Lines in Algebra: Point-Slope, Slope-Intercept, and Parallel vs Perpendicular Forms
Mastering Lines in Algebra: Point-Slope, Slope-Intercept, and Parallel vs Perpendicular Forms Algebra begins with numbers but grows into relationships—and one of the most important relationships is the linear equation. This final page of the Ultimate Cheat Sheet focuses entirely on writing and understanding equations of lines in all major forms. Whether you're graphing,…
Midpoints, Quadratic Solutions, and Graphing Lines- Finishing Your Algebra Toolbox
Midpoints, Quadratic Solutions, and Graphing Lines: Finishing Your Algebra Toolbox As we close out the Ultimate Cheat Sheet series, this final reference sheet brings together three essential tools: the midpoint formula, the proof and application of the quadratic formula, and a simple but powerful way to graph linear equations. With these in hand, you’ll have mastered the core operations…
Functions, Symmetry, and Distance- The Final Concepts to Close the Algebra Foundation
Functions, Symmetry, and Distance: The Final Concepts to Close the Algebra Foundation In mathematics, everything eventually comes back to functions. They’re the machines of the subject—take an input, perform a transformation, and deliver an output. This final sheet in the Ultimate Cheat Sheet series wraps up your understanding of how functions behave, how we measure their change, and…