Expressions Of Pj Problems

Pj Problems - Overview

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COHN - Natures Engineering Of The Human Body

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Painting

Range Of A Projectile

The parametric equations of a projectile are: x = 20t and y = -16t^{2} + 30t.

Determine the range of the projectile.

**The string**: S_{7}P_{4}A_{42} (Curved Motion);
**The Math**:

Pj Problem of Interest (PPI) is of the type *motion*. The range of a projectile is the horizontal ground distance the projectile covered when it lands on the ground. At this time the vertical distance y is zero.

So setting y = 0, we have 16t = 30. From which we have t = 15/8. This t is the time that elapsed before the projectile reached the ground, that is, the time it took to cover the range.

So range = x = 20 x 15/8 = 75/2 = 37.5 ft.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Single Variable Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

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Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

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