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Unit 21 Common Formulas and Equations

Area of a rectangle

$A=lw$

⠠⠁⠀⠨⠅⠀⠇⠺

Area of a triangle

$A={\displaystyle \frac{1}{2}}bh$

⠠⠁⠀⠨⠅⠀⠹⠂⠌⠆⠼⠃⠓

Area of a circle

$A=\pi r^2$

⠠⠁⠀⠨⠅⠀⠨⠏⠗⠘⠆

Circumference of a circle

$C=2\pi r$

⠠⠉⠀⠨⠅⠀⠼⠆⠨⠏⠗

Distributive Law

$a\left(b+c\right)=ab+ac$

⠁⠷⠃⠬⠉⠾⠀⠨⠅⠀⠁⠃⠬⠁⠉

Pythagorean Theorem

$a^2+b^2=c^2$

⠁⠘⠆⠐⠬⠃⠘⠆⠀⠨⠅⠀⠉⠘⠆

Product of a sum and difference

$\left(x-y\right)\left(x+y\right)=x^2-y^2$

⠷⠭⠤⠽⠾⠷⠭⠬⠽⠾⠀⠨⠅⠀⠭⠘⠆⠐⠤⠽⠘⠆

First law of exponents

$a^n{a}^m=a^{n+m}$

⠁⠘⠝⠐⠁⠘⠍⠀⠨⠅⠀⠁⠘⠝⠬⠍

Second Law of Exponents

${\left(ab\right)}^n=a^n{b}^n$

⠷⠁⠃⠾⠘⠝⠀⠨⠅⠀⠁⠘⠝⠐⠃⠘⠝

Fractional addition

${\displaystyle \frac{a}{b}}+{\displaystyle \frac{c}{d}}={\displaystyle \frac{ad+bc}{bd}}$

⠹⠁⠌⠃⠼⠬⠹⠉⠌⠙⠼⠀⠨⠅⠀⠹⠁⠙⠬⠃⠉⠌⠃⠙⠼

Fractional multiplication

${\displaystyle \frac{a}{b}}\times {\displaystyle \frac{c}{d}}={\displaystyle \frac{ac}{bd}}$

⠹⠁⠌⠃⠼⠈⠡⠹⠉⠌⠙⠼⠀⠨⠅⠀⠹⠁⠉⠌⠃⠙⠼

Fractional exponent

$a^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}=\sqrt[n]{a}$

⠁⠘⠹⠂⠸⠌⠝⠼⠀⠨⠅⠀⠣⠝⠜⠁⠻

Negative exponent

$a^{-n}={\displaystyle \frac{1}{a^n}}$

⠁⠘⠤⠝⠀⠨⠅⠀⠹⠂⠌⠁⠘⠝⠼

Power of a power

${\left(a^n\right)}^m=a^{nm}$

⠷⠁⠘⠝⠐⠾⠘⠍⠀⠨⠅⠀⠁⠘⠝⠍

Power of a quotient

${\left({\displaystyle \frac{a}{b}}\right)}^n={\displaystyle \frac{a^n}{b^n}}$

⠷⠹⠁⠌⠃⠼⠾⠘⠝⠀⠨⠅⠀⠹⠁⠘⠝⠐⠌⠃⠘⠝⠼

Slope Formulas

$m={\displaystyle \frac{y_2-y_1}{x_2-x_1}}$

⠍⠀⠨⠅⠀⠹⠽⠆⠤⠽⠂⠌⠭⠆⠤⠭⠂⠼

$m={\displaystyle \frac{\Delta y}{\Delta x}}$

⠍⠀⠨⠅⠀⠹⠨⠠⠙⠽⠌⠨⠠⠙⠭⠼

Slope Intercept

$y=mx+b$

⠽⠀⠿⠀⠍⠭⠬⠃

Newton's Second Law

$\overrightarrow{F}=m\overrightarrow{a}$

⠐⠠⠋⠣⠫⠕⠻⠀⠨⠅⠀⠍⠐⠁⠣⠫⠕⠻

Compound interest

$A=P{\left(1+{\displaystyle \frac{r}{n}}\right)}^{nt}$

⠠⠁⠀⠨⠅⠀⠠⠏⠷⠂⠬⠹⠗⠌⠝⠼⠾⠘⠝⠞

Distance Formula

$d=\sqrt{{\left(x_1-x_2\right)}^2}+{\left(y_1-y_2\right)}^2$

⠙⠀⠨⠅⠀⠜⠷⠭⠂⠤⠭⠆⠾⠘⠆⠐⠻⠬⠷⠽⠂⠤⠽⠆⠾⠘⠆

Quadratic Equation

$x={\displaystyle \frac{-b\pm \sqrt{b^2-4ac}}{2a}}$

⠭⠀⠨⠅⠀⠹⠤⠃⠬⠤⠜⠃⠘⠆⠐⠤⠲⠁⠉⠻⠌⠆⠁⠼

Tangent Formula

$\tan \theta ={\displaystyle \frac{\sin \theta }{\cos \theta }}$

⠞⠁⠝⠀⠨⠹⠀⠨⠅⠀⠹⠎⠊⠝⠀⠨⠹⠌⠉⠕⠎⠀⠨⠹⠼

Expansion of a Sum

${\left(1+x\right)}^n=1+{\displaystyle \frac{nx}{1!}}+{\displaystyle \frac{n\left(n-1\right)x^2}{2!}}+\dots$

⠷⠂⠬⠭⠾⠘⠝⠀⠨⠅⠀⠼⠂⠬⠹⠝⠭⠌⠂⠯⠼⠬⠹⠝⠷⠝⠤⠂⠾⠭⠘⠆⠐⠌⠆⠯⠼⠬⠀⠄⠄⠄