A Formula Reference
This appendix collects formulas used repeatedly in the book. Each formula should be used with the domain restrictions, units, and assumptions developed in its chapter.
Algebra and geometry
\[V_{\text{rectangular}}=LWH,\qquad A_{\text{circle}}=\pi r^2,\qquad V_{\text{cylinder}}=\pi r^2h.\]
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a},\qquad D=b^2-4ac.\]
Functions and rates
\[m=\frac{y_2-y_1}{x_2-x_1},\qquad \text{average rate}=\frac{f(b)-f(a)}{b-a}.\]
\[ (f\circ g)(x)=f(g(x)). \]
Exponential and logarithmic models
\[A(t)=A_0(1+r)^t,\qquad A(t)=A_0e^{kt},\]
\[A(t)=P\left(1+\frac rn\right)^{nt},\qquad P(t)=\frac{d}{1+ke^{-ct}}.\]
\[\log_b(MN)=\log_bM+\log_bN,\] \[\log_b(M/N)=\log_bM-\log_bN,\] \[\log_b(M^p)=p\log_bM,\qquad \log_bx=\frac{\ln x}{\ln b}.\]
Trigonometry
\[\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}},\quad \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}},\quad \tan\theta=\frac{\text{opposite}}{\text{adjacent}}.\]
\[180^\circ=\pi\ \text{radians},\qquad a^2+b^2=c^2.\]
\[\sin^2\theta+\cos^2\theta=1,\] \[\sin(s+t)=\sin s\cos t+\cos s\sin t,\] \[\cos(s+t)=\cos s\cos t-\sin s\sin t.\]