Profit, or the surplus money after your costs are covered, is Revenue - Costs.
so in this case the profit P(x) = R(x) - C(x).
![\bf P(x)=(135x)-(93x+35000)\implies P(x)=135x-93x-35000 \\\\\\ P(x)=42x-35000 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{selling 5000 mp3s}}{P(5000)=42(5000)-35000}\implies P(5000)=210000-35000 \\\\\\ P(5000)=175000](https://tex.z-dn.net/?f=%5Cbf%20P%28x%29%3D%28135x%29-%2893x%2B35000%29%5Cimplies%20P%28x%29%3D135x-93x-35000%0A%5C%5C%5C%5C%5C%5C%0AP%28x%29%3D42x-35000%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill%5C%5C%5C%5C%0A%5Cstackrel%7B%5Ctextit%7Bselling%205000%20mp3s%7D%7D%7BP%285000%29%3D42%285000%29-35000%7D%5Cimplies%20P%285000%29%3D210000-35000%0A%5C%5C%5C%5C%5C%5C%0AP%285000%29%3D175000)
The same constant value(s)
True because tan(20)=2.1 and cot(20)=is o.44
![\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\ slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bperpendicular%2C%20negative-reciprocal%20slope%20for%20slope%7D%5Cquad%20%5Ccfrac%7Ba%7D%7Bb%7D%5C%5C%5C%5C%0Aslope%3D%5Ccfrac%7Ba%7D%7B%7B%7B%20b%7D%7D%7D%5Cqquad%20negative%5Cimplies%20%20-%5Ccfrac%7Ba%7D%7B%7B%7B%20b%7D%7D%7D%5Cqquad%20reciprocal%5Cimplies%20-%20%5Ccfrac%7B%7B%7B%20b%7D%7D%7D%7Ba%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
![\bf \boxed{5i+12j}\implies \begin{array}{rllll} \ \textless \ 5&,&12\ \textgreater \ \\ x&&y \end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5} \\\\\\ slope=\cfrac{12}{{{ 5}}}\qquad negative\implies -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12} \\\\\\ \ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}](https://tex.z-dn.net/?f=%5Cbf%20%5Cboxed%7B5i%2B12j%7D%5Cimplies%20%0A%5Cbegin%7Barray%7D%7Brllll%7D%0A%5C%20%5Ctextless%20%5C%205%26%2C%2612%5C%20%5Ctextgreater%20%5C%20%5C%5C%0Ax%26%26y%0A%5Cend%7Barray%7D%5Cquad%20slope%3D%5Ccfrac%7By%7D%7Bx%7D%5Cimplies%20%5Ccfrac%7B12%7D%7B5%7D%0A%5C%5C%5C%5C%5C%5C%0Aslope%3D%5Ccfrac%7B12%7D%7B%7B%7B%205%7D%7D%7D%5Cqquad%20negative%5Cimplies%20%20-%5Ccfrac%7B12%7D%7B%7B%7B%205%7D%7D%7D%5Cqquad%20reciprocal%5Cimplies%20-%20%5Ccfrac%7B%7B%7B%205%7D%7D%7D%7B12%7D%0A%5C%5C%5C%5C%5C%5C%0A%5C%20%5Ctextless%20%5C%2012%2C%20-5%5C%20%5Ctextgreater%20%5C%20%5C%20or%5C%20%5C%20%5Ctextless%20%5C%20-12%2C5%5C%20%5Ctextgreater%20%5C%20%5Cimplies%20%5Cboxed%7B12i-5j%5C%20or%5C%20-12i%2B5j%7D)
if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.
so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.
so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.
or using a unit vector for those above, then
Circumference=pid
d=diameter
circumference=12pi
if you aprox pi=3.141592
c=37.699104 ft