so the sand pile looks more or less like the one in the image below.
let's check its circumference first. We know that dC/dt = 5π
![C=2\pi r\implies \cfrac{dC}{dt}=2\pi \cfrac{dr}{dt}\implies 5\pi =2\pi \cfrac{dr}{dt}\implies \cfrac{5\pi }{2\pi }=\cfrac{dr}{dt}\implies \boxed{\cfrac{5}{2}=\cfrac{dr}{dt}}](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r%5Cimplies%20%5Ccfrac%7BdC%7D%7Bdt%7D%3D2%5Cpi%20%5Ccfrac%7Bdr%7D%7Bdt%7D%5Cimplies%205%5Cpi%20%3D2%5Cpi%20%5Ccfrac%7Bdr%7D%7Bdt%7D%5Cimplies%20%5Ccfrac%7B5%5Cpi%20%7D%7B2%5Cpi%20%7D%3D%5Ccfrac%7Bdr%7D%7Bdt%7D%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B5%7D%7B2%7D%3D%5Ccfrac%7Bdr%7D%7Bdt%7D%7D)
hmmm when the circumference C = 8π, what's the radius "r"?
![8\pi =2\pi r\implies \cfrac{8\pi }{2\pi }=r\implies 4=r](https://tex.z-dn.net/?f=8%5Cpi%20%3D2%5Cpi%20r%5Cimplies%20%5Ccfrac%7B8%5Cpi%20%7D%7B2%5Cpi%20%7D%3Dr%5Cimplies%204%3Dr)
now let's take the derivative to the volume equation, and check what dV/dt is
![V=\cfrac{r^3}{3}\implies V=\cfrac{1}{3}r^3\implies \cfrac{dV}{dt}=\stackrel{\textit{chain rule}}{\cfrac{3}{3}r^2\cdot \cfrac{dr}{dt}}\implies \cfrac{dV}{dt}=r^2\cdot \cfrac{5}{2}\implies \cfrac{dV}{dt}=\cfrac{5r^2}{2} \\\\\\ \stackrel{\textit{when }C=8\pi \textit{ we know that }r=4}{\cfrac{dV}{dt}=\left. \cfrac{5r^2}{2}\right|_{r=4}} \implies \cfrac{dV}{dt}=\cfrac{5(4)^2}{2}\implies \cfrac{dV}{dt}=40](https://tex.z-dn.net/?f=V%3D%5Ccfrac%7Br%5E3%7D%7B3%7D%5Cimplies%20V%3D%5Ccfrac%7B1%7D%7B3%7Dr%5E3%5Cimplies%20%5Ccfrac%7BdV%7D%7Bdt%7D%3D%5Cstackrel%7B%5Ctextit%7Bchain%20rule%7D%7D%7B%5Ccfrac%7B3%7D%7B3%7Dr%5E2%5Ccdot%20%5Ccfrac%7Bdr%7D%7Bdt%7D%7D%5Cimplies%20%5Ccfrac%7BdV%7D%7Bdt%7D%3Dr%5E2%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20%5Ccfrac%7BdV%7D%7Bdt%7D%3D%5Ccfrac%7B5r%5E2%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bwhen%20%7DC%3D8%5Cpi%20%5Ctextit%7B%20we%20know%20that%20%7Dr%3D4%7D%7B%5Ccfrac%7BdV%7D%7Bdt%7D%3D%5Cleft.%20%5Ccfrac%7B5r%5E2%7D%7B2%7D%5Cright%7C_%7Br%3D4%7D%7D%20%5Cimplies%20%5Ccfrac%7BdV%7D%7Bdt%7D%3D%5Ccfrac%7B5%284%29%5E2%7D%7B2%7D%5Cimplies%20%5Ccfrac%7BdV%7D%7Bdt%7D%3D40)
Answer:
-25
Step-by-step explanation: the negative/ opposite of 25 is -25
Answer:
(c) 31.2-60
Step-by-step explanation:
Given that
60 – 31.2 + ? = 0
![\Rightarrow ?=31.2-60](https://tex.z-dn.net/?f=%5CRightarrow%20%3F%3D31.2-60)
This is the same as the expression in option (c) 31.2-60.
Hence, option (c) is correct.
Answer:
b
Step-by-step explanation:
Answer:
Well I think it is A because domain is the x values.
Step-by-step explanation:
So when you plug this in your calculator (mine is a ti-84 plus ce) you would hit graph. After it graphs it press Zoom, 0 to center it then press 2nd, trace which pulls up parabola menu's. Press 0 and find the left bound, right bound and then press enter which would give you x values of 2.9375 < t< 6
At the same time I don't know if this is right. I never really excelled at parabolas just trying to help.