Question

How do you solve these two questions? Answer and Explanation Please!
gyazo.com/d0950b43c16f5cf91d2db25e4d527b68
gyazo.com/47b9c66487d55f11ba22b65fc2285cf9

Answer 1

see Kat:

https://www.jiskha.com/questions/1786627/Hello-Im-trying-to-create-a-study-sheet-to-help-myself-If-someone-could-give

Answer 2

If it's listed as 3t^8 - 2t^5 what answer choice does that match up with?

Answer 3

Also, how do I find the answer for the water tank one? I can't seem to figure it out from the link you sent

Answer 4

dV/dy =pi/y^2
so
dV/dt =(pi/y^2) (dy/dt)
so
when y =2
1.5 = (pi/4) dy/dt
dy/dt = 4 *1.5 / pi
a little less than 2 so 1.91

now by the way I suspect a typo because the tank bottom is at y = 1 so really the depth is 2 at y = 3. but
9*1.5/pi or about 4.30 is not listed

Answer 5

sorry - my bad. I saw the water tank problem and thought it was Kat's post again.

Also, either I misread this one, or it was wrong online

recall that if F(t) = ∫[u,v] f(x) dx, then d/dt F(t) = f(v) dv/dt - f(u) du/dt
This is just the chain rule in reverse.
So, if F(t) = ∫[t^2,t^3] sin(x^2) dx
dF/dt = sin((t^3)^2)(3t^2) - sin((t^2)^2)(2t)
= (A)

Answer 6

Thank you so much for your time and help!!

Answer 7

sorry go with oobleck on the sin x^2 , t one. I forgot to do dv/dt and du/dt