Hi, can someone help me solve these 4 questions please? Thank you! 1) 2) 3) 4) G

Question

Hi, can someone help me solve these 4 questions please? Thank you!

1)

2)

3)

4)

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 15 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V = 1/3 pi r2 h The linearization at a = 0 to 2 + 3x is A + Bx where A is and where B is: The differential of the function y = (x2 + 6)3 is dy = dx. When x = 2 and dx = 0.05, the differential dy = If f(x) = 4 sin(x) + 2xx, find f(2).

Explanation / Answer

1) V = (1/3)*pi*h*r^2
We are given that 2*r = h so r = h/2
V = (1/12)*pi*h^3

dV/dt = [(1/4)*pi*h^2]dh/dt
dV/dt = 50 so dh/dt = (50*4)/(pi*h^2) = 0.283 ft/min

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