25 POINTS FOR WHOEVER ANSWERS THIS QUESTION PLEASE HELP! An inverted conical tank with a height of 10 ft and a radius of 5 ft is drained through a hole in the vertex at a rate of 5 ft^3/s. What is the rate of change when the water depth is at 4 ft?

a.) Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h.

b.)Differentiate both sides of the equation with respect to t. dV/dt = () dh/dt

c.) when the water depth is 4 ft, the rate of change of the water depth is about . (Round to nearest hundredth if needed.)

So just use Cyclander formula. That’s how you solve!

Part A)

Part B)

Part C)

Step-by-step explanation:

Please refer to the attachment.

We know that the conical tank has a height of 10 feet and a radius of 5 feet.

The rate at which water is being drained through a hole in the vertex is 5 cubic feet per second.

Part A)

Recall the volume formula for a cone:

Since this is a cone, we can draw two similar triangles (refer to the attachment). Then, by properties of similar triangles, we can write:

Therefore:

So:

Substituting this into our formula yields:

Simplify:

Part B)

Let’s take the derivative of both sides with respect to t. So:

The left will simply be dV/dt. We can move the coefficient from the right:

Implicitly differentiate:

Simplify. So, our derivative is:

Part C)

We want to find the rate of change of the water depth (in other words, dh/dt) when h=4.

Since our water is being drained at a rate of 5 cubic feet per second, this means that dV/dt=5.

So, substituting, we get:

Simplify:

Therefore:

So, the change of the water depth is about 0.4 feet per second.

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d