The transformer (grey box) on this power line is how far above the ground?
Round to the nearest tenth.

The transformer is 27.5 ft above the ground.

Solution:

The given image is like a triangle.

Angle 'L' represents the triangle is right triangle.

Use Pythagoras theorem to find the answer.

Base of the triangle = 12 ft

Hypotenuse of the triangle = 30 ft

Height of the triangle = x

Using Pythagoras theorem,

Subtract 144  on both sides of the equation.

Taking square root on both sides.

Hence the transformer is 27.5 ft above the ground.

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.