Question

A trough has ends shaped like isosceles triangles, with a width of 3 meters and a height of 4 meters. The trough is 10 meters long, as shown in the figure below. Water is being pumped into the trough at a constant rate. The goal is to determine how fast the water level is rising when the water is a certain height.

Answer 1

A trough has ends shaped like isosceles triangles, with a width of 3 meters and a height of 4 meters. To determine how fast the water level is rising, calculate the volume of the trough and differentiate it with respect to time.

Step-by-step explanation:

Trough Dimensions:

A trough has ends shaped like isosceles triangles, with a width of 3 meters and a height of 4 meters.

The trough is 10 meters long.

Rate of Water Level Rising:

To determine how fast the water level is rising, we can use the fact that the trough is partially filled with water and the dimensions of the trough.

From the given information, we know the width, height, and length of the trough. We can calculate the volume of the trough using the formula:

Volume = Length x Width x Height

Once we determine the volume of water in the trough, we can differentiate it with respect to time to find the rate of change of volume with respect to time, which will give us the rate at which the water level is rising.