The power produced by a dam is given by E = 16x^2 - 12x - 1000 MW where x is the height of the water. If the water level drops at 14 m/s what is the rate of change of power production.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The power produced by a dam is given by E = 16x^2 - 12x - 1000 MW where x is the height of the water. The water level is dropping at a rate of 14 m/s. The rate of change of power due to this has to be determined. The rate of change of the water level `(dx)/(dt) = -14` .

The rate of change of the power production is given by `(dW)/(dt) = 32x*(dx/dt) - 12*(dx)/(dt)` . As the water level drops at 14 m/s, the power produced changes at a rate `32*x*(-14) - 12*(-14)`

=> -448x + 168 MW/s

The rate of change of the power production -448x + 168 MW/s

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial