Question

please don't do this unless you can do all parts, circle answer and show work please

part 1)

Assume x and y are functions of t. Evaluate dy/dt  given that

y^2−8x^3=225 dx/dt=5, x=−3, y=3

Answer: dy/dt=

part 2)

Assume x and y are functions of t. Evaluate dy/dt given that

5xy+ sqrt(2x+y)=48 dx/dt=-4; x=3 ,y=3.

Answer: dy/dt=

part 3)

Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by

C=70000+40x, R=400−x^2/30,,

where the production output in one week is xx calculators. If the production rate is increasing at a rate of 500 calculators per week when the production output is 6000 calculators, find each of the following

Rate of change in cost =

Rate of change in revenue =

Rate of change in profit =

part 4)

A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 40 ft from the base of the pole?

ft/sec

How fast is the length of her shadow increasing?

ft/sec

part 5)

A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how fast will the foot be moving away from the wall when the top is 9 feet above the ground?

The foot will be moving at  ft/s.

Answer 1