Related Rates

If  $xy=10$  , find  $\frac{dx}{dt}$  when  $y=5$  and  $\frac{dy}{dt}=20$ . 

•  $-8$  

•  $\frac{-1}{8}$  

•  $-50$  

•  $-\frac{1}{50}$  

A 75-inch tall man walks away from a 100-inch lamp post  at a rate of 15 inches/second. Find the rate at which the tip of the man's shadow is lengthening at the moment that the man is 20 inches from the lamp post.

•  $45\ \frac{in}{\sec}$  

•  $30\ \frac{in}{\sec}$  

•  $48\ \frac{in}{\sec}$  

•  $75\ \frac{in}{\sec}$  

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

An observer, who is 1200-feet from a rocket launch, sees a rocket ascend vertically at a rate of 300-feet/min. Find the rate of change of the angle of elevation when the height of the rocket is 500 feet.

•  $\frac{36}{169}\ \frac{rad}{\min}$  

•  $\frac{12}{169}\ \frac{rad}{\min}$  

•  $\frac{1}{169}\ \frac{rad}{\min}$  

•  $\frac{12}{13}\ \frac{rad}{\min}$  

Tags

CCSS.HSF.TF.B.7

The volume of a sphere is decreasing at a rate of 8 cubic mm per second. How fast, in square mm, is the surface area of the sphere decreasing at the instant when the diameter is 100 mm.

•  $\frac{-8}{25}\ \frac{mm^2}{\sec}$  

•  $\frac{-8}{50}\ \frac{mm^2}{\sec}$  

•  $\frac{-3}{25}\ \frac{mm^2}{\sec}$  

•  $\frac{-3}{50}\ \frac{mm^2}{\sec}$  

Devin set up a toy rocket. For safety, he stands 6 meters from the rocket. He sets off the rocket and it heads straight up at a constant rate of 4 m/s.  How fast is the distance between the rocket and Devin changing after 2s?

• -2.5 m/s
• 2.5 m/s
• 3.2 m/s
• -3.2 m/s

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSS.ID.C.7