Given that A= f(B), by the chain rule, dA/dt= df/dB dB/dt. That's the whole point of every "related rates" problem. You get some "static" formula (not involving the time, t) connecting the quantities given in a problem, then differentiate with respect to t.
Yes, . What is dA/dr? So then what is dA/dt= dA/dr dr/dt? After you have that, put in the given specific values.
Have you drawn a picture? Draw the pole, the woman, and the ground. Draw the path of the light from lamp to the top of the womans head to the ground (at the tip of her shadow, of course). You should see two similar right triangles, both having the ground as one leg, one having the woman as the other leg, the other triangle, the lamp post.3. 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 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?
It said to use two triangles to compare. I am not sure how to do this problem. I feel like I am missing something here...
Thank you for the help and insight!