1. How fast is the shadow of the tightrope walker's feet moving along the ground when he is midway between the buildings?

I got 20/7 ft/s. I used similar triangles and didnt even have an X in the deriv (just x') so the rate would always be the same no matter where the guy is on the rope....is that right?

2. How far from point A is he when the shadow of his feet reaches the base of B building?

You did your calculation correctly,but you calculated how far he is from building B and it asks for how far he is from building A. So 50ft - 35 ft = 15 ft

3. How fast is the shadow of the tightrope walker's feet moving up the wall of the B building when he is 10 feet from point B?

I got 4.375 ft/s

Let x = distance between walker and point B

Let y = distance from shadow to top of bulding B

dx = rate of walker

dy = rate of shadow moving up building B

I have:

y = 17.5 (from similar triangles)

x = 10 (given)

dx = 2 ft/s

dy = ?

Assuming you obtained your function using the derivative of the pathagorean theorum:

So,

Double check me, (as I am so tired I'm about to drop) but I'm pretty sure this is right.

and another: Car B is 30 miles directly east of Car A and begins moving west at 90 mph. At the same time, car A begins movie north at 60 mph.

a. after 1/10 of an hour has elapsed, at what rate are the cars getting closer together.

used distance formula and got 277.4033 mph. (that doesnt seem right)

For this problem, you will need to find dz. You are given two rates in the problem, dx = 90 mph & dy = 60mph

Ok, so first,

Let's get our x and y values. We know how long they travelled and how fast they were going:

distance = rate x time

For each car,

So,

y = 6 miles

x = 30-9 = 21 miles (car B backtracked on our 30 mile distance by 9 miles)

To find z, use pathagorean theorum. You can do that part.

Then plug and chug for dz, which should be the rate after 1/10 hour.

2ydy +2xdx = 2zdz

Hope this helps. I have to go to bed, sorry I can't help with the last part!