If you drive 70 miles per hour, how many minutes does it take to drive 110 miles?

127.6 mins

Step-by-step explanation:

70m per 1hr

1 mile per 1.16 min

110 mile × 1.16 min per mile

127.6 minutes

The rate of change of the top of the ladder with respect to x is -x/y

Step-by-step explanation:

The given parameters are;

The length of the ladder = 10 ft.

The horizontal distance of the bottom of the ladder from the wall = x

The distance of the top of the ladder from the floor = y

By Pythagoras's theorem, we have;

10 = y² + x²

Therefore, we have;

x² = 10 - y²

d(x²)/dx = 2·x =  d(10 - y²)/dx = -2·y·dy/dx

∴ 2·x = -2·y·dy/dx

dy/dx = 2·x/(-2·y) = -x/y

Therefore, the rate of change of the top of the ladder with respect to x, dy/dx = -x/y.