A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the boat 10 feet below the pulley. If the rope is pulled through the pulley at a rate of 20 ft/min, at what rate will the boat be approaching the dock when 125 ft of rope is out?

101.6 ft/min

Step-by-step explanation:

let x be the horizontal distance to the dock. And the rope is attached to the boat 10 feet below the pulley

Using pythagorean theorem

x^2=R^2-10^2

where R is rope length to the pulley.

Differentiates with respect to time t

2x dx/dt=2RdR/dt

Xdx/dt = RdR/dt (1)

If the boat be approaching the dock when 125 ft of rope is out

This is R = 125ft

Using pythagorean theorem again

X^2 = R^2 - 10^2

X^2 = 125^2 - 10^2

X^2 = 15525

X = 124.6 ft

The rate the boat be approaching the dock = dx/dt

While

the rope is pulled through the pulley at a rate of 20 ft/min = dR/dt

Solve for dx/dt when R is 125, x= 124.6 and dR/dt= 20ft/min

Substitute all in equation 1

124.6 dx/dt = 125 × 20

dx/dt = 2500/124.6

dx/dt = 101.6 ft/min

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.