Answer:
The boat is approaching the dock at rate of 2.14 ft/s
Step-by-step explanation:
The situation given in the question can be modeled as a triangle, please refer to the attached diagram.
A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.
The length of rope from bow to pulley is 13 feet that means y = 13 ft.
We know that Pythagorean theorem is given by

Differentiating the above equation with respect to time yields,


dx/dt = 0 since dock height doesn't change


The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s
First we need to find z
z² = (5)² + (13)²
z² = 194
z = √194
z = 13.93 ft
So,



Therefore, the boat is approaching the dock at rate of 2.14 ft/s
Step-by-step explanation:
First you convert 10 to 30/3 and then convert 8 2/3 to 26/3 and then you subtract 30-26 which will be 4/3.
I'm not sure about this question. There is so many positive integers and try to search it on Google. That might be a lot of integers to count.
His investment would be B.$5,700
Reasoning:
1400 x 3 = 4200
500 x 3= 1500
1500+4200= 5700