Use the derivative formula, (dx/dy), of a function, f(x) = y , is its instantaneous rate of change with respect to the variable x.

Question

Part 1) Mr. C decided to save on installation fees on his satellite system so he decided to install it himself. He used a 13 foot ladder to climb the roof of his house. As he stepped on the the top rung of the ladder the bottom of the ladder started sliding away from the wall at the rate of five feet per second. How fast was Mr. C falling when the top of the ladder was 5 feet from the ground?

Part2) Fortunately, Mr. C didn't hurt himself when he fell but decided to take some aspirin anyway. He went into the house and used a small paper conical cup that was 5 inches high and 3 inches wide. He then poured water from a pitcher at the rate of 1/2 cubic inch per minute. How fast was the water level rising in the cup when the water was 3 inches high?

Answer 1

ladder = hypotenuse

h^2 =a^2 +b^2,

take the derivative and plug in values

a=5, b'=5, h=17

b^2=17^2-25 =289-25= 264

b=sqr264= about 16.25

0= aa' +bb'= 5a'+16.25(5)

-5a' =16.25(5)

a'= -16.25 ft/sec = rate of change of ladder top's height