AboutAbe Mantell Expertise Hello,
I am a college professor of mathematics and regularly teach all levels
from elementary mathematics through differential equations, and would
be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Question 1- A ladder 25 feet long is leaning against the wall of aa house. The base of the ladder is pulle away from the wall at a rate of 2 feet per second. How fast is the top moving down the wall when the base of the ladder is (a) 7 feet, (b) 15 feet, and (c) 24 feet from the wall?
2- Consider the right formed by the moving ladder, the side of the house, and the ground in Exercise 1. When the base is 7 feet from the wall, find the rate at which the ares of the triangle is changing
Answer 1. Let x=the distance the base of the ladder is from the bldg, and y=the height. Thus, x^2 + y^2 = 25^2 = 625
differentiating wrt 't': 2x x' + 2y y'=0 ==> y'=-(x/y) x'
y=sqrt(625-x^2)...y'=-(x/sqrt(625-x^2)) x'
(a) x=7 ==> x'=-(7/24) 2 ft/sec = -7/12 ft/sec
(b) x=15 ==> x'=-(15/20) 2 ft/sec = -3/2 ft/sec
(c) x=24 ==> x'=-(24/7) 2 ft/sec = -48/7 ft/sec
