Question

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (Do not use mixed numbers. Round your answers to three decimal places.)

(a) How fast is the top of the ladder moving down the wall when the base is given below?
15 feet away from the wall
_____ ft/sec

20 feet away from the wall
_____ ft/sec

24 feet away from the wall
_____ ft/sec

Answer 1

(b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 15 feet from the wall.
______ ft2/sec

(c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 15 feet from the wall.
_____rad/sec

Answer 2

its a long one worth 5 points...lol the pressure is building now i have until midnight and two more problems after this.lol

Answer 3

:X

Answer 4

wow, very comprehensive problem!

Answer 5

YEAH its liek diffrent parts

Answer 6

can u help me?

Answer 7

satellite hey

Answer 8

last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez
\[x^2+y^2=25\] calculus says
\[2xx'+2yy'=0\] and you are told that
\[y'=2\] so you know
\[2xx'+4y=0\] or
\[x'=-\frac{2y}{x}\]

Answer 9

plug in the numbers to get what you want.

Answer 10

for example if x = 15 then you know
\[15^2+y^2=25^2\]
\[y=20\] so
\[x'=-\frac{2\times 20}{15}\]
\[x'=-\frac{8}{3}\]

Answer 11

minus because it is going down

Answer 12

k

Answer 13

so after plugging in the frst 3 answers would be?

Answer 14

if x = 20 then y = 15 and so on

Answer 15

maybe i got that backwards
first one you are told that y = 15 so x = 20
second one you are told that y = 20 so x = 15

Answer 16

(a) How fast is the top of the ladder moving down the wall when the base is given below?
15 feet away from the wall ...ft/sec

20 feet away from the wall
..... ft/sec

24 feet away from the wall ..........ft/sec

Answer 17

omg i have 5 mins:0