Question

A 25-foot ladder is leaning against a house. If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of r=2x/ sqrt(625-x^2) ft per second. (where x is the distance between the base of the ladder and the house.

(a) Find the rate r when x is 7 feet.
(b) Find the rate r when x is 15 feet.
(c) Find the limit of r as x--> 25 from the left.

Answer 1

@jim_thompson5910 last one! :)

Answer 2

a) Plug in x = 7 and simplify

b) Plug in x = 15 and simplify

c) Plug in values that are close to 25 (like 24.95 and 25.05) and see what happens to r

Answer 3

ooh related rates ?

Answer 4

oh wait nope =[

Answer 5

ok @jim_thompson5910 can u see if I'm doing it right/.

Answer 6

for a, I got 7/12

Answer 7

one moment

Answer 8

b I got 3/2

Answer 9

hmm I'm getting radicals in my answer, not sure how you're getting clean fractions like that

Answer 10

well you said plug in 7 for a, so I did 14/sqrt 625-49

Answer 11

and 15 for b, I did 30/20 which is 3/2

Answer 12

oh sry, i made a silly typo...

Answer 13

yes, a) is 7/12

Answer 14

ok!

Answer 15

then I plugged in 24.95 for c, since it wants values from the left of 30, and I got 31.575

Answer 16

25 i mean, not 30

Answer 17

and b) is also 3/2, so nice work

Answer 18

ok and then c^

Answer 19

so what happens when x = 25 ?

Answer 20

what do you mean

Answer 21

after plugging in 24.95 for x, I got 31.575

Answer 22

notice how x = 24.95 gives you 31.575

Answer 23

what about 24.99?

Answer 24

That would give me...2(24.99) / .4999

Answer 25

right @jim_thompson5910

Answer 26

sqrt of .499

Answer 27

which gives you roughly 70.6894

Answer 28

I got 70.753

Answer 29

yeah

Answer 30

so as you get closer and closer to 25 (but never actually get there), what's going on with r?

Answer 31

increases?

Answer 32

im not sure

Answer 33

good, its increasing forever basically

Answer 34

as you get closer and closer to 25

Answer 35

okay

Answer 36

so it approaches infinity as x --> 25

Answer 37

from the left

Answer 38

ok! from the left? since that was the question

Answer 39

yes

Answer 40

you can use a graph to confirm this as well

Answer 41

so the answer for c is it approaches infinity as x approaches 25 from the L ?

Answer 42

yes

Answer 43

thx!!

Answer 44

you're welcome