Question

A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how fast will the foot of the ladder be moving away from the wall when the top is 9 feet above the ground?

Answer 1

You just want an answer huh?

Answer 2

well now i do because all i have tried doesnt work

Answer 3

and im fed up

Answer 4

ive got all courses materials to study. i dont have time to sit around and do trials and errors

Answer 5

if someone can just solve it showing steps. i will learn

Answer 6

I see. Well your first step should be drawing out the situation.

Answer 7

Then you should notice that they say the side labeled b in the picture is changing at a rate of 2 m/s so that gives you the relation db/dt = 2 (m/s)

Answer 8

i have got the first two steps

Answer 9

Also note that the ladder does not change in length (side C...not labeled in picture) so dC/dt = 0. Now they want you to find the rate of change of a when b has a length of 9 feet. An equation that relates the sides of a right triangle is the Pythagorean theorem which is \[c^2 = b^2 +a^2\] and since the sides are changing you will have to implicitly derive this equation and you'll get \[2c {dc \over dt} = 2b{db \over dt} + 2a{da \over dt}\] and then to make things easier plug in your values for \[{dc \over dt} = 0\] and \[{db \over dt} = 2\] and since you want to find the rate of change when b is 9 feet you plug in that value for b and then solve for \[{da \over dt}\] which is the rate of change of the a side with respect to time. I hope that helps.

Answer 10

ok kool thanks

Answer 11

The main idea here is implicit differentiation and related rates.

Answer 12

2 13.85) dx/dt + 2 (14) (2) = 0
dx/dt= 56/27.7= 2.02???

Answer 13

do you agree with 2.02?

Answer 14

I don't think that's right...check your length of a when b = 9 and c = 14...it should be \[\sqrt(115)\].

Answer 15

Also\[ {db \over dt} = -2 {m \over s}\] since the side is decreasing... I may have failed to mention that.

Answer 16

ok kool

Answer 17

0 =(2)(9)(2) + 2sqrt (14^2 - 9^2)a
\[0=36 +2a \sqrt{14^{2}-9^{2}}\]

Answer 18

I got 1.67851 for the answer.

Answer 19

@sonic, did I correctly plug in the values?

Answer 20

18/sqrt(115)

Answer 21

kool

Answer 22

thanks for the help

Answer 23

\[0=36 +2a \sqrt{115}\]\[2a=-36/\sqrt{115}\]\[a=-18/\sqrt{115}=\]

Answer 24

@radar I don't think you put the value of db/dt as -2....you should get a positive answer.

Answer 25

you're right I overlooked that, because it is moving down ? right?

Answer 26

alright thanks i got it. hey radar can you tell me what i am doing wrong here

Find the linear approximation L(x) of the function f(x)=x^8+6x^2 at a=−1.

L(x)=A+Bx where A= and B=

what is A? isn't A the sum of the original equation with -1 plug in plus the sum of the derivative of the equation with -1 plug in

Answer 27

Jinnie, I am afraid that is above my pay grade lol. It looks like it can easily be differentiated, I would try it. Do you have an approved solution available? To verify?

Answer 28

my software lets me know if the answer is right. thats about it