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jarp0120
 one year ago
a ladder 6 m long leans against a vertical wall. The lower end of the ladder is moved away from he wall at the rate of 2 m/min. Find the rate of change of the area formed by the wall, the floor and the ladder when the lower end is 4 m from the wall.
please help
jarp0120
 one year ago
a ladder 6 m long leans against a vertical wall. The lower end of the ladder is moved away from he wall at the rate of 2 m/min. Find the rate of change of the area formed by the wall, the floor and the ladder when the lower end is 4 m from the wall. please help

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Jarp0120
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443859889821:dw

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1It doesnt seem right for some reason

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0can you think of an equation that connects l and b in your drawing?

Jarp0120
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443860176242:dw

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Using the pythagorean theorem, we can find the rate of change for everything moving

dan815
 one year ago
Best ResponseYou've already chosen the best response.1oh boy a ladder problem :)

Jarp0120
 one year ago
Best ResponseYou've already chosen the best response.0what is the area if the base?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1You don't necessarily need to know that. You're simply looking for \(\dfrac{dl}{dt}\) when \(x=4\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1The area is constantly changing w.r.t time as the ladder moves down the wall

dan815
 one year ago
Best ResponseYou've already chosen the best response.1This question you are doing right now, will make or break your mathematical career

Jarp0120
 one year ago
Best ResponseYou've already chosen the best response.0there's no change in y right? the ladder?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443860459057:dw \[\frac{ dx }{ dt } = 2\] I thought this

Jarp0120
 one year ago
Best ResponseYou've already chosen the best response.0so i'll just substitute dy/dt and dx/dt?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Yeah you're right, it `moved away from the wall` at that rate, whoops.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0yes dy/dt is what you need

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1I think i read the question wrong, fml.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Oh okay, as the ladder moves down the wall, the ladder increases the base of the triangle but shortens the height of the triangle, therefore you're looking for the rate of change of the height

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0\[x^2+y^2=36\] \[2x \frac{ dx }{ dt }+2y \frac{ dy }{ dt }=0\] \[\frac{ dy }{ dt }=\frac{ x }{ y }\frac{ dx }{ dt }\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0So x here is the distance from the bottom of the ladder to the wall and y is the distance of the top of the ladder to the ground, as the image shows. The second part of the equation we simply use chain rule, \[2x \frac{ dx }{ dt }+2y \frac{ dy }{ dt }=0\] and we just solve for dy/dt then

Jarp0120
 one year ago
Best ResponseYou've already chosen the best response.0wait is this right? dh/dt =2sqrt5 / 5 that means the Area now is 6/sqrt5?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0The rate should be negative because the ladder is decreasing

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0it just defines the direction

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Well what did Pythagorean theorem give you? x=4, r=6 \[x^2+y^2=r^2 \implies y=\sqrt{3616} = \sqrt{20}\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0And we know \[\frac{ dy }{ dt }=\frac{ x }{ y }\frac{ dx }{ dt }\] just plugging in the values at this point

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Yes dy/dt =  2/sqrt(5)
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