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anonymous
 5 years ago
A 26 foot long ladder is leaning against a vertical wall. The foot of the ladder is 10 feet away from the base of the wall. The foot of the ladder is being pulled away from the base of the wall at a rate of 4 feet per second. How fast is the top of the ladder sliding down the wall at this instant? (related rates)
anonymous
 5 years ago
A 26 foot long ladder is leaning against a vertical wall. The foot of the ladder is 10 feet away from the base of the wall. The foot of the ladder is being pulled away from the base of the wall at a rate of 4 feet per second. How fast is the top of the ladder sliding down the wall at this instant? (related rates)

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myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0related rates problem awesome!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0could both answers be correct?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0lol there are two different answers let me see if i made a mistake

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You used 4 instead of 10

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i used y' for y my bad

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we both win because we spent energy working on the problem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in the writing in the purple, isn't the derivative of s^2 2s, not just 2?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the right hand side should have been 2s ds/dt I knew something was amiss.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0since s is a constant (it doesnt change) s'=0 so 2ss'=0

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0so it doesnt change the answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yep it makes no difference but it looks logical

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0right and it is best to be logical during to look crazy

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but what happens to the 2s? does it cancel out? and how does the x (dx/dt) becomes negative?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0the derivative of s^2 is 2ss' but since s doesnt change s'=0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0factor out the 2 s and devide both sides by 2 0/2 = 0

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0cyter did you draw that on the computer? it looks very mechanical like

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0lol looks better than my horrible hand writing

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\text{2((xdx/dt)+(ydy/dt) = 2sds = 0/dt}\] dividing both sides by 2 we have \[\text{((xdx/dt)+(ydy/dt) = sds/dt = 0}\] now subtract both sides by (xdx/dt) we get \[\text{(ydy/dt) = (xdx/dt)}\] and then divide both sides by y to get dy/dt alone \[\text{(dy/dt) = (x/y)dx/dt}\] Then plug and play

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes I used paint which isn't very good

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Your handwriting is legible, unlike mine where I have to use a drawing program on my computer

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i have a scanner haha

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok i get it now, thank you both of you for your help

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Using cyter's solution diagram, \[y=x \text{Tan}[\text{ArcCos}[x/26]] \] then \[y=26 \sqrt{1\frac{x^2}{676}} \] The total derivative of the above is: \[\text{Dt}[y]==\frac{x \text{Dt}[x]}{26 \sqrt{1\frac{x^2}{676}}} \] Replace x with 10 and Dt[x] with 4 and simplify, \[\text{Dt}[y]==\frac{5}{3} \] I hope there are no errors. First DE solved in years.
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