OpenStudy (anonymous):

related rates problem

4 years ago
OpenStudy (anonymous):

A 13ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12ft from the house the base is moving at the rate of 5ft/sec b) at what rate is the area of the triangle formed by the ladder, wall, and ground changing at that moment

4 years ago
OpenStudy (anonymous):

In part a I found da/dt (height change) to be 12 ft/sec

4 years ago
OpenStudy (anonymous):

I got negative -12 when I did the work in part a though

4 years ago
OpenStudy (anonymous):

I think that the book said just 12 because they were just giving the magnitude and ignoring direction

4 years ago
OpenStudy (kira_yamato):

It should be -12 to be exact, but if they're looking at the rate of decrease, then yes, 12 is the right answer.

4 years ago
OpenStudy (anonymous):

ok so how do I do b because they say the answer is -119/2 ft^2/sec

4 years ago
OpenStudy (anonymous):

I used A1/2bh

4 years ago
OpenStudy (anonymous):

did implicit differentiation using the product rule and got\[\frac{ dA }{ dt }=\frac{ 1 }{ 2 }a \frac{ da }{ dt }+b \frac{ db }{ dt }\]

4 years ago
OpenStudy (anonymous):

but that ended up giving me -120/2

4 years ago
OpenStudy (kira_yamato):

|dw:1382889992109:dw|

4 years ago
OpenStudy (anonymous):

we know a is 5 from pythagorean

4 years ago
OpenStudy (kira_yamato):

\[A = \frac{ab}{2}\] \[2\frac{dA}{dt} = a \frac{db}{dt} + b \frac{da}{dt}\] \[\frac{dA}{dt} = \frac{5(5) + 12(12)}{2} = \frac{169}{2}\] I got a totally different answer....

4 years ago
OpenStudy (anonymous):

it still isnt right according to the book the book says it's -119/2

4 years ago
OpenStudy (kira_yamato):

I know... I'm calling in a third party to check.

4 years ago
OpenStudy (kira_yamato):

Wait, my bad, \[\frac{dA}{dt} = \frac{5(5) + 12(-12)}{2} = -119/2\]

4 years ago
OpenStudy (kira_yamato):

You made a mistake in the product rule formula. It should be \[(uv)' = uv' + vu'\]

4 years ago
OpenStudy (anonymous):

I see it now too you're right

4 years ago
OpenStudy (anonymous):

could you check me on part c now

4 years ago
OpenStudy (anonymous):

it's asking for the rate of change of theta

4 years ago
OpenStudy (anonymous):

|dw:1382890911492:dw|

4 years ago