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mathcalculus
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hello, i have a related rate problem with area. (attached below)
 11 months ago
 11 months ago
mathcalculus Group Title
hello, i have a related rate problem with area. (attached below)
 11 months ago
 11 months ago

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mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i first started the problem like this: facts: altitude: increasing 2.000 A=4.000 altitude: increasing 11.500 A=82.000 so Area= (1/2) * base* height At what rate is the base of the triangle changing when the altitude is 11.500 centimeters and the area is 82.000 square centimeters? 82.000=(1/2)*base* 11.500 82.000=5.75b 14.2609=b ?? help
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
the derivative of 1/2bh?
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
yes i know the product rule
 11 months ago

Psymon Group TitleBest ResponseYou've already chosen the best response.0
Yep. Thats what these related rate problems require. If you have a change in area then you definitely need an area equation. And since the area is changing, you know its the derivative of the area. And yeah, the derivative of 1/2bh.
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.0
if it helps, the area A, base B and height H are all functions of time (they are changing) A(t) = 0.5 * H(t) * B(t) take the derivative with respect to time
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
so not respect to b?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.0
the change in Area with respect to time is also known as the rate you want dA/dt , and so on..
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
I'm confused with finding the derivative.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
alli know is this formula: a=pi^2 r but im guessing it's not relevant for this problem.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
and also a=1/2*b*h
 11 months ago

Psymon Group TitleBest ResponseYou've already chosen the best response.0
This is a triangle, though, so we don't even have pi. But yes, you would use 1/2bh since its the area of a triangle, which is what we have.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
right
 11 months ago

Psymon Group TitleBest ResponseYou've already chosen the best response.0
Now its just that every time you take the derivative of a variable, you also write dx/dt, dy/dt, etc along with it. These dx/dt things represent the changes given in your problem. So if you decided to make the altitude h, when you take the derivative of it, you would have dh/dt. This dh/dt is what gets replaced with 2.000cm/min value given. But if I'm confusing ya I'm sure phi can help.
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.0
to take the derivative of A with respect to time you write a little d in front, and divide by dt
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
dA/dt
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.0
yes that is the left side you have dA/dt = 0.5 * d/dt ( B * H) use the product rule on B*H
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
oh okay so we ignore the 0.5 for now?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.0
You don't ignore constants, but you can keep them on the outside of the derivative just like d/dt (2x) = 2 *dx/dt
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
so here: dA/dt=1/2(dh/dt)+(db/dt)
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.0
except that is not the product rule http://www.1728.org/chainrul.htm
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.0
the product rule of d/dt (x * y) = x * dy/dt + y * dx/dt
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@phi sorry connection went off
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i understand what you're saying up there.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
is this right? dA/dt= 1/2 (b*dh/dt)+(h*db/dt)
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@Psymon
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@phi
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.0
is this right? dA/dt= 1/2 (b*dh/dt)+(h*db/dt) yes, but the 1/2 multiplies both terms \[ \frac{dA}{dt}= \frac{1}{2}\left( b\frac{dh}{dt} + h\frac{db}{dt} \right)\\ 2\frac{dA}{dt}= b\frac{dh}{dt} + h\frac{db}{dt} \] now fill in the various quantities and solve for db/dt
 11 months ago
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