Posted by <3 on Thursday, June 4, 2009 at 10:07pm.
The altitude of a triangle is increasing at a rate of 2.500 centimeters/minute while the area of the triangle is increasing at a rate of 1.500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10.500 centimeters and the area is 93.000 square centimeters?

Math (:  MathMate, Thursday, June 4, 2009 at 10:35pm
Given
A=bh/2, b=2*93/10.5=17.714
differentiate with respect to t (by the product rule on the right hand side).
The only unknown left is the rate of change of the base.
Hint: it is negative.

Math (:  Reiny, Thursday, June 4, 2009 at 10:38pm
let the area be A
let the base be x
let the height be y
given: at a time of t minutes,
dA/dt = 1.5 cm^2/min
dy/dt = 2.5 cm^2/min
find:
dx/dt when A = 93 and y = 10.5
A = xy/2 or
2A = xy (equ#1)
differentiate implicitly with respect to t, using the product rule
2dA/dt =x(dy/dt) + y(dx/dt) (equ#2)
we know A=93 when y = 10.5, so x = 17.714
sub into equ#2
2(1.5) = 17.714(2.5) + 10.5dx/dt
solve for dx/dt

Math (:  <3, Thursday, June 4, 2009 at 10:54pm
My answer is 3.9319, but it's wrong.

Math (:  MathMate, Thursday, June 4, 2009 at 10:58pm
I have 3.932 too.
Can you check the numbers in the question?

Math (:  <3, Thursday, June 4, 2009 at 11:01pm
I copied & pasted this from my online homework. It said the answer is wrong.

Math (:  Reiny, Thursday, June 4, 2009 at 11:02pm
I also had 3.932
What answer did the book have?

Math (:  <3, Thursday, June 4, 2009 at 11:07pm
I use an online homework program called WebWork. It just tells you if your answer is correct or not.

Math (:  MathMate, Thursday, June 4, 2009 at 11:10pm
Try 3.93, 3.932.

Math (:  <3, Thursday, June 4, 2009 at 11:16pm
The answer is 3.9300. Thanks!
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