Posted by Joe on Tuesday, July 12, 2011 at 7:11pm.
The altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 1500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9500 centimeters and the area is 87000 square centimeters?

Calculus  Damon, Tuesday, July 12, 2011 at 7:17pm
A = .5 b h
so
87,000 = .5 b (9500)
b = 18.32
then calculus
dA/dt = .5 (b dh/dt + h db/dt)
1500 = .5 ( 18.32 * 3000 + 9500 * db/dt)

Calculus  Reiny, Tuesday, July 12, 2011 at 7:22pm
strange .....
http://www.jiskha.com/display.cgi?id=1310504428

Calculus  Joe, Tuesday, July 12, 2011 at 7:24pm
13.67?? ...

Calculus  Damon, Tuesday, July 12, 2011 at 7:33pm
I got 5.47
If the base were constant the area would be increasing faster than 1500cm^2/min due to the rapid altitude increase. Therefore the base must be decreasing.

Calculus  Joe, Tuesday, July 12, 2011 at 7:36pm
positive 5.47

Calculus  Damon, Tuesday, July 12, 2011 at 8:11pm
1500 = .5 ( 18.32 * 3000 + 9500 * db/dt)
3000 = 54960 + 9500 db/dt
9500 db/dt = 51,960
db/dt = 5.47
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