# Calculus

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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 -

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 -

strange .....

http://www.jiskha.com/display.cgi?id=1310504428

• Calculus -

-13.67?? ...

• Calculus -

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 -

positive 5.47

• Calculus -

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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