posted by kwack on .
The altitude of a triangle is increasing at a rate of 1500 centimeters/minute while the area of the triangle is increasing at a rate of 1000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 99000 square centimeters?
This is a calculus problem.
When the altitude H is 1000 and the area A is 99000, the base width is
B = 2A/B =2*99,000/ 10,000 = 198 cm
A = (1/2)*altitude*base = H*B/2
dA/dt = (1/2)[H*dB/dt + B*dH/dt]
1000 = (1/2)[1000*dB/dt + 198*1500]
solve for dB/dt in cm per minute
1000 = (1/2)[10,000dB/dt + 198*dH/dt]
for dB/dt, i got -295 is that correct?
so i just plug it in to find dH/dt?