antnway l alatus Prot ??The Following Table × SC Secure https//edfinity.com/asse

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antnway l alatus Prot ??The Following Table × SC Secure https//edfinity.com/assessments/5b561e45c839ef49bd2ffef 1 edfinity My Courses Q Search Section 3.5 The alitrude of a triangle is increasing at a rate of 1.000 centimeter/iminute while the area of the triangle is incresing at a mat of 2 500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.500 centimeters square centimeters Note: The "altitude" is the "height" of the triangle in the formula Arca (12) base'heighrt. Draw yourselfa general representative triangle and label the base one variable and the altitude (height) another variable. Note that to solve this problem you dont need to know how big nor what shape the triangle really is. and the area is 96.000 * Submit

Explanation / Answer

Area of a triangle is given by:

A = B*H/2

B = base

H = Height

Given that

dH/dt = 1.000 cm/min, at that time

dA/dt = 2.500 cm^2/min

We need to find dB/dt, when H = 8.500 cm and B = 96.000 cm^2

A = B*H/2

B = 2*A/H = 2*96.000/8.500 = 22.588 cm

Now rate of change of area will be gvien by:

A = B*H/2

dA/dt = (B/2)*(dH/dt) + (H/2)*(dB/dt)

Using known values:

2.500 = (22.588/2)*(1.000) + (8.500/2)*(dB/dt)

dB/dt = [2.500 - 22.588/2]*(2/8.500)

dB/dt = -2.069 cm/min

So the base of triangle is decreasing at a rate of 2.069 cm/min

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