The altitude (i. e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at a rate of 1.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 12 centimeters and the area is 99 square centimeters

A = 1/2 B H       area = 1/2 base X height

B = 2 A / H = 2 * 99 / 12 = 16.5 cm

dA / d t = 1/2 * (B dH / dt + H dB / dt)

dB / dt = (2 dA / dt - B dH / dt) / H

dB / dt = (2 * 1.5 cm^2 / min - 16.5 cm * 2 cm / min) / 12 cm

dB / dt = (3 - 33) / 12 cm/min = -2.5 cm/min

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

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