The base of a triangle is decreasing at the rate of 1 ft/sec, while the height is increasing at the rate of 2 ft/sec. At what rate is the area of the triangle changing when the base is 10 ft and the height is 70 ft? Remember to use the product rule when you find the expression for dA, dt.

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Mathematics

Gummy Pop

11 September, 09:23

The base of a triangle is decreasing at the rate of 1 ft/sec, while the height is increasing at the rate of 2 ft/sec. At what rate is the area of the triangle changing when the base is 10 ft and the height is 70 ft? Remember to use the product rule when you find the expression for dA, dt.

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Titus Calhoun · Answer 1

We are given with the rate of change of the base, db/dt equal to 1 ft / sec and the rate of change of the height of the triangle, dh/dt equal to 2 ft/sec. b is 10 ft and h is 70 ft. Area of triangle is equal to A = 0.5 bh The rate of change of the area is equal to dA/dt = 0.5 b dh/dt + 0.5 h db/dt. Substituting, dA = 0.5*10*2 + 0.5*70 * 1 equal to 45 ft2 / sec.