A square pyramid and a triangular pyramid each have a base that measures 36 square inches. The volume of the square pyramid is twice as large as that of the triangular pyramid. What can be said about the heights of the pyramids? A. The heights can only be compared once the exact volumes of both pyramids are known. B. The height of the square pyramid must be larger than the height of the triangular pyramid. C. The height of the triangular pyramid must be larger than the height of the square pyramid. D. The heights of the two pyramids must be equal.

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).