The cloth top of the gazebo in Mr. Chang’s backyard has ripped from weathering. He needs to know the area of the cloth so he can replace it. A square pyramid with a base of 6 feet by 6 feet. The triangular sides have a height of 5 feet. The height of the pyramid is 4 feet. How much cloth, in square feet, will Mr. Chang need, assuming he does not need to replace the cloth at the bottom of the figure? 60 96 120 156

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).