Baseball: The bases on a baseball
diamond form a square 90 ft on a
side. The pitcher's plate is 60 ft
6 in. from the back corner of
home plate.

a. About how far is the pitcher's
plate from second base?

b. A line drive is 10 ft high when it
passes over the third baseman,
who is 100 ft from home plate.
At what angle did the ball leave
the bat? (Assume the ball is 4 ft
above the ground when it is hit.)

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).