· Timmins Bears' star player Bud is edging away from first base, trying to steal second. Peter the pitcher for the Red Barons, knows that if Bud is more than 15 ft from first
base, he can throw the ball to first in time to get Bud out. Glancing over his shoulder,
Peter observes Bud at an angle of 12° away from first base. The baseball diamond is
square, with each side length equal to 90 ft. Peter is equidistant from all bases.
Second Base
1o
B
Third Base
First base
90 ft
Home Plate
a) Determine the distance between Peter and first base to 4 d. p.
b) Can Peter pick Bud off at first? Justify your answer.

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).