Determine the vector equation of movement of a plane that is moving in a straight line passing through the point (10, 5, 6) and is parallel to the vector v→ = 12i→+ −34j→+ −6k→. A. r(t) = (10 + −34t, 5 + 12t, 6+ −6t)

B. r(t) = (10 + −34t, 5 + 12t, 6 + −34t)

C. r(t) = (6 + 12t, 5 + −34t, 10 + −6t)

D. r(t) = (10 + 12t, 5 + −34t, 6 + −6t)

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).