Huang yi works as a paleontologist and a sculptor. she earns \$5{,}500$5,500dollar sign, 5, comma, 500 per month as a paleontologist and \$4{,}500$4,500dollar sign, 4, comma, 500 per month as a sculptor. huang yi wants to make more than \$50{,}000$50,000dollar sign, 50, comma, 000 this year. in the inequality shown above, ppp represents the number of months huang yi can work as a paleontologist and sss represents the number of months she can work as a sculptor to reach her goal. if huang yi worked for 666 months as a paleontologist this year, what is the minimum whole number of months that she must work as a sculptor to reach her goal?

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).