Work out the ratio between the surface area of sphere of radius 6cm and the total surface area of a hemisphere of radius 9cm.

Match the scale and the actual area to the area of the corresponding scale drawing. scale: 1 inch to 4 feet actual area: 128 square feet scale: 1 inch to 7 feet actual area: 147 square feet scale: 1 inch to 8 feet actual area: 256 square feet scale: 1 inch to 5 feet actual area: 225 square feet area of scale drawing scale and actual area scale drawing area: 3 square inches arrowright scale drawing area: 8 square inches arrowright scale drawing area: 4 square inches arrowright scale drawing area: 9 square inches arrowright

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).

Crickets can jump with a vertical velocity of up to 14 ft/s. which equation models the height of such a jump, in feet, after t seconds? h(t) = –16t2 + v0t + h0 h(t) = –16t2 + v0t + 14 h(t) = –16t2 + 14t h(t) = –16t2 + 14t + 14 what is the maximum height the cricket reaches? round to the nearest thousandth. h = feet