Need help with problems 31-40. Answers only is fine if you want. I'll give helpful rating.

31 Select the correct answer. The radius of a sphere is increasing at the rate 7.7 cm/s. When the surface area of the sphere becomes 520 cm2, what is the rate at which the volume is increasing? (S = 47/2 : V= ] WIA O A. 2,002 cm3/s O B. 4,004 cm3/s O C. 6,006 cm3/s O D. 12,012 cm3/s32 Select the correct answer. Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3 and the volume is increasing at a rate of 5 cm3/s. Find the rate of change of height at h= 15cm. 1 2 V = 7rr h ( 3 i O A. 0.0106 cm/s O B. 0.0159 cm/s O c. 0.1592 cm/s O D. 0.5305 cm/s 33 Select the correct answer. If the total area of the pen in the gure below is 1,750 square feet and the cost of materials is $9 per foot, which of these dimensions would cost the minimum to construct a fence around the pen? (7 is the radius of the semi circle) I O A. r= 18.44 and a= 36.97 0 B. r=17.08 and a=34.16 O C. r= 21.85 and a= 21.85 0 D. r= 22.14 and a= 22.14 34 Select the correct answer. Find a point on the line y= 6x+ 2 that is closest to the origin. 0 A. (-0.333, 0.002) O B. (-0.324, 0.054) O C. (0.333, 3.998) O D. (-0.32, 0.08) 35 Select the correct answer. Find the point on the curve y= -x2 - 2 that is closest to the point (0, 1). O A. (0, O) O B. (0, -2) O C. (1, -3) O D. (-1, -3) 36 Select the correct answer. A manufacturer has been selling 1,000 refrigerators every month at $450 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of refrigerators sold will increase by 100 per month. How much rebate should the manufacturer offer the buyer to maximize its revenue? 0 A. $75 0 B. $100 0 C. $175 0 D. $275 37 Select the correct answer. How many real roots does the following function have? f(x) = x3+5x2+7x+15 OA. 0 OB. - OC. 2 OD. 338 Select the correct answer. Using Newton's method, find the third approximation of the function fix) = x2 + 20x+ 35, where X0 = -2. O A. 1.9377 0 B. -1 .3977 O C. -1 .9375 O D. -1 .9377 39 Select the correct answer. Why does the function fix) = x2 + 6x- 42, where x0 = -1, fail when using Newton's method? 0 A. for) = 0 O B. The initial approximation value is wrong. 0 C. Iterations don't converge. O D. There is no solution. 40 Select the correct answer. Find the second approximation value of 5 75 using Newton's method where X0 = 2. O A. 2.3575 0 B. 2.5375 0 c. 2.3918 0 D. 2.7355