Provide an appropriate response. A spherical balloon is being inflated. Find the approximate change in volume if the radius increases from 6.1 cm to 6.3 cm. (Recall that V= 0.976T cm 29.768TT cm 302.64 cm 148.84TT cm =r) Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C(x)=0.0003x3 -0.024x + 100x + 50,000 R(x) = 400x O C'(x) = 0.0009x - 0.048x + 100 R'(x) = 400 P'(x) = 0.0009x2 -0.048x - 300 OC'(x)=0.0009x2 + 0.048x + 100 R'(x) = 400 P'(x) = 0.0009x + 0.048x + 300 OC'(x) = 0.0009x2 -0.048x + 100 R'(x) = 400 P'(x) = -0.0009x + 0.048x + 300 A spherical balloon is being inflated. Find the approximate change in volume if the radius increases from 5.1 cm to 5.2 cm. (Recall that V = 10.404T cm 176.87 cm 0.204TT cm 104.04T cm A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by: C(x) = 350+2x-0.01x2, 0x 100 Find the marginal cost at a production level of 70 dozen pens and interpret the result. The marginal cost is $0.59/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.59. The marginal cost is $0.62/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.62. The marginal cost is $0.58/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.58. The marginal cost is $0.60/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.60. A spherical balloon is being inflated. Find the approximate change in volume if the radius increases from 5.4 cm to 5.6 cm. (Recall that V = +r.) 116.64T cm 0.864TT cm 23.328T cm 209.95 cm One hour after x milligrams of a particular drug are given to a person, the change in body temperature T (in degrees Fahrenheit) is given by T => hundredth when necessary. 1.63F 2.93F 0.25F 1.3F where 0 x 3. Approximate the changes in body temperature produced by changing the drug dosage from 1 to 1.8 milligrams. Round to the nearest Provide an appropriate response. Find: if y=31-4-51-1 dt O-1215-51-2 0.12 5 O -12+5+5+2 O -12 +5 - 5t Suppose the demand for a certain item is given by D(p) = -3p + 2p + 6, where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price. D'(p) = -6p + 2 D'(p)=-6p +2 D'(p)=-3p+ +2 D'(p) = -3p+2 V = r, where r is the radius, in centimeters. By approximately how much does the volume of a sphere increase when the radius is increased from 3.0 cm to 3.1 cm? (Use 3.14 for T.) 11.3 cm 0.4 cm 11.5 cm 11.1 cm Suppose the demand for a certain item is given by D(p) = -3p + 7p+ 5, where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price. D'(p) = -3p + 7 D'(p) = -3p+7 D'(p)=-6p +7 D'(p)=-6p+7