Monthly sales of a particular personal computer are expected to decline at a rate of S'(t) = - 4te .2 computers per month, where t is time in months, and S(t) is the number of computers sold each month. The company plans to stop manufacturing this computer when monthly sales reach 900 computers. If monthly sales now (t= 0) are 2,000 computers, find S(t). How long, to the nearest month, will the company continue to manufacture the computer? S(t) = The company will continue to manufacture the computer for approximately |months.Find the area bounded by the graphs of the indicated equations over the given interval. y= -x2 +29; y=0; -35x53 . . . The area is square units.Use Simpson's rule with n = 2 (so there are 2n = 4 subintervals) to approximate (3x2+ 6x + 2) dx and use the fundamental theorem of calculus to find the exact value of the definite integral. w The approximate value of the integral from Simpson's rule is (Simplify your answer.) The exact value of the definite integral is (Simplify your answer.)The life expectancy (in years) for a particular brand of microwave oven is a continuous random variable with the probability density function below. Find d such that the probability of a randomly selected microwave oven lasting d years or less is 0.5. 2 if x 20 f( x ) = (x+ 2)2 otherwise The probability of a randomly selected microwave oven lasting |years or less is 0.5.Find the consumers' surplus and the producers' surplus at the equilibrium price level for the given price-demand and price-supply equations. Include a graph that identifies the consumers' surplus and the producers' surplus. Round all values to the nearest integer. p = D(x) = 90 - 0.07x; p = S(x) = 30e0.001x What is the consumers' surplus, CS? CS = (Round to the nearest integer as needed. Round all intermediate steps to the nearest integer.) What is the producers' surplus, PS? PS = (Round to the nearest integer as needed. Round all intermediate steps to the nearest integer.) Which one of the following graphs correctly identifies the consumers' surplus and the producers' surplus? O A. O B. O C. AP 200- Ap S(x) 150-T S(x) 100 AP S(X) . . . . . . . . . . ...... " . . . . . . . . ....... . . . . ........ CS PS PICS . . .' PS .. ..... Ups D(X) X 10- D(X) X TTTT 10- D(X) v X 950 TITTT TITTT X 700 10- XI 1500