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A company determined that the marginal cost, C'(x) of producing the xth unit of a product is given by C'(x) = x" -6x. Find the total cost function C, assuming that C(x) is in dollars and that fixed costs are $5000. C(x) =A particle is released as part of an experiment. Its speed t seconds after release is given by v(t) = - 0.3t" + 4t, where v(t) is in meters per second. a) How far does the particle travel during the first 3 sec? b) How far does it travel during the second 3 sec? a) The particle travels meters in the first 3 sec. (Round to two decimal places as needed.) b) The particle travels meters in the second 3 sec. (Round to two decimal places as needed.)A company determines that its weekly online sales, S(t), in hundreds of dollars, t weeks after online sales began, can be estimated by the equation below. Find the average weekly sales for weeks 2 through 7 (t = 1 to t = 7). S(t) = et . . . The average weekly sales amount is $ (Round to the nearest cent as needed.)Evaluate. (Be sure to check by differentiating!) B dx, x # - N - 4 + 8x 8 dx = 4+ 8x (Type an exact answer. Use parentheses to clearly denote the argument of each function.)A ball is thrown upward from a height of 432 feet above the ground, with an initial velocity of 96 feet per second. From physics it is known that the velocity at time t is utt) = 95 32t feet per second. a] Find 5{t}. the function giving the height of the ball at time t. b) How long will the ball take to reach the ground? c] How high will the ball go? a] slt)= b) The ball will reach the ground after seconds. c] The ball will go feet high. Data from an independent research company.r found that the annual cost per worker for insurance (health, life, liability. etc.) was increasing according to the function f(x) = T1 34304\Ay The curve to the right is the graph of the equation y = - x , 256 - x 200- Find the total area of the shaded regions in the graph. 400 -20 10 20 100 200 The total area of the shaded regions is (Simplify your answer.)Find L., Ro, and their average for the definite integral below using the indicated value of n. 4 [ (4x3 - x) dx, n=6 The left Riemann sum, L, is (Do not round until the final answer. Then round to three decimal places as needed.) The right Riemann sum, R., is (Do not round until the final answer. Then round to three decimal places as needed.) The average of the two sums is (Type an integer or decimal rounded to three decimal places as needed.)