10. [1'1 Points] LARCALCS 2.3.084. ASK YOUI The radius of a right circular cylinder is given by \\f t + 6 and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume with respect to time. 11. [-11 Points] in3/s LARCALC9 2.3.083. ASK YOUI The length of a rectangle is given by 5t 4- 4 and its height is VT; where I is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time. A'(t) = Submit Answer 12. [!4 Points] LARCALCS 2.3.085. ASK YOUI The ordering and transportation cost Cfor the components used in manufacturing a product is given below, where C is measured in thousands of dollars and x is the order size in hundreds. (Round your answers to two decimal F 227 x c=115(i+ ,xz1 (a) Find the rate of change of Cwith respect to x when x = ll]. C(10) = I: thousand dollars/IUD components (1)) Find the rate of change of C With respect to x when x = 15. C(15) = I: thousand dollars/IUD components (c) Find the rate of change of C'with respect to x when x = 20. C(20) = |: thousand dollars/IUD components What do these rates of change imply about increasing order size? The cost per item With increasing order size. 13. [0/1 Points] DETAILS PREVIOUS ANSWERS LARCALC9 2.3.087. MY NOTES ASK YOUR TEACHER PRACTIC A population of 400 bacteria is introduced into a culture and grows in number according to the equation below, where t is measured in hours. Find the rate at which the population is growing when t = 5. (Round your answer to two decimal places.) 5t P(t) = 400 ( 1+ - 23 + + 2 ) P'(5) = 608.33 * bacteria/hour 4. [1/1 Points] DETAILS PREVIOUS ANSWERS LARCALC9 2.3.093.MI. MY NOTES ASK YOUR TEACHER PRACTIC Find the second derivative of the function. f(x) = x4 + 4x3 - 5x2 - 8x f"(x) = 12x + 24x - 10 Need Help? Master It 15. [0/1 Points] DETAILS PREVIOUS ANSWERS LARCALC9 2.3.095. MY NOTES ASK YOUR TEACHER PRACTICE Find the second derivative of the function. f(x) = 5x3/2 f " ( x) = 15/4x X