Water is being pumped into an inverted (point down) conical tank at a constant rate. The tank has height 20 mi and the diameter at the top is 6 m. if the water level is rising at a rate of 40 cm/min when the height is 15 m, find the rate at which the rate at which water is being pumped into the tank' Let h be the height of the water surface and let r be the radius of the water surface. You may find the for the volume of a cone If"! Vzr'i 3 l and the similar triangles relation h height of tank _ I"; _________'_---"- r radius of top of tank helpful, Also recall that 1 m z 100 cm. Use 535131 for 11". Rate at which water is being pumped in: cm/min K' ds in all directions. Assuming the radius of the circle is 7 decimal point. tu'red hull of a graunded tanker sprea area is increasing when I . cl; Give your answer to exactly one m the run determine how fast the {(1.61 metersfseclqn meters squared per second i 1, ' ' ' ' in calm waters, the oil spilling fro that the polluted area is circular, meters and is increasing at the rate 0 Consider the function f(x) = _ 3 . x - 30 . x + 75 x2 - 10 - x + 52 which has derivatives f ( x) = _ 810 - 162 - x (x2 - 10 . x + 52) and f" ( x) = _ 486 - x2 - 4860 - x + 7776 (x2 - 10 . x + 52)' Enter a number into each of the boxes below. There is one correct answer for each box. y-intercept: y = x-intercept: x = Horizontal asymptote: y - Local extremum at x = Leftmost inflection point at x = Rightmost inflection point at x = Continuing the previous problem, please write the following onto a sheet of paper and then photograph your answer and upload: 1. The function you were given in the previous problem (just copy from the question) 2. Its first derivative f' (just copy from the question) 3. Its second derivative f" (just copy from the question) 4. Intervals on which the function is increasing/decreasing 5. Intervals on which the function is concave up/concave down 6. A sketch of the graph of the function, showing intercepts, asymptotes, extrema, and inflection points