Water is leaking out of an inverted conical tank at a rate of 7,500 cm³/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. (Round your answer to the nearest integer.)

_____cm³/min

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22 Jan 2019

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a)Water is leaking out of an inverted conical tank at a rate of 8,000 cm³/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. (Round your answer to the nearest integer.)
_________cm³/min

b)Brain weight B as a function of body weight W in fish has been modeled by the power function B = 0.007W^2/3, where B and W are measured in grams. A model for body weight as a function of body length L (measured in centimeters) is W = 0.12L^2.53. If, over 10 million years, the average length of a certain species of fish evolved from 13 cm to 21 cm at a constant rate, how fast was this species' brain growing when the average length was 18 cm? (Round your answer to four significant figures.)

________g/yr

c)Two people start from the same point. One walks east at 4 mi/h and the other walks northeast at 1 mi/h. How fast is the distance between the people changing after 15 minutes? (Round your answer to three decimal places.)

______mi/h

Awater tank has the shape of a conical
frustum with bottom radius 1 m, top radius
3 m and height 2 m. If water is being
pumped into the tank at a rate 2 m3/min,
find the rate at which the water level is
rising when the water is 1 m deep. The volume of the
bottom part of height h(seethe Figure) of a conical frustum with bottom radiusR1,top radius R2andheight H is given by theformula:

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