The volume, Vm³, of liquid in a container is given by V = (3h² + 4) - 8, where h m is the depth of the liquid. Which of the following is/are true? Liquid is leaking from the container. It is observed that, when the depth of the liquid is 1 m, the depth is decreasing at a rate of 0.5 m per hour. The rate at which the volume of liquid in the container is decreasing at the instant when the depth is 1 m is 4.5√7. dV 6h√3h² +4. dh The value of at h = 1 m is 9√√7. Non of the above is true. d²V 9h√3h² +4. dh² = = M

Q2: In the two-tank mixing process shown in Fig.(2), x varies from 0 lb salt/ft³ to 1 lb salt/ft³ according to a step function. At what time does the salt concentration in tank 2 reach 0.6 lb salt/ft³? The volume of each tank is 6 ft³. 3ft/min 777 Tank 1 Fig.(2) Tank 2

Assume that the dynamics of caffeine absorption are given by Ct+1 = 0.87Ct , where t is time in hours and Ct is the concentration of caffeine. If C0 = 1000, estimate the time needed for 80% of the caffeine to be eliminated from the body (i.e. 20% left). What if C0 = 500?

A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of 967 cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V = Tr2h. The surface area Sof a cylinder, not including the top and bottom of the cylinder, is S = 2πrh.) (A) B C (D The surface area is increasing by 28 square millimeters per second. The surface area is decreasing by 287 square millimeters per second. The surface area is increasing by 32π square millimeters per second. The surface area is decreasing by 32π square millimeters per second.

Suppose that the production Q (in gallons of paint) of a paint manufacturer can be modeled by Q = 140K/2L/2, where K is the company's capital expenditures in thousands of dollars and L is the size of the labor force (in hours worked). Find aQ/ƏK when capital expenditures are $230,000 and the labor hours are 900. (Round your answer to two decimal places.) aQ/ək = Interpret aQ/ƏK. If labor hours remain at 900 and K increases by $1000, will increase about gallons of paint. Find aQ/ƏL when capital expenditures are $230,000 and the labor hours are 900. (Round your answer to two decimal places.) aQ/Ək = Interpret aQ/aL. If capital expenditures remain at $230,000 and L increases by one hour, Q will increase about gallons of paint. Need Help? Read It Watch It

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 12 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 2 feet high? (Hint: The formula for the volume of a cone is V = {mr?h.)