Carrie, marine biologist is performing experiments along the continental slope off of the coast of California where the biodiversity is very dynamic. Earlier scientists have found that the speed of ocean current as a function of depth. The speed, S, depends on depth, d, according to the following formula. S(d) = 3d +1 %3D Where S is measured in meters per second and d is measured in meters! Suppose that the depth of a research robot depends on time, t, according to the formula: d(t)=(1/27)t² Use function composition to write the speed of the current at the depth of the robot as a function of time. Give a simplified expression. What is the speed of the current at the depth of the robot after 9 seconds? Round your answer, if necessary, to the nearest integer. Blank # 1 Blank # 2

When you use a spray can and press the valve at the top, you decrease the pressure of the gas in the can. This decrease of pressure causes the volume of the gas in the can to increase. Because the gas needs more room than is provided in the can, it expands in spray form through the small hole near the valve. In general, if the temperature is constant, the pressure, P, of a gas in a container varies inversely as the volume, V, of the container. The pressure of a gas sample in a container whose volume is 8 cubic inches is 12 pounds per square inch. If the sample expands to a volume of 22 cubic inches, what is the new pressure of the gas?

Give a real life example of where you might be interested in the rate of change of y relative to x. That is, replace “y” with a variable name, and “x” with a variable name (e.g., y = heart rate, x = running speed

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