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- Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.When a skydiver jumps from an airplane, his downward velocity increases until the force of gravity matches air resistance. The velocity at which this occurs is known as the terminal velocity. It is the upper limit on the velocity a skydiver in free fall will attain (in a stable, spread position), and for a man of average size, its value is about 176 feet per second (or 120 miles per hour). A skydiver jumped from an airplane, and the difference D = D(t) between the terminal velocity and his downward velocity in feet per second was measured at 2-second intervals and recorded in the following table. t = seconds intofree fall D = velocitydifference 0 176.00 2 124.19 4 87.63 6 61.83 8 43.63 10 30.79 (a) Show that the data are exponential. (Round your answer to two decimal places.) The successive ratios in D values are always , so the data can be modeled with an exponential function. Find an exponential model for D. (Let t be the seconds into free fall and D be the…(a) If A is the area of a circle with radius and the circleexpands as time passes, find dA/dt in terms of dr/dt.(b) Suppose oil spills from a ruptured tanker and spreads ina circular pattern. If the radius of the oil spill increasesat a constant rate of 1m/s , how fast is the area of thespill increasing when the radius is 30 m?
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- From the following answer what is asked: f(x,y) = x√y ,(2,4), v = 2i - j d) In which direction is the minimum temperature? e) What is the minimum rate of change?Suppose that D = √x² + y² is the length of the diagonal of a rectangle whose sides have lengths x and y that are allowed to vary. Find a formula for the rate of change of D with respect to x if x varies with y held constant, and use this formula to find the rate of change of D with respect to x at the point where x = 3and y = 4.Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the volume of the cube changing at the moment the cube has a side length of 20 inches? Let s(t) denote the side length of the cube which is increasing over time. Then V(t) =s(t)3 is the relation between the volume function and the side length function of the cube with respect to the variable t.