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Chapter 3 | Derivatives
323. [T] The number of cell phones produced when x dollars is spent on labor and y dollars is spent on capital invested by a manufacturer can be modeled by the equation 60 x 3/4 y 1/4 =3240. a. Find and evaluate at the point (81, 16). b. Interpret the result of a. 324. [T] The number of cars produced when x dollars is spent on labor and y dollars is spent on capital invested by a manufacturer can be modeled by the equation 30 x 1/3 y 2/3 =360. (Both x and y are measured in thousands of dollars.) a. Find dy dx and evaluate at the point (27, 8). b. Interpret the result of a. 325. The volume of a right circular cone of radius x and height y is given by V = 1 3 πx 2 y . Suppose that the volume of the cone is 85 π cm 3 . Find when x =4 and dy dx
dy dx
y =16.
For the following exercises, consider a closed rectangular box with a square base with side x and height y . 326. Find an equation for the surface area of the rectangular box, S ( x , y ). 327. If the surface area of the rectangular box is 78 square feet, find when x =3 feet and y =5 feet. For the following exercises, use implicit differentiation to determine y ′. Does the answer agree with the formulas we have previously determined? dy dx
328. x = sin y 329. x =cos y 330. x = tan y
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