A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. и (a) Find a function that models the total area of the four pens. A(w) (b) Find the largest possible total area of the four pens. ft2

A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x. F(x) = Find the derivative F'(x). F'(x) = Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft Submit Answer

A rectangular parcel of land has width, w feet. The length of the diagonal, d, between opposite corners is 18 feet more than the length of the parcel. Note that d is lowercase. (a) Express the length, L, of the parcel as a function of d. (b) Express the width, w, of the parcel as a function of d. (c) Express the area, A, of the parcel as a function of d. L = W = A = (d) Suppose a fence is to be built around the perimeter of the rectangular parcel of land. The fencing material will cost $25 per foot. Express the total cost, C, of fencing the parcel as a function of d. C =

You purchased a car for $30 000. It depreciates by 25% of its current value every year. a) Write a function that can be used to model the value of the car after x years. b) How much will the car be worth 3 years after it is purchased? c) How long would it take for the car to depreciate to a value of $20 000?