Question 2 Construction Problem A farmer has 180 ft. of fencing to be used in the construction of two identical rectangular pens sharing a common side (see figure). Assuming all the fencing is used. a) Write an equation for the 180 ft. of fencing in terms of x and y ly. b) Write y in terms of x from the equation in a) c) Write the total area A enclosed by both pens as a function of the width x d) Find the dimensions of the pens that will make the total area enclosed area maximum

3. The surface area, SA, of a sphere is related to its volume, V, according to the equation 3V S.A. =4n 4T a) Determine the surface area, to the nearest tenth of a square centimetre, of a sphere with volume 2400 cm. " b) Rearrange S.A.= 47 3V to write the equation for volume, V, of the sphere in terms of surface area, SA.

I only need the correct answer, I don't need any work shown.

An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a 200-meter single-lane running track. (a) Draw a diagram that illustrates the problem. Let x and y represent the length and width of the rectangular region, respectively.(b) Determine the radius r, in terms of y, of the semicircular ends of the track. r =   Determine the distance d, in terms of y, around the inside edge of the two semicircular parts of the track. d =  (c) Use the result of part (b) to write an equation, in terms of x and y, for the distance traveled in one lap around the track. Solve for y. y =  (d) Use the result of part (c) to write the area A of the rectangular region as a function of x. A =  (e) Use a graphing utility to graph the area function from part (d). Use the graph to approximate the dimensions that will produce a rectangle of maximum area. (Round your answers to two decimal places.) x  =    y  =