Question

Question #4 using the following the formula (-b/2a,f(-b/2a))

Find two positive real numbers whose product is a maximum. 1. The sum is 110 2. The sum of the first and twice the second is 24 Numerical, Graphical, and Analytical Analysis 3. A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals (see figure) (a) Write the area A ofthe corral as a function of (b.) Write the area function in standard (vertex) form to find the dimensions that will produce the maximum area. Geometry 4. An indoor physical fitness room consists of a rectangular region with a semicircle on each end (see figure). The perimeter of the room is to be 200-meter single-lane running track. CE (a.) Determine the radius of the semicircular ends of the room. Determine the distance, in terms of y, around the inside edge of the two semicircular parts of the track. (b.) Use the result in part (a) to write an equation, in terms of x and y, for the distance traveled in one lap around the track. Solve for y (c.) Use the result of part (b) to write the area A of the rectangular region as a function of x. What dimensions will produce a maximum area of the rectangle? Path of a Diver 5. The path of a diver is given by 4 24 x+x+12 where y is the height (in feet) and x is the horizontal distance from the end of the diving board (in feet). What is the maximum height of the diver?

Answer 1