Consider an isosceles triangle (shown in blue) whose bottom base is 10 units long. A rectangle (shown in red) is inscribed inside the triangle as shown in the figure below: What are the dimensions of such a rectangle with the greatest possible Area? Hint: Let x be the first coordinate of the point (x,y) shown, and find an equation of the blue line/side of the triangle. Give an equation for the Area of the Rectangle as a function of z. Area A = Optimal Solution: Width - Height = and the Maximal Area is

Find the diameter in simplest form, for a circle with equation x2 + y + 6y- 3 = 0 O 12 O sqrt(12) O 3 O 4sqrt(3) O 2 sqrt(3) W Aa étv

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  =