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Find the absolute maximum and minimum of the function f(x,y) = (8x - 2x-) cosy on the z= (8x -2x-) cos y rectangular plate 1sx$3, - - sysSolve the equation by the zero-factor property. The solution set is (Use a comma to separate answers as needed.) b2 - 7b + 12 =0Solve the given equation by the zero-factor property. 49x - 14x + 1=0 The solution set is (Simplify your answer. Type each solution only once. Use a comma to separate answers as needed. Type an integer or a fraction.)b Find two numbers a and b with a s b such that . a (3-2x -x7) dx has its largest value. and b =A flat circular plate has the shape of the region x"+y" $ 1. The plate, including the boundary where x" + y- 2 =1, is 4 heated so that the temperature at the point (x,y) is T(x,y) = x" + 3y - - 7X. Find the temperatures at the hottest and coldest points on the plate. 29 The hottest temperature on the plate is 9 degrees. (Type an integer or a simplified fraction.) The coldest temperature on the plate is degrees. (Type an integer or a simplified fraction.)dw For the functions w= -7x~ +7y", x= cost, and y = sint, express dt as a function of t, both by using the chain rule dw and by expressing w in terms of t and differentiating directly with respect to t. Then evaluate at t = dt 4Among all the points on the graph of z = 8- x" - y that lie above the plane x + 2y + 7z =0, find the point farthest from the plane. What are the values of x, y, and z for the point? X= y = Z = (Type integers or simplified fractions.)Find three numbers whose sum is 33 and whose sum of squares is a minimum. The three numbers are (Use a comma to separate answers as needed.)