Question

in urgent need with help on these three

What point on the line y-7x + 8 is closest to the origin? Let D be the distance between the two points. What is the objective function in terms of the x-coordinate? (Type an expression.) a. Find the radius and height of a cylindrical soda can with a volume of 398 cm3 that minimize the surface area. b. Compare your answer in part (a) to a real soda can, which has a volume of 398 cm, a radius of 3.1 cm, and a height of 13.5 cm, to conclude that real soda cans do not seem to have an optimal design. Then use the fact that real soda cans have a double thickness in their top and bottom surfaces to find the radius and height that minimizes the surface area of a real can (the surface areas of the top and bottom are now twice their values in part (a)). Are these dimensions closer to the dimensions of a real soda can? a. Write a function for the surface area of the soda can, S, in terms of the radius, r. Type an expression.) a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 7 ft by 5 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way b. Suppose that in part (a) the original piece of cardboard is a square with sides of length s. Find the volume of the largest box that can be formed in this way. a. To find the objective function, express the volume V of the box in terms of x. Type an expression.)

Answer 1

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For minima (or) maxim 24 - Jt is a rminima TF954 r5.5o18 (v)- -', volume ◆|15-50F δ1ft

3.163 C 398と378 31.448 ex L'o the diner sions of α.aeaf Soda con These climensions 3) 5-2乂 Volume u(x)-γ(7-2x)(Ta) 5-x Noui 2 取 1@n -48xt 35

As we have done n paot (a) ne In S-ax 2 に 2. c 2

3,- (v), Volume 54 : volume (v)2S 2A