could you help with 32, I'm doing random problems on my own for fun, got stuck on this one 28637. Optimal garden A rectangular flower garden with an area of30 m is surrounded by a grass border 1 m wide on two sides and2 m wide on the other two sides (see figure). What dimensions ofthe garden minimize the combined area of the garden andborders?3.5 miPowerstationShore8 mi29. Laying cable again Solve the problem in Exercise 28, but this timeminimize the cost with respect to the smaller angle 0 between theunderwater cable and the shore. (You should get the same answer.)2 mFlower garden30. Shortest ladder A 10-ft-tall fence runs parallel to the wall of ahouse at a distance of 4 ft. Find the length of the shortest ladderthat extends from the ground to the house without touching thefence. Assume the vertical wall of the house and the horizontal38. Rectangles beneath a lineground have infinite extent.31. Shortest ladder-more realistic An 8-ft-tall fence runs parallelto the wall of a house at a distance of 5 ft. Find the length of thea. A rectangle is constructed with one side on the positive x-axis,one side on the positive y-axis, and the vertex opposite the ori-gin on the line y = 10 – 2x. What dimensions maximize theshortest ladder that extends from the ground to the house withouttouching the fence. Assume the vertical wall of the house is 20 fthigh and the horizontal ground extends 20 ft from the fence.area of the rectangle? What is the maximum area?b. Is it possible to construct a rectangle with a greater area thanthat found in part (a) by placing one side of the rectangle onthe line y = 10the positive x- and y-axes? Find the dimensions of the rect-angle of maximum area that can be constructed in this way.2x and the two vertices not on that line on32. Circle and square A piece of wire of length 60 is cut, and theresulting two pieces are formed to make a circle and a square.Where should the wire be cut to (a) maximize and (b) minimizethe combined area of the circle and the square?9. Designing a box Two squares of length x are cut out of adjacentcorners of a 18" × 18" piece of cardboard and two rectangles oflength 9 and width x are cut of out the other two corners of thecardboard (see figure). The resulting piece of cardboard is thenfolded along the dashed lines to form an enclosed box (see figure).Find the dimensions and volume of the largest box that can beformed in this way.33. Maximum-volume cone A cone is constructed by cutting a sectorfrom a circular sheet of metal with radius 20. The cut sheet is thenfolded up and welded (see figure). Find the radius and height ofthe cone with maximum volume that can be formed in this way.202034. Slant height and cones Among all right circular cones with aslant height of 3, what are the dimensions (radius and height) thatmaximize the volume of the cone? The slant height of a cone isthe distance from the outer edge of the base to the vertex.40. Folded boxesa. Squares with sides of length x are cut out of each corner ofa rectangular piece of cardboard measuring 5 ft by 8 ft. Theresulting piece of cardboard is then folded into a box withouta lid, Find the volume of the largest box that can be formed inthis way.35. Optimal soda cana. Classical problem Find the radius and height of a cylindricalsoda can with a volume of 354 cm that minimize the surfacearea.b. Real problem Compare your answer in part (a) to a real sodacan, which has a volume of 354 cm, a radius of 3.1 cm, and aheight of 12.0 cm, to conclude that real soda cans do not seemb. Squares with sides of length x are cut out of each corner of asquare piece of cardboard with sides of length l. Find the vol-ume of the largest open box that can be formed in this way.ст,

Name: could you help with 32, I'm doing random problems on my own for fun, g
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Description: could you help with 32, I'm doing random problems on my own for fun, got stuck on this one 28637. Optimal garden A rectangular flower garden with an area of30 m is surrounded by a grass border 1 m wide on two sides and2 m wide on the other two sides

Question

could you help with 32, I'm doing random problems on my own for fun, got stuck on this one 28637. Optimal garden A rectangular flower garden with an area of30 m is surrounded by a grass border 1 m wide on two sides and2 m wide on the other two sides (see figure). What dimensions ofthe garden minimize the combined area of the garden andborders?3.5 miPowerstationShore8 mi29. Laying cable again Solve the problem in Exercise 28, but this timeminimize the cost with respect to the smaller angle 0 between theunderwater cable and the shore. (You should get the same answer.)2 mFlower garden30. Shortest ladder A 10-ft-tall fence runs parallel to the wall of ahouse at a distance of 4 ft. Find the length of the shortest ladderthat extends from the ground to the house without touching thefence. Assume the vertical wall of the house and the horizontal38. Rectangles beneath a lineground have infinite extent.31. Shortest ladder-more realistic An 8-ft-tall fence runs parallelto the wall of a house at a distance of 5 ft. Find the length of thea. A rectangle is constructed with one side on the positive x-axis,one side on the positive y-axis, and the vertex opposite the ori-gin on the line y = 10 – 2x. What dimensions maximize theshortest ladder that extends from the ground to the house withouttouching the fence. Assume the vertical wall of the house is 20 fthigh and the horizontal ground extends 20 ft from the fence.area of the rectangle? What is the maximum area?b. Is it possible to construct a rectangle with a greater area thanthat found in part (a) by placing one side of the rectangle onthe line y = 10the positive x- and y-axes? Find the dimensions of the rect-angle of maximum area that can be constructed in this way.2x and the two vertices not on that line on32. Circle and square A piece of wire of length 60 is cut, and theresulting two pieces are formed to make a circle and a square.Where should the wire be cut to (a) maximize and (b) minimizethe combined area of the circle and the square?9. Designing a box Two squares of length x are cut out of adjacentcorners of a 18&#34; × 18&#34; piece of cardboard and two rectangles oflength 9 and width x are cut of out the other two corners of thecardboard (see figure). The resulting piece of cardboard is thenfolded along the dashed lines to form an enclosed box (see figure).Find the dimensions and volume of the largest box that can beformed in this way.33. Maximum-volume cone A cone is constructed by cutting a sectorfrom a circular sheet of metal with radius 20. The cut sheet is thenfolded up and welded (see figure). Find the radius and height ofthe cone with maximum volume that can be formed in this way.202034. Slant height and cones Among all right circular cones with aslant height of 3, what are the dimensions (radius and height) thatmaximize the volume of the cone? The slant height of a cone isthe distance from the outer edge of the base to the vertex.40. Folded boxesa. Squares with sides of length x are cut out of each corner ofa rectangular piece of cardboard measuring 5 ft by 8 ft. Theresulting piece of cardboard is then folded into a box withouta lid, Find the volume of the largest box that can be formed inthis way.35. Optimal soda cana. Classical problem Find the radius and height of a cylindricalsoda can with a volume of 354 cm that minimize the surfacearea.b. Real problem Compare your answer in part (a) to a real sodacan, which has a volume of 354 cm, a radius of 3.1 cm, and aheight of 12.0 cm, to conclude that real soda cans do not seemb. Squares with sides of length x are cut out of each corner of asquare piece of cardboard with sides of length l. Find the vol-ume of the largest open box that can be formed in this way.ст,

Accepted Answer

Let x represent the circumference of the circle
60-x represent the perimeter of the square…