A rectangular garden of area 208 square feet is to be surrounded on three sides by a brick wall costing $ 8 per foot and on one side by a fence costing $ 5 per foot. Find the dimensions of the garden such that the cost of the materials is minimized.

Therefore the dimensions of the garden is 16 feet by 13 feet.

Step-by-step explanation:

Let the length of the garden be x and the width of the garden be y.

Given that the area of the rectangular garden is 208 square feet.

Therefore,

xy =208

Again given that,

The garden is to be surrounded on three sides by a brick wall costing $ 8 per feet and the remaining sides by a fence costing $5 per feet.

The perimeter of the rectangle is = 2(length+ breadth)

                                                       = 2(x+y)

                                                       =2x+2y

The total cost of fence

   = (16x+ 8y +5y)

To find the maximum or minimum point, we need to find out and set =0.

Then

Again

Therefore at x= 13 , the cost is minimum.

Therefore x = 13 feet.

The other side of the garden is feet = 16 feet.

Therefore the dimensions of the garden is 16 feet by 13 feet.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

a net is a diagram that shows a “flattened” view of a solid. in a net, each face and base is shown with all of its dimensions. a net can also serve as a pattern to build a three-dimensional solid.

a pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

" the net of a triangular pyramid consists of four triangles. the base here we are given of the pyramid is a equilateral   triangle, and the lateral faces are also triangles "