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The budget for painting one side of the backdrop is $103222, and
the budget for the reflecting tape is $240.
It is given that the backdrop is in the hexagonal shape shown on the coordinate plane.
It is required to find the budget for painting one side of the backdrop and the budget for the reflecting tape.
It is defined as a polygon that has 6 equal sides with an interior angle of 120° and an exterior angle is 60°.
We have a hexagon shown in the picture:
Since each unit on the coordinate plane represents 5 feet.
Hence each side length of the hexagon = 20 feet
The area of the hexagon:
[tex]\rm A = \frac{3\sqrt{3} }{2}a ^2[/tex] (a = 20 feet)
[tex]\rm A = \frac{3\sqrt{3} }{2}20 ^2[/tex]
A = 1.5×1.732×400
A = 1039.2 square feets
We are assuming the painting cost for each square unit is $10.
∴Total budget for painting one side of the backdrop = 1032.2×10
= $103222
We know the perimeter of the hexagon is given by:
P = 6a
P = 6×20
P = 120 feet
Again we are assuming that each unit cost for reflecting tape is $2.
∴Total budget for the reflecting tape:
= 120×2
= $240
Thus, the budget for painting one side of the backdrop is $103222, and
the budget for the reflecting tape is $240.
Learn more about the hexagon here:
https://brainly.com/question/3295271
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Rewritten by : Barada
To find the volume of a parallelepiped with edges formed by three vectors, use the scalar triple product.
To find the volume of a parallelepiped with edges formed by the three vectors (B, C, and A), we can use the scalar triple product. The scalar triple product is defined as (B x C) . A, where B x C is the cross product of vectors B and C, and . represents the dot product. The result of the scalar triple product will give us the volume of the parallelepiped.
For example, if we have vectors B = (1, 2, 3), C = (4, 5, 6), and A = (7, 8, 9), we can calculate the volume by finding the cross product of B and C, which is (-3, 6, -3), and then taking the dot product with A, which is (-3, 6, -3) . (7, 8, 9) = (-3)(7) + (6)(8) + (-3)(9) = 74.
