Among all rectangles that have a perimeter of 134, find the dimensions of the one whose area is largest. write your answers as f
1 answer:
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Answer:
units to the right and
units down
Step-by-step explanation:
we have
This is a vertical parabola open upward with vertex at point
Step 1
Convert the function g(x) into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
The function g(x) is a vertical parabola with the vertex at point
Step 2
Find the rule of the translation
That means
The translation is units to the right and
units down
<u>Given</u>:
The given figure is composed of a rectangular prism and a triangular prism.
The length of the rectangular prism is 30 inches.
The width of the rectangular prism is 14 inches.
The height of the rectangular prism is 14 inches.
The base of the triangle is 7 inches.
We need to determine the volume of the composite figure.
<u>Volume of the rectangular prism:</u>
The volume of the rectangular prism can be determined using the formula,
Substituting l = 30, w = 14 and h = 14, we get;
Thus, the volume of the rectangular prism is 5880 cubic inches.
<u>Volume of the triangular prism:</u>
The volume of the triangular prism can be determined using the formula,
where b is the base of the triangle,
h is the height of the triangle and
l is the length of the prism.
Substituting b = 7, h = 14 and l = 30, we get;
Thus, the volume of the triangular prism is 1470 cubic inches.
<u>Volume of the composite figure:</u>
The volume of the composite figure can be determined by adding the volume of the rectangular prism and the volume of the triangular prism.
Thus, we have;
Hence, the volume of the composite figure is 7350 cubic inches.