A camera company packs each camera in a cube­shaped box with side lengths of 1/2 ft. Then the company ships the cameras in a container with dimensions of 5 1/2 ft by 7 1/2 ft by 4 1/2 ft. What is the maximum number of camera boxes that will fit in the container?

1,485 camera boxes

Step-by-step explanation:

1/2 ft is 6 inches. So, the cube-shaped camera box has side lengths of 6 inches. Meaning, the volume of the camera box is (6 * 6 * 6) inches^3, or 216 inches^3. Same principle for finding the volume of the container. 5 1/2 ft = 66 inches, 7 1/2 ft = 90 inches, and 4 1/2 ft = 54 inches. So, the volume of the container is (66 * 90 * 54) inches^3, or 320,760 inches^3. Since we are trying to find out how many camera boxes can fit in the container, we divide the volume of the container by the volume of one camera box. The problem looks like this: 320,760 / 216. The quotient, 1,485, is how many camera boxes that can fit inside the container, and is thus our final answer.

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step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)