Greatest common factor of 8y³ and 64y²
1 answer:
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Answer:
b: See first attached photo
c: V = x²y
d and e: V = x(3 - 2x)²
f: 2 cubic feet
Step-by-step explanation:
a: Sketch several boxes and calculate the volumes.
b: See first attached photo a diagram of this situation
The diagram is a square. We are cutting out squares from the corners. We don't know the size of the square yet. The side lengths were 3, but now they are 3 - 2x (since each corner has one side of the square, there are 2 sides of the cut out square on each side of the larger square)
c: The equation for volume is: V = x²y
The length and width of the box are the x values, the height would be the y value
d and e: It wants the equation for the volume for our situation. The base of the box is (3 - 2x)(3 - 2x) or (3 - 2x)². The height of the box is x, so the volume is
V = x(3 - 2x)²
f: Take the derivative, find the critical values, then plug that into x and solve for the volume. See second attached photo for the work for finding the x value that maximizes the box, and the third attached photo for the evaluation of the maximum volume...
