Mathematics, 11.10.2020 05:01 ridzrana02
The following sketch shows how to make an open-top box from a flat sheet of cardboard with cuts (heavy lines) and folds (dashed lines) as indicated. The dimensions of the resulting box depend on the length x of the corner cuts. 12 40 20
a. Show ow the volume of the box depends on length x of the corner cuts.
i. Excess each dimension of the box-length, width, and height-as a furation of x.
ii. Us: the formula for volume V of a box to write V as a function of x.
iii. Write the volume expression in expanded standard polynomial form.
b. Analyze the volume function for the box by answering the following questions.
i. Sketch a graph of y = V(x) for values of x that make sense in this situation.
ii. Estimate coordinates of the x-intercepts and local maximum and minimum points on the graph of V(x).
iii. Explain what the x-intercepts and local maximum and minimum points tell about the way the volume of such a box depends on the length x of the cuts.
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The following sketch shows how to make an open-top box from a flat sheet of cardboard with cuts (hea...
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