In case you're not already aware, the expression is called the "difference quotient" and represents the average rate of change of a function
over an interval
.
For the function , by substituting
we get
Then the difference quotient is
where the last equality holds as long as .
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Answer:
7. d. l = 6.48 cm, w = 6.48 cm
8. d. square
Step-by-step explanation:
For a given area, the perimeter can always be shortened by reducing the length of the long side and increasing the length of the short side. When you get to the point where you can't do that, then you have the minimum perimeter. You will reach that point when the sides are the same length: the rectangle is a square.
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7. In light of the above, the best dimensions are √42 ≈ 6.48 cm for length and width.
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8. In light of the above, the shape is a square.
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The attached graph shows the length of one side (x) and the associated perimeter. The other side is 42/x, which will also be 6.48.
