You roll a fair six-sided die twice. The
1 answer:
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Answer:
x ≈ 1.8 cm gives the greatest volume
Step-by-step explanation:
After cutting x cm from each corner in each direction, the cardboard can be folded up to make a box that is x cm deep and (12 -2x) by (10 -2x) in length and width. Clearly, values of x are limited to 5 or less, since cutting 5 cm from each side would leave a width of zero. Then the volume is given by ...
V = x(12 -2x)(10 -2x)
The plot below shows the value of this cubic equation for volume, and identifies the peak as (x, V) ≈ (1.8, 96.8). That is, a cut of 1.8 cm will result in a box of approximate volume 96.8 cm³.
Refer to the diagram shown below.
BE = 2x² - x
DE = x² + 6
The intersecting diagonals bisect one another.
Therefore BE = DE, so that
2x² - x = x² + 6
x² - x - 6 = 0
Factorize.
(x + 2)(x - 3) = 0
x = -2, or x = 3.
When x = -2,
BE = 2(-2)² - (-2) = 10
DE = (-2)² + 6 = 10
Therefore BD = 20
When x = 3;
BE = 2(3²) - 3 = 15
DE = 3² + 6 = 15
Therefore BD = 30
Answer: Either 20 or 30.
BE = 2x² - x
DE = x² + 6
The intersecting diagonals bisect one another.
Therefore BE = DE, so that
2x² - x = x² + 6
x² - x - 6 = 0
Factorize.
(x + 2)(x - 3) = 0
x = -2, or x = 3.
When x = -2,
BE = 2(-2)² - (-2) = 10
DE = (-2)² + 6 = 10
Therefore BD = 20
When x = 3;
BE = 2(3²) - 3 = 15
DE = 3² + 6 = 15
Therefore BD = 30
Answer: Either 20 or 30.