Find the surface area of each shipping package. Which package has the greater surface area? Does the same package have a greater
1 answer:
Answer:
- greater area: A
- no, B has the greater volume
Step-by-step explanation:
The relevant area and volume formulas are ...
A = 2(LW +H(L +W))
V = LWH
When there are multiple instances of the calculations to be done, it is convenient to let a spreadsheet do them. The results are attached.
Figure A has the larger area.
Figure B has the larger volume.
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<em>Additional comment</em>
The more "cube-like" the prism is, the less area it will have for the same volume. Here, package B is more "cube-like" than package A. (The ratio of largest-to-smallest dimensions is smaller for package B.)
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Answer: The two roots are x = 3/2 and x = -2
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Explanation:
You have the right idea so far. But the two numbers should be 3 and -4 since
- 3*(-4) = -12
- 3+(-4) = -1
The -1 being the coefficient of the x term.
This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.
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Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.
If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2
Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x
So we have the factor -x-2 along the top
The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.
We have the factor 2x-3 along the left side.
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The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)
The last thing to do is set each factor equal to 0 and solve for x
- 2x-3 = 0 solves to x = 3/2 = 1.5
- -x-2 = 0 solves to x = -2
The two roots are x = 3/2 and x = -2
