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butalik [34]
2 years ago
14

An open box is to be made by using a piece of sheet metal with the dimensions of 4m by 2m. Determine the dimensions the box shou

ld be to maximize volume by cutting out the four corners of the material and folding up the edges to make the box. The material that is cut out is waste and cannot be used.
Mathematics
1 answer:
Natali5045456 [20]2 years ago
7 0

Answer:

Dimensions: 0.4 by 3.2 by 1.2

Step-by-step explanation:

I'm assuming here that we are cutting out squares out of each of the metal's corners:

Let x = the length of each cut-out square,

Each base (of the desired net square folded) is 4-2x, and 2-2x respectively,

Volume = x(4-2x)(2-2x)

             = 4x^3 - 12x + 8x

Now we take the derivative:

\frac{d}{dx}\left[4x^3-12x^2+8x\right]\\\\= \frac{d}{dx}\left(4x^3\right)-\frac{d}{dx}\left(12x^2\right)+\frac{d}{dx}\left(8x\right)\\\\= 12x^2-24x+8

We equate to 0 (0 for max volume), and solve using the quadratic formula:

12x^2-24x+8=0,\\\\x_{1,\:2}=\frac{-\left(-24\right)\pm \sqrt{\left(-24\right)^2-4\cdot \:12\cdot \:8}}{2\cdot \:12}\\\\= \frac{-\left(-24\right)\pm \:8\sqrt{3}}{2\cdot \:12}\\\\\mathrm{Separate\:the\:solutions}:\\\\x_1=\frac{-\left(-24\right)+8\sqrt{3}}{2\cdot \:12},\:x_2=\frac{-\left(-24\right)-8\sqrt{3}}{2\cdot \:12}\\\\x =\frac{3+\sqrt{3}}{3},\:x=\frac{3-\sqrt{3}}{3}\\\\x=1.57735\dots ,\:x=0.42264\dots

So we approximate the side lengths to be 1.6 and 0.4 respectively. But when we plug in 1.6 for x, we get the volume as negative. Therefore x has to be 0.4.

Side lengths: 0.4, 4-2(0.4) => 3.2, 2-2(0.4) => 1.2

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280 years old

Step-by-step explanation:

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3 years ago
5 x (h + 3) for h = 2
olya-2409 [2.1K]

Answer:

25

Step-by-step explanation:

If h=2 it would be 2+3 which equals 5. Then multiply 5 by 5 and get 25.

Hope this helps :)

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3 years ago
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There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f
Ann [662]

Answer:

0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647

0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

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Solution to the problem

The estimated population proportion for this case is:

\hat p = \frac{350}{500}=0.7

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 99% confidence interval the value of \alpha=1-0.99=0.01 and \alpha/2=0.005, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.58

And replacing into the confidence interval formula we got:

0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647

0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

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3 years ago
Can you guys help me with Unit 3 mixed review???¿
Gwar [14]
7. 335*0.2=67

8. 4.5/0.6=7.5

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3 years ago
During a game, a basketball team scored 38 points worth of two-pointers, 33
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Answer:

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