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2 years ago

The diagram shows a 5 cm x 5 cm x 5 cm cube.

Mathematics

2 answers:

mylen [45]2 years ago

5 0

Answer:

~8.66cm

Step-by-step explanation:

The length of a diagonal of a rectangular of sides a and b is

$\sqrt{a^2+b^2}$

in a cube, we can start by computing the diagonal of a rectangular side/wall containing A and then the diagonal of the rectangle formed by that diagonal and the edge leading to A. If the cube has sides a, b and c, we infer that the length is:

$\sqrt{\sqrt{a^2+b^2}^2 + c^2} = \sqrt{a^2+b^2+c^2}$

Using this reasoning, we can prove that in a n-dimensional space, the length of the longest diagonal of a hypercube of edge lengths $a_1, a_2, a_3, \ldots, a_n$ is

$\sqrt{a_1^2 + a_2^2 + a_3^2 + \ldots + a_n^2}$

So the solution here is

$\sqrt{(5cm)^2 + (5cm)^2 + (5cm)^2} = \sqrt{75cm^2} = 5\sqrt{3cm^2} \approx 5\cdot 1.732cm = 8.66cm$

Masja [62]2 years ago

3 0

Answer:

8.7

Step-by-step explanation:

hope this help!

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3 years ago

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Answer:

Option D.

Step-by-step explanation:

Suppose that we have a set of N values:

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$M = \frac{(x_1 + x_2 + x_3 ... + x_n)}{N}$

Because here we have "the median" then we will assume that N is odd, and there is only one median, the value "k" (if N was even, the median would be the mean of the two middle values, that case is really similar to the case where N is odd, so solving only one of the cases is enough)

Now we add 7 to all the values greater than the median

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The new mean will be:

$M' = \frac{(x_1 - 7) + (x_2 - 7) + ... + (x_{k}) + ... + (x_n + 7)}{N} = \frac{(x_1 + x_2 + ... + x_n) + (-7)*(n/2 - 0.5) + 7*(n/2 - 0.5)}{N} = \frac{(x_1 + x_2 + ... + x_n)}{N} = M$

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Because the mean is computed as the sum of the numbers divided by N, and the mean does not change, and N does not change, then the sum of the numbers does not change.

Finally, the standard deviation is computed as:

$SD = \sqrt{\frac{(x_1 - M)^2 + ... + (xn - M)^2}{N} }$

Because M does not change, if we add or subtract numbers to some of the values, the standard deviation will change (Because all the terms are squared, so the added and subtracted sevens don't cancel like in the previous cases)

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