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otez555 [7]
3 years ago
14

15. Harriet needs to ship a small vase. The box she will use has a volume of 216 cubic inches. If the side lengths are all the s

ame, what is the length of each side of the box? Hint: V = s^3
Mathematics
1 answer:
kirza4 [7]3 years ago
6 0
The box here is assumed to have equal side lengths so that it is a cube. The formula for the volume of a cube would be calculated by raising the side length to the power of 3. We calculate the value of the side lengths as follows:

V = s^3
216 = s^3
s = 6 in

Hope this answers the question. Have a nice day.
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Find the angle between the given vectors. Round your answer, in degrees, to two decimal places. u=⟨2,−6⟩u=⟨2,−6⟩, v=⟨4,−7⟩
NISA [10]

Answer:

\theta = 108.29

Step-by-step explanation:

Given

u =

v =

Required:

Calculate the angle between u and v

The angle \theta is calculated as thus:

cos\theta = \frac{u.v}{|u|.|v|}

For a vector

A =

A = a * b

cos\theta = \frac{u.v}{|u|.|v|} becomes

cos\theta = \frac{.}{|u|.|v|}

cos\theta = \frac{2*6+4*-7}{|u|.|v|}

cos\theta = \frac{12-28}{|u|.|v|}

cos\theta = \frac{-16}{|u|.|v|}

For a vector

A =

|A| = \sqrt{a^2 + b^2}

So;

|u| = \sqrt{2^2 + 6^2}

|u| = \sqrt{4 + 36}

|u| = \sqrt{40}

|v| = \sqrt{4^2+(-7)^2}

|v| = \sqrt{16+49}

|v| = \sqrt{65}

So:

cos\theta = \frac{-16}{|u|.|v|}

cos\theta = \frac{-16}{\sqrt{40}*\sqrt{65}}

cos\theta = \frac{-16}{\sqrt{2600}}

cos\theta = \frac{-16}{\sqrt{100*26}}

cos\theta = \frac{-16}{10\sqrt{26}}

cos\theta = \frac{-8}{5\sqrt{26}}

Take arccos of both sides

\theta = cos^{-1}(\frac{-8}{5\sqrt{26}})

\theta = cos^{-1}(\frac{-8}{5 * 5.0990})

\theta = cos^{-1}(\frac{-8}{25.495})

\theta = cos^{-1}(-0.31378701706)

\theta = 108.288386087

<em></em>\theta = 108.29<em> (approximated)</em>

4 0
2 years ago
2 and 5. What is the LCM?
Masja [62]
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2= 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
5=5, 10, 15, 20
  So now, you have to pick out the numbers that are common to both numbers. So;
10, 20
  10 and 20 are the only common numbers. So you have to look for the lowest common number. And that is 10. So the LCM is 10.. Hope i helped. Have a nice day. 
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3 years ago
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Answer:

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Step-by-step explanation:

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Goryan [66]
Yes so this is just waffle and it is hard hope this helps
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