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Bas_tet [7]
3 years ago
8

A bag contains 5 red marbles, 3 green marbles,2 orange marbles and 1 blue marble

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0

Answer:

orange

Step-by-step explanation:

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[25 POINTS] A cylinder has a volume of 400π cm3. Find the dimensions that minimize its surface area.
miss Akunina [59]

Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

Surface area: SA=2\pi rh+2\pi r^2

Volume: V=\pi r^2h

Therefore, the height of a cylinder given its volume would be h=\frac{V}{\pi r^2}, thus:

SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r

0=-\frac{800}{r^2}+4\pi r

0=800\pi+4\pi r^3

-800\pi=4\pi r^3

-200=r^3

r\approx5.848

If 0If [tex]r>5.848, then the surface area of the cylinder increases

Therefore, the surface area is minimized when the radius is r=5.848cm, making the minimum height h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm.

In conclusion, the 2nd option is correct.

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2 years ago
Solve the following system of equations graphically on the set of axes below.
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Answer:

Step-by-step explanation:

I can't use the same graph that you have supplied, but I can show you what the answer looks like. Just use two points from my answer that will fit on your graph. Suggest points

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Blue line: (3,0) and (0,3)

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The depth of water at a dock can be modeled as y = 3 sin (7x) + 7. At
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Answer:C

Step-by-step explanation:

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Answer:

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3 years ago
Blake has 864 square inches of material with which to create a hollow three-dimensional container. He decides to make either a c
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