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Brut [27]
2 years ago
14

What is the degree of the polynomial?

Mathematics
1 answer:
BaLLatris [955]2 years ago
8 0

Given:

5 z^{3}-2 z^{4}-9 z^{2}+z

To find:

Degree of the polynomial

Solution:

Degree of a polynomial:

The degree of the polynomial is highest power of the variable in the polynomial.

5 z^{3}-2 z^{4}-9 z^{2}+z

Here, the highest power is 4.

The degree of the polynomial is 4.

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What are the dimensions of the lightest​ open-top right circular cylindrical can that will hold a volume of 2197 cm cubed​?
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Answer:

  radius = height ≈ 8.88 cm

Step-by-step explanation:

If the weight is proportional to the surface area, then we need to find the minimum surface area for the given volume.

The volume of the can is given by ...

  V = πr²h . . . . . . for radius r and height h

The surface area includes that of the bottom and the sides:

  SA = πr² +2πrh

Solving the first equation for h, we can write the second equation as ...

  SA = πr² +2πr(V/(πr²)) = πr² +2V/r

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The minimum area for the volume will be found where the derivative is zero.

  d(SA)/dr = 2πr -2V/r² = 0

  πr³ = V . . . . . multiply by r²/2 and add V

Then the can radius is ...

  r = ∛(V/π)

and the height is ...

  h = V/(π(V/π)^(2/3)) = ∛(V/π) = r

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For the given volume, the dimensions are ...

  r = h = ∛(2197/π) ≈ 8.8762 cm

The lightest can with that volume has a radius and height of about 8.88 cm.

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<em>Comment on cylinder aspect ratio</em>

You may notice that the lateral area is equal to twice the bottom area for this cylinder. If the can had a top, the minimum weight would be such that the lateral area is twice the total of top and bottom area. In that case, the height is equal to the diameter, not the radius.

4 0
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Can someone tell me if this is correct if not please correct me in the wrong ones
Montano1993 [528]

Answer:

The answer to 2 is "acute".

The answer to 6 is "right triangle"

For 10, it actually is possible. An example is 50, 50, 80

Step-by-step explanation:

An acute triangle is when each angle is less than 90 degrees.

Any triangle with 90 degrees for one angle counts as a right triangle.

all angle measures in a triangle must add up to 180 degrees. Hope this helps!

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2 years ago
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Answer:

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