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aniked [119]
3 years ago
11

Write an inequality that expresses the range in the volume of acceptable tennis balls.

Mathematics
1 answer:
Rudik [331]3 years ago
4 0

Answer:

the smallest number is the lower bound and the largest number is the upper bound, your inequality would be

8.2 ≤ x ≤ 9.5, where x represents the volume of tennis balls.

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In cylindrical coordinates, the equations of the surfaces become

z = 4 - 4r^2 \\\\ z = (r^2)^2 - 1 = r^4 - 1

These surfaces intersect on the cylinder of radius 1 with cross sections parallel to the x,y-plane:

4 - 4r^2 = r^4 - 1 \\\\ \implies r^4 + 4r^2 - 5 = (r-1)(r+1)(r^2+5) = 0 \\\\ \implies r=1

Then in cylindrical coordinates, the volume of the space bounded by these surfaces is

\displaystyle \int_0^{2\pi}\int_0^1\int_{r^4-1}^{4-4r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^1 \int_{r^4 - 1}^{4-4r^2}r\,\mathrm dz\,\mathrm dr \\\\ = \pi \int_0^1 (4-4r^2)^2 - (r^4-1)^2 \,\mathrm dr \\\\ = \pi \int_0^1 (15-32r^2+18r^4-r^8)\,\mathrm dr = \boxed{\frac{352\pi}{45}}

7 0
3 years ago
Is 0 a solution to 2x+10=4x+10
Advocard [28]

Answer:

x=0

Step-by-step explanation:

2x+10=4x+10

4x-2x=10-10

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x=0

6 0
3 years ago
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The prime factorization of 25 is
Lady_Fox [76]
25 is a composite number, and it is 5 squared. 25 = 1 x 25 or 5 x 5. Factors of 25: 1, 5, 25. Prime factorization: 25 = 5 x 5, which can also be written 25 = 5².
8 0
4 years ago
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morpeh [17]

Answer:

20 < x < 38.

Step-by-step explanation:

An obtuse angle has a value between 90 and 180.

90 < 5x - 10 < 180

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4 years ago
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Nonamiya [84]

Answer:

The answer is 10

Step-by-step explanation:

Equation to find the hypotenuse (c) is \sqrt{a^{2} +b^{2} }

5^{2} x 2^{2} = 100 (which is your c^{2})

\sqrt{100} = 10

5 0
4 years ago
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