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3 years ago

The volume of the sphere is 500/3pi cubic units. What is the value of x

Mathematics

1 answer:

Sphinxa [80]3 years ago

5 0

Answer:

Step-by-step explanation:

Formula for the volume of a sphere is V = (4/3) (π) r³

3V 4²

and so the cube of the radius, "r," is r³ = ------------- * -----

4 4²

Taking the cube root of both sides, we get

∛[3V / 4²] 3V

and so the radius, "r," is r = ------------------ = ∛ ( --------- ) = (1/4)*∛(3*v)

∛[4³] 4³

Then

r = (1/4)*∛(3*V), after substituting 500/(3π) for V, becomes:

r = (1/4)*∛[ 3*500/3π ] = (1/4)*∛[ 500/π ]

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The point (Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, StartFraction StartRoot 2 EndRoot Over 2 EndFraction)

sveticcg [70]

The values of cosine Ф and cotangent Ф are $\frac{-\sqrt{2} }{2}$ and -1

Step-by-step explanation:

When a terminal side of an angle intersect the unit circle at

point (x , y), then:

The x-coordinate is equal to cosine the angle between the positive part of x-axis and the terminal side
The y-coordinate is equal to sine the angle between the positive part of x-axis and the terminal side
If x and y coordinates are positive, then the angle lies in the 1st quadrant
If x-coordinate is negative and y-coordinate is positive, then the angle lies in the 2nd quadrant
If x and y coordinates are negative, then the angle lies in the 3rd quadrant
If x-coordinate is positive and y-coordinate is negative, then the angle lies in the 4th quadrant

∵ The terminal ray of angle Ф intersects the unit circle at point $(\frac{-\sqrt{2} }{2},\frac{\sqrt{2} }{2})$

- According to the 1st and 2nd notes above

∴ cosФ = x-coordinate of the point

∴ sinФ = y-coordinate of the point

∵ The x-coordinate of the point is negative

∵ They-coordinate of the point is positive

- According the the 4th note above

∴ Angle Ф lies in the 2nd quadrant

∵ x-coordinate = $\frac{-\sqrt{2} }{2}$

∴ cosФ = $\frac{-\sqrt{2} }{2}$

∵ y-coordinate = $\frac{\sqrt{2} }{2}$

∴ sinФ = $\frac{\sqrt{2} }{2}$

- cotФ is the reciprocal of tanФ

∵ tanФ = sinФ ÷ cosФ

∴ cotФ = cosФ ÷ sinФ

∴ cotФ = $\frac{-\sqrt{2} }{2}$ ÷ $\frac{\sqrt{2} }{2}$

∴ cotФ = -1

The values of cosine Ф and cotangent Ф are $\frac{-\sqrt{2} }{2}$ and -1

Learn more:

You can learn more about the trigonometry function in brainly.com/question/4924817

#LearnwithBrainly

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3 years ago

Read 2 more answers

What does A equal to

ruslelena [56]

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Angle R should be the same as angle P.
A triangle is equal to 180 degrees.
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Or, since there are two right triangles, you can add 47 and 90. Subtract 180 from that and you will get a.

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3 years ago

Jake has decided to invest in three business ventures. The total cost of investing in all three ventures is $15,000. The combine

Arte-miy333 [17]

X = first venture, y = second venture, z = third venture

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these are ur equations.....

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x - y + z = 7000
--------------------add
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x + y + z = 15,000....multiply by -2
3x + 2y + 2z = 39,000
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z = 4000/2
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x + y + z = 15,000
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second venture (y) = 4,000 <==
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