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Over [174]
3 years ago
12

the volume of a cylinder is 54 Pi centimeters to the third if the radius is 3 cm what is the height of the cylinder

Mathematics
1 answer:
padilas [110]3 years ago
6 0
The height of the cylinder is 6 cm. 

If the volume of the cylinder is 54π cm³, and we know the radius, we can use the formula for the volume of a cylinder to figure out the length of the height. 

V = πr²h

Substitute

54π = 9h<span>π
</span>
Divide each side by <span>π
54 = 9h

Get h by itself

h = 6, which means that the height of the cylinder is 6 cm. </span>
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A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is ce
lubasha [3.4K]
<h2>Answer:</h2>

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

<h2>Step-by-step explanation:</h2>

The origin of the coordinate system is the center of the circle. So we have an angle that measures 5\pi/12=75^{\circ}. so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})

Finally, the exact value of the position of the rider after the carousel rotates 5\pi/12 radians is:

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

3 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B9x%7D%5E%7B2%7D%20-%20%7B%28x%7D%5E%7B2%7D%20-%204%29%20%7B%7D%5E%7B2%7D%20
Alenkinab [10]

Answer:

{ x^2+3x-4}

Step-by-step explanation:

Factor top and bottom.

The numerator is a difference of two squares, and the denominator is a quadratic.

\frac{ {9x}^{2} - {(x}^{2} - 4)^{2} }{4 + 3x - {x}^{2} }

= \frac{ (3x+x^2-4)(3x-x^2+4) }{(1+x)(4-x)}

= \frac{ (x-1)(x+4) (1+x)(4-x) }{(1+x)(4-x)}

If x does not equal -1 and does not equal 4, we can cancel the common factors in italics to give

= { (x-1)(x+4)}

= { x^2+3x-4}

3 0
3 years ago
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almond37 [142]
4.065323 × 10^13
Hope this helps!
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3 years ago
What is a 10% margin increase on 1,810.69?
Elis [28]

Answer:

1991.759

Step-by-step explanation:

1810.69×%10=181.069

1810.69+181.069=1991.759

7 0
2 years ago
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Westkost [7]
Start on (0,1) go down 4, and over 1
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