I think the answer is going to be 18.. but I don’t know if im right
Answer:
![V_2 = 37.5](https://tex.z-dn.net/?f=V_2%20%3D%2037.5)
Step-by-step explanation:
Given
![Volume = 16](https://tex.z-dn.net/?f=Volume%20%3D%2016)
Represent the height of the smaller cylinder with h and its radius with r.
The height (H) of the larger cylinder is
![H = h + 50\% * h](https://tex.z-dn.net/?f=H%20%3D%20h%20%2B%2050%5C%25%20%2A%20h)
And the radius (R) is;
![R = r + 25\% * r](https://tex.z-dn.net/?f=R%20%3D%20r%20%2B%2025%5C%25%20%2A%20r)
Required
Determine the volume of the larger cylinder
Volume of the smaller cylinder is:
![V_1 = \pi r^2h](https://tex.z-dn.net/?f=V_1%20%3D%20%5Cpi%20r%5E2h)
Substitute 16 for V1
![16 = \pi r^2h](https://tex.z-dn.net/?f=16%20%3D%20%5Cpi%20r%5E2h)
While the volume of the larger cylinder is:
![V_2 = \pi R^2H](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20R%5E2H)
We have that:
and ![R = r + 25\% * r](https://tex.z-dn.net/?f=R%20%3D%20r%20%2B%2025%5C%25%20%2A%20r)
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Simplify both expressions
![H = h + 50\% * h](https://tex.z-dn.net/?f=H%20%3D%20h%20%2B%2050%5C%25%20%2A%20h)
![H = h + 0.50*h](https://tex.z-dn.net/?f=H%20%3D%20h%20%2B%200.50%2Ah)
![H = h + 0.50h](https://tex.z-dn.net/?f=H%20%3D%20h%20%2B%200.50h)
![H = 1.50h](https://tex.z-dn.net/?f=H%20%3D%201.50h)
![R = r + 25\% * r](https://tex.z-dn.net/?f=R%20%3D%20r%20%2B%2025%5C%25%20%2A%20r)
![R = r + 0.25*r](https://tex.z-dn.net/?f=R%20%3D%20r%20%2B%200.25%2Ar)
![R = r + 0.25r](https://tex.z-dn.net/?f=R%20%3D%20r%20%2B%200.25r)
![R = 1.25r](https://tex.z-dn.net/?f=R%20%3D%201.25r)
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Substitute values for R and H in ![V_2 = \pi R^2H](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20R%5E2H)
![V_2 = \pi * (1.25r)^2 * 1.50h](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20%2A%20%281.25r%29%5E2%20%2A%201.50h)
![V_2 = \pi * 1.5625r^2 * 1.50h](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20%2A%201.5625r%5E2%20%2A%201.50h)
Collect Like Terms
![V_2 = 1.50 * 1.5625* \pi*r^2 * h](https://tex.z-dn.net/?f=V_2%20%3D%201.50%20%2A%201.5625%2A%20%5Cpi%2Ar%5E2%20%2A%20h)
![V_2 = 2.34375* \pi*r^2 * h](https://tex.z-dn.net/?f=V_2%20%3D%202.34375%2A%20%5Cpi%2Ar%5E2%20%2A%20h)
![V_2 = 2.34375* \pi r^2h](https://tex.z-dn.net/?f=V_2%20%3D%202.34375%2A%20%5Cpi%20r%5E2h)
Recall that: ![16 = \pi r^2h](https://tex.z-dn.net/?f=16%20%3D%20%5Cpi%20r%5E2h)
![V_2 = 2.34375* 16](https://tex.z-dn.net/?f=V_2%20%3D%202.34375%2A%2016)
![V_2 = 37.5](https://tex.z-dn.net/?f=V_2%20%3D%2037.5)
<em>Hence, the volume of the larger cylinder is 37.5</em>
9514 1404 393
Answer:
x^(1/6)
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
__
Here, we have a=X, b=1/2, c=1/3, so the quotient is ...
(X^(1/2))/(X^(1/3)) = X^(1/2 -1/3) = X^(1/6)
_____
Expressed as a radical, this is ...
![\displaystyle X^{\frac{1}{6}}=\sqrt[6]{X}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%3D%5Csqrt%5B6%5D%7BX%7D)
Answer:
The perimeter is doubled.
Step-by-step explanation:
Let's pretend we have a triangle with side measurements p,q, and r.
The perimeter will be the sum of the side measurements of this triangle which is p+q+r.
If we decide to dilate the figure by a factor of 2, then we are multiply each side by 2. So the perimeter of the new triangle becomes 2p+2q+2r.
Factoring this gives us 2(p+q+r). The perimeter has doubled.
The same thing would happen if we look at a quadrilateral. There would be 4 measurements multiplied by 2 and you would factor out the 2 giving you 2(old perimeter) for the new perimeter of the dilated shape.