Answer:
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Step-by-step explanation:
is this a question or what
Find where the two curves intersect:
<em>y</em> = 6<em>x</em> - 2<em>x</em> ²
<em>y</em> = <em>x</em> ²
6<em>x</em> - 2<em>x</em> ² = <em>x</em> ² → 3<em>x</em> ² - 6<em>x</em> = 3<em>x</em> (<em>x</em> - 2) = 0 → <em>x</em> = 0 and <em>x</em> = 2
Now, for a shell of radius <em>x</em> units away from the axis of revolution, the height of the shell would be the vertical distance between the upper curve and the lower curve. For 0 ≤ <em>x</em> ≤ 2, we have 6<em>x</em> - <em>x</em> ² ≥ <em>x</em> ², so the height of any given shell is (6<em>x</em> - <em>x</em> ²) - <em>x</em> ² = 6<em>x</em> - 2<em>x</em> ².
Then volume of the solid is
![\displaystyle 2\pi \int_0^2 x(6x-2x^2)\,\mathrm dx = 2\pi \left(2x^3-\frac{x^4}2\right)\bigg|_0^2 = \boxed{16\pi}](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5Cpi%20%5Cint_0%5E2%20x%286x-2x%5E2%29%5C%2C%5Cmathrm%20dx%20%3D%202%5Cpi%20%5Cleft%282x%5E3-%5Cfrac%7Bx%5E4%7D2%5Cright%29%5Cbigg%7C_0%5E2%20%3D%20%5Cboxed%7B16%5Cpi%7D)
Answer:
3.1
Step-by-step explanation:
Answer:
add each fraction together to make a whooe number
Step-by-step explanation:
for example 6/1+6/5=1 so add each fractiin together to make a whole number
Answer:
1.75 lt (1750 ml)
Step-by-step explanation:
Bottle size conversion
2.5 Lt = 2500 ml
Calculate how much is used to fill glasses
125*6=750 ml
Now you subtract the lemonade used from the bottle size and calc how much is left
2500-750=1750 ml or 1.75 Lt