Because they show exactly how much of something is there/needed.
Answer:
0
Step-by-step explanation:
0 because you said each topping can only be used once
Answer:
If its just 15 then its 1
Step-by-step explanation:
Because 15 divided by 1 is 15 which is the fraction.
Answer:
16π square units.
Step-by-step explanation:
Please refer to the graph below.
So, if we draw a representative rectangle, the width of the rectangle will be (x), and the height of the rectangle at each (x) will be given by f(x) - g(x).
By the shell method:
![\displaystyle V=2\pi\int_a^bp(x)h(x)\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D2%5Cpi%5Cint_a%5Ebp%28x%29h%28x%29%5C%2Cdx)
We are integrating from x = 0 to x = 2. p(x) is x and h(x) is f(x) - g(x):
![\displaystyle V=2\pi\int_0^2(x)((8-x^2)-(x^2))\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D2%5Cpi%5Cint_0%5E2%28x%29%28%288-x%5E2%29-%28x%5E2%29%29%5C%2Cdx)
Evaluate. Simplify:
![\displaystyle V=2\pi \int_0^2(8x-2x^3)\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D2%5Cpi%20%5Cint_0%5E2%288x-2x%5E3%29%5C%2Cdx)
Hence:
![\displaystyle V=2\pi\Big(4x^2-\frac{1}{2}x^4\Big|_{0}^{2}\Big)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D2%5Cpi%5CBig%284x%5E2-%5Cfrac%7B1%7D%7B2%7Dx%5E4%5CBig%7C_%7B0%7D%5E%7B2%7D%5CBig%29)
Evaluate:
![\displaystyle \begin{aligned} V &= 2 \pi \Big[(4(2)^2-\frac{1}{2}(2)^4)-(4(0)^2-\frac{1}{2}(0)^4)\Big]\\ &=2\pi(8) \\&=16\pi\text{ square units} \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20V%20%26%3D%202%20%5Cpi%20%5CBig%5B%284%282%29%5E2-%5Cfrac%7B1%7D%7B2%7D%282%29%5E4%29-%284%280%29%5E2-%5Cfrac%7B1%7D%7B2%7D%280%29%5E4%29%5CBig%5D%5C%5C%20%26%3D2%5Cpi%288%29%20%5C%5C%26%3D16%5Cpi%5Ctext%7B%20square%20units%7D%20%5Cend%7Baligned%7D)