Answer:
24 ounces of butter
21 ounces of sugar
30 ounces of flour
12 eggs
3 teaspoon of baking powder
Step-by-step explanation:
Simple. All you had to do was multiply each quantity by 3, because you needed 3 lots of each.
Hope this helps.
Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:
![\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac2n%5Cright%5D%2C%5Cleft%5B%5Cdfrac2n%2C%5Cdfrac4n%5Cright%5D%2C%5Cleft%5B%5Cdfrac4n%2C%5Cdfrac6n%5Cright%5D%2C%5Cldots%2C%5Cleft%5B%5Cdfrac%7B2%28n-1%29%7Dn%2C2%5Cright%5D)
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,
![r_i=\dfrac{2i}n](https://tex.z-dn.net/?f=r_i%3D%5Cdfrac%7B2i%7Dn)
where
. Each interval has length
.
At these sampling points, the function takes on values of
![f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}](https://tex.z-dn.net/?f=f%28r_i%29%3D7%7Br_i%7D%5E3%3D7%5Cleft%28%5Cdfrac%7B2i%7Dn%5Cright%29%5E3%3D%5Cdfrac%7B56i%5E3%7D%7Bn%5E3%7D)
We approximate the integral with the Riemann sum:
![\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Enf%28r_i%29%5CDelta%20x_i%3D%5Cfrac%7B112%7Dn%5Csum_%7Bi%3D1%7D%5Eni%5E3)
Recall that
![\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Eni%5E3%3D%5Cfrac%7Bn%5E2%28n%2B1%29%5E2%7D4)
so that the sum reduces to
![\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Enf%28r_i%29%5CDelta%20x_i%3D%5Cfrac%7B28n%5E2%28n%2B1%29%5E2%7D%7Bn%5E4%7D)
Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:
![\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E27x%5E3%5C%2C%5Cmathrm%20dx%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac%7B28n%5E2%28n%2B1%29%5E2%7D%7Bn%5E4%7D%3D%5Cboxed%7B28%7D)
Just to check:
![\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E27x%5E3%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B7x%5E4%7D4%5Cbigg%7C_0%5E2%3D%5Cfrac%7B7%5Ccdot2%5E4%7D4%3D28)
Answer:
-25
Step-by-step explanation:
You begin with -40, then decrease by 20 so your new value is -60, then increase by 35 so your final value is -25m... hope this helps (:
Answer: i think it is 8.93
Step-by-step explanation:
The answer is C. Use the quadratic formula to solve it and you should be just fine!