Answer:
Since the
then we have this:
![\int_{-\infty}^{-1} (x-2)^{-3} dx =-\frac{1}{18}](https://tex.z-dn.net/?f=%5Cint_%7B-%5Cinfty%7D%5E%7B-1%7D%20%28x-2%29%5E%7B-3%7D%20dx%20%3D-%5Cfrac%7B1%7D%7B18%7D)
And we see that our integral on this case converged to -1/18.
Step-by-step explanation:
For this case we need to determine if the following integral converges or not:
We can rewrite the integral like this:
![\int_{-\infty}^{-1} \frac{1}{(x-2)^3} dx](https://tex.z-dn.net/?f=%20%5Cint_%7B-%5Cinfty%7D%5E%7B-1%7D%20%5Cfrac%7B1%7D%7B%28x-2%29%5E3%7D%20dx)
Then we can use the substitution
and then
and we have this:
![\int_{-\infty}^{-3} \frac{1}{u^3} du=\int_{-\infty}^{-3} u^{-3} du](https://tex.z-dn.net/?f=%20%5Cint_%7B-%5Cinfty%7D%5E%7B-3%7D%20%5Cfrac%7B1%7D%7Bu%5E3%7D%20du%3D%5Cint_%7B-%5Cinfty%7D%5E%7B-3%7D%20u%5E%7B-3%7D%20du%20)
If we solve the integral we got:
![=\frac{u^{-3+1}}{-3+1} =-\frac{u^{-2}}{2}=-\frac{1}{2}\frac{1}{u^2}](https://tex.z-dn.net/?f=%20%3D%5Cfrac%7Bu%5E%7B-3%2B1%7D%7D%7B-3%2B1%7D%20%3D-%5Cfrac%7Bu%5E%7B-2%7D%7D%7B2%7D%3D-%5Cfrac%7B1%7D%7B2%7D%5Cfrac%7B1%7D%7Bu%5E2%7D)
And then the integral would be equal to:
![\int_{-\infty}^{-1} (x-2)^{-3} dx = -\frac{1}{2(x-2)^2}\Big|_{-\infty}^{-1}](https://tex.z-dn.net/?f=%5Cint_%7B-%5Cinfty%7D%5E%7B-1%7D%20%28x-2%29%5E%7B-3%7D%20dx%20%3D%20-%5Cfrac%7B1%7D%7B2%28x-2%29%5E2%7D%5CBig%7C_%7B-%5Cinfty%7D%5E%7B-1%7D)
And if we replace and using the fundamental theorem of calculus we got:
![= -\frac{1}{2} [\frac{1}{(-1-2)^2} -\lim_{x\to -\infty} \frac{1}{(x-2)^2}]](https://tex.z-dn.net/?f=%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%20%5B%5Cfrac%7B1%7D%7B%28-1-2%29%5E2%7D%20-%5Clim_%7Bx%5Cto%20-%5Cinfty%7D%20%5Cfrac%7B1%7D%7B%28x-2%29%5E2%7D%5D)
Since the
then we have this:
![\int_{-\infty}^{-1} (x-2)^{-3} dx =-\frac{1}{18}](https://tex.z-dn.net/?f=%5Cint_%7B-%5Cinfty%7D%5E%7B-1%7D%20%28x-2%29%5E%7B-3%7D%20dx%20%3D-%5Cfrac%7B1%7D%7B18%7D)
And we see that our integral on this case converged to -1/18.
Step-by-step explanation:
50-3n
or,50=3n
or,50/3=n
or,n=16.67
Thus,the value of n is 16.67.
10 because 30 divided by 10 equals 3 and 50 divided by 10 equals 5 and 3 and 5 only have a GCF of 1 so 10 is your answer
Answer:
I think its (6,8) if im wrong i will write the correct answer here or i will right it in the comments
Step-by-step explanation:
The correct answer is c.
because he ordered 45 pounds of oranges
twice as many pounds of apples as oranges so:45*2=90 pounds of apples
and 20 pounds more strawberries than apples so: 90+20=110 pounds strawberries
in total:45+90+110=245 pounds of fruits!!