Answer:
x=3 and y=4x=3 and y=4
Step-by-step explanation:
x=3 and y=4
Answer:
27% and 37%
Step-by-step explanation:
Percentage of students who oppose the year-round school = 68%
Percentage of students who support the year-round school = 32%
Margin of error = ± 5%
We have to set up the absolute valued equation to find the range(least and greatest) percentages of students who could be in favor of year-round school.
Since, the percentage of students who support the year-round school is 32% and the margin of error is 5%, this means, the difference between 32% and the least and greatest possible percentages is 5%. It can be either +5% or -5%
This thing can be expressed as absolute valued equation as:
| x - 32 | = 5
Here x represents the least and greatest percentages.
Expanding the equation, we can write:
x - 32 = -5 or x - 32 = 5
x = -5 + 32 or x = 5 + 32
x = 27% x= 37%
This means the least percentage of students who be in favor is 27% and the greatest percentage of students is 37%.
Answer:
And when we apply the limit we got that:
Step-by-step explanation:
Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"
We have the following formula in order to find the sum of cubes:
We can express this formula like this:
![\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7Di%5E3%20%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2
![\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
If we operate and we take out the 1/4 as a factor we got this:
We can cancel 
and we got
We can reorder the terms like this:
We can do some algebra and we got:
We can solve the square and we got:
And when we apply the limit we got that:
Answer:
8 / 17
Step-by-step explanation:
So cosine is adjacent ÷ hypotenuse.
Adjacent = 8
Hypotenuse = 17
8 / 17
