Answer:
Step-by-step explanation:
abs(9 - 12) = abs(-3) = 3
abs(-3 + 6) = abs(3) = 3
abs(9 - 12) + abs(-3 + 6) = 3 + 3 = 6
Answer:
36
Step-by-step explanation:
to know the 1/4
divide 48 to 4 = 12
12-48=36
IF THIS HELPED YOU PLS MARK ME BRAINLIEST I NEED IT
Answer:
6+(-2)
Step-by-step explanation:
6 is positive but we are subtracting 2. Therefore, the expression is 6 plus -2. It is negative because that is what we are taking away. The plus sign does not mean anything because there is a negative number. When you look at it, you immediately read 6 plus -2 and since it is a negative not a positive then it's subtracting not adding.
Answer:
b. about 91.7 cm and 44.6 cm
Step-by-step explanation:
The lengths of the diagonals can be found using the Law of Cosines.
Consider the triangle(s) formed by a diagonal. The two given sides will form the other two sides of the triangle, and the corner angles of the parallelogram will be the measure of the angle between those sides (opposite the diagonal).
For diagonal "d" and sides "a" and "b" and corner angle D, we have ...
d² = a² +b² -2ab·cos(D)
The measure of angle D will either be the given 132°, or the supplement of that, 48°. We can use the fact that the cosines of an angle and its supplement are opposites. This means the diagonal measures will be ...
d² = 60² +40² -2·60·40·cos(D) ≈ 5200 ±4800(0.66913)
d² ≈ {1988.2, 8411.8}
d ≈ {44.6, 91.7} . . . . centimeters
The diagonals are about 91.7 cm and 44.6 cm.
Complete Question
Find a formula for the sum of n terms. ![\sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bi%3D1%7D%5En%20%20%28%208%20%2B%20%5Cfrac%7Bi%7D%7Bn%7D%20%29%28%5Cfrac%7B2%7D%7Bn%7D%20%29)
Use the formula to find the limit as ![n \to \infty](https://tex.z-dn.net/?f=n%20%5Cto%20%5Cinfty)
Answer:
![K_n = \frac{n + 73 }{n}](https://tex.z-dn.net/?f=K_n%20%20%3D%20%20%5Cfrac%7Bn%20%2B%2073%20%7D%7Bn%7D)
![\lim_{n \to \infty} K_n = 1](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20K_n%20%20%3D%20%201)
Step-by-step explanation:
So let assume that
![K_n = \sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )](https://tex.z-dn.net/?f=K_n%20%20%3D%20%20%5Csum%5Climits_%7Bi%3D1%7D%5En%20%20%28%208%20%2B%20%5Cfrac%7Bi%7D%7Bn%7D%20%29%28%5Cfrac%7B2%7D%7Bn%7D%20%29)
=> ![K_n = \sum\limits_{i=1}^n ( \frac{16}{n} + \frac{2i}{n^2} )](https://tex.z-dn.net/?f=K_n%20%20%3D%20%20%5Csum%5Climits_%7Bi%3D1%7D%5En%20%20%28%20%5Cfrac%7B16%7D%7Bn%7D%20%2B%20%5Cfrac%7B2i%7D%7Bn%5E2%7D%20%29)
=> ![K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)](https://tex.z-dn.net/?f=K_n%20%20%3D%20%5Cfrac%7B2%7D%7Bn%7D%20%20%5Csum%5Climits_%7Bi%3D1%7D%5En%20%288%29%20%2B%20%5Cfrac%7B2%7D%7Bn%5E2%7D%20%20%20%5Csum%5Climits_%7Bi%3D1%7D%5En%28i%29)
Generally
![\sum\limits_{i=1}^n (k) = \frac{1}{2} n (n + 1)](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bi%3D1%7D%5En%20%28k%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%20n%20%20%28n%20%2B%201%29)
So
![\sum\limits_{i=1}^n (8) = \frac{1}{2} * 8* (8 + 1)](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bi%3D1%7D%5En%20%288%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%208%2A%20%20%288%20%2B%201%29)
![\sum\limits_{i=1}^n (8) = 36](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bi%3D1%7D%5En%20%288%29%20%3D%2036)
and
![\sum\limits_{i=1}^n (i) = \frac{1}{2} n (n + 1)](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bi%3D1%7D%5En%20%28i%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%20n%20%20%28n%20%2B%201%29)
Therefore
![K_n = \frac{72}{n} + \frac{2}{n^2} * \frac{1}{2} n (n + 1 )](https://tex.z-dn.net/?f=K_n%20%20%3D%20%5Cfrac%7B72%7D%7Bn%7D%20%2B%20%5Cfrac%7B2%7D%7Bn%5E2%7D%20%20%20%2A%20%20%5Cfrac%7B1%7D%7B2%7D%20%20n%20%28n%20%2B%201%20%29)
![K_n = \frac{72}{n} + \frac{1}{n} (n + 1 )](https://tex.z-dn.net/?f=K_n%20%20%3D%20%5Cfrac%7B72%7D%7Bn%7D%20%2B%20%20%20%20%5Cfrac%7B1%7D%7Bn%7D%20%20%20%28n%20%2B%201%20%29)
![K_n = \frac{72}{n} + 1 + \frac{1}{n}](https://tex.z-dn.net/?f=K_n%20%20%3D%20%5Cfrac%7B72%7D%7Bn%7D%20%2B%20%20%201%20%2B%20%20%5Cfrac%7B1%7D%7Bn%7D)
![K_n = \frac{72 + 1 + n }{n}](https://tex.z-dn.net/?f=K_n%20%20%3D%20%20%5Cfrac%7B72%20%2B%20%201%20%2B%20%20n%20%7D%7Bn%7D)
![K_n = \frac{n + 73 }{n}](https://tex.z-dn.net/?f=K_n%20%20%3D%20%20%5Cfrac%7Bn%20%2B%2073%20%7D%7Bn%7D)
Now ![\lim_{n \to \infty} K_n = \lim_{n \to \infty} [\frac{n + 73 }{n} ]](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20K_n%20%20%3D%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5B%5Cfrac%7Bn%20%2B%2073%20%7D%7Bn%7D%20%5D)
=> ![\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [\frac{n}{n} + \frac{73 }{n} ]](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5B%5Cfrac%7Bn%20%2B%2073%20%7D%7Bn%7D%20%5D%20%20%3D%20%20%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5B%5Cfrac%7Bn%7D%7Bn%7D%20%20%2B%20%20%5Cfrac%7B73%20%7D%7Bn%7D%20%20%5D)
=> ![\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 + \frac{73 }{n} ]](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5B%5Cfrac%7Bn%20%2B%2073%20%7D%7Bn%7D%20%5D%20%20%3D%20%20%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5B1%20%2B%20%20%5Cfrac%7B73%20%7D%7Bn%7D%20%20%5D)
=> ![\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 ] + \lim_{n \to \infty} [\frac{73 }{n} ]](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5B%5Cfrac%7Bn%20%2B%2073%20%7D%7Bn%7D%20%5D%20%20%3D%20%20%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5B1%20%5D%20%2B%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%20%5B%5Cfrac%7B73%20%7D%7Bn%7D%20%20%5D)
=> ![\lim_{n \to \infty} [\frac{n + 73 }{n} ] = 1 + 0](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5B%5Cfrac%7Bn%20%2B%2073%20%7D%7Bn%7D%20%5D%20%20%3D%20%201%20%20%2B%20%200)
Therefore
![\lim_{n \to \infty} K_n = 1](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20K_n%20%20%3D%20%201)