Answer:
1/18
Step-by-step explanation:
the common denominator is 18 which changed the problem to 9/18-8/18 which is 1/18
hope this helps!
Answer:
The result is 2 > 1. Hence, the series diverges
Step-by-step explanation:
You have the following series:
(1)
You use the ratio test to determine if the series is convergent or divergent. The ratios test is given by:
(2)
Then, you replace the series (1) in (2):
![\lim_{n \to \infty} \frac{\frac{2^{n+1}}{(n+1)^2}}{\frac{2^n}{n^2}}= \lim_{n \to \infty} \frac{(2^n2)(n^2)}{2^n(n+1)^2}\\\\\lim_{n \to \infty} \frac{2n^2}{n^2+2n+1}= \lim_{n \to \infty} \frac{2n^2}{n^2[1+\frac{2}{n}+\frac{1}{n^2}]} \\\\\lim_{n \to \infty} \frac{2}{1+\frac{2}{n}+\frac{1}{n^2}}=\frac{2}{1+0+0}=2](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Cfrac%7B2%5E%7Bn%2B1%7D%7D%7B%28n%2B1%29%5E2%7D%7D%7B%5Cfrac%7B2%5En%7D%7Bn%5E2%7D%7D%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%282%5En2%29%28n%5E2%29%7D%7B2%5En%28n%2B1%29%5E2%7D%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B2n%5E2%7D%7Bn%5E2%2B2n%2B1%7D%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B2n%5E2%7D%7Bn%5E2%5B1%2B%5Cfrac%7B2%7D%7Bn%7D%2B%5Cfrac%7B1%7D%7Bn%5E2%7D%5D%7D%20%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B2%7D%7B1%2B%5Cfrac%7B2%7D%7Bn%7D%2B%5Cfrac%7B1%7D%7Bn%5E2%7D%7D%3D%5Cfrac%7B2%7D%7B1%2B0%2B0%7D%3D2)
In the ratio test you have that if the limit is greater than 1, the series diverges.
The result is 2 > 1. Hence, the series diverges.
The ratio of flour cups to sugar cups can be illustrted as below:
4 cups of flour= 2 cups of of sugar cups
so x cups of flour = 42 cups of sugar
Lets cross multiply :
x * 2 = 4 * 42
2x = 168 ..... divide by 2 both sides :
x =168/2 = 84
• This means 84 cups of flour is needed in order to correspond with 42 cups of sugar.
Answer:
Z = Ma = ba
You made a typo. One of those = signs should either
be a + and a -. Here are all possibilities:
1. Z+Ma = ba, solve for a
Ma-Ba = -Z
a(M-B) = -Z
a = -Z/(M-B)
2. Z = Ma+ba, solve for a
Ma+ba = Z
a(M+b) = Z
a = Z/(M+b)
3. Z-Ma = ba, solve for a
Z = Ma+ba
Ma+ba = Z
a(M+b) = Z
a = Z/(M+b)
4. Z = Ma-ba, solve for a
Ma-ba = Z
a(M-b) = Z
a = Z/(M-b)
Step-by-step explanation:
(72% + 89%) divided by 2 (the number of total grades)
