You can use the root test here. The series will converge if
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}](https://tex.z-dn.net/?f=L%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cfrac%7B%284-x%29%5En%7D%7B4%5En%2B9%5En%7D%7D%3C1)
You have
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}=|4-x|\lim_{n\to\infty}\frac1{\sqrt[n]{4^n+9^n}}](https://tex.z-dn.net/?f=L%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cfrac%7B%284-x%29%5En%7D%7B4%5En%2B9%5En%7D%7D%3D%7C4-x%7C%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac1%7B%5Csqrt%5Bn%5D%7B4%5En%2B9%5En%7D%7D)
Notice that
![\dfrac1{\sqrt[n]{4^n+9^n}}=\dfrac1{\sqrt[n]{9^n}\sqrt[n]{1+\left(\frac49\right)^n}}=\dfrac1{9\sqrt[n]{1+\left(\frac49\right)^n}}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%5Csqrt%5Bn%5D%7B4%5En%2B9%5En%7D%7D%3D%5Cdfrac1%7B%5Csqrt%5Bn%5D%7B9%5En%7D%5Csqrt%5Bn%5D%7B1%2B%5Cleft%28%5Cfrac49%5Cright%29%5En%7D%7D%3D%5Cdfrac1%7B9%5Csqrt%5Bn%5D%7B1%2B%5Cleft%28%5Cfrac49%5Cright%29%5En%7D%7D)
so as
, you have
, which means you end up with
This is the interval of convergence. The radius of convergence can be determined by finding the half-length of the interval, or by solving the inequality in terms of
so that
is the ROC. You get
Answer:
A) b= 8 students
B) 1) 19/55 2) 28/55
Step-by-step explanation:
I'm sorry if I'm getting this whole concept wrong cause it felt way too easy to be right so I'm sorry if you get it wrong.
The reason the first question is 8 is because of the fact that you first have to add the students charted on the Venn-diagram and subtract that from 55, getting you to 8 students.
For the second one, the first part would be 19/55 becuase in the Venn-diagram it is shown that only 19 people passed both and so that be the numerator and the denominator would be the total of students, so it would be 55.
Same thing for part two except the fact that you have to add the students who only passed one subject, so combine 17 and 11, getting you to 28, thus getting the answer 28/55.
Answer:
alternate interior angles are always congruent.
Step-by-step explanation:
- Consecutive [Same-side] exterior angles are always supplementary.
- Consecutive [Same-side] interior angles are always supplementary.
- Corresponding angles are always congruent.
I am joyous to assist you anytime.
Answer:
54 mm
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Given
x² - 3x - 12 = 0 ( add 12 to both sides )
x² - 3x = 12
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(-
)x + 
= 12 +
(x - )² = 
( take the square root of both sides )
x - = ± 
= ± 
( add to both sides )
x = ±
Then
x = + ≈ 5.27 ( to the nearest hundredth )
x = - ≈ - 2.27 ( to the nearest hundredth )
