45°. I’m not sure what the relationship is but I think it’s linear pair ?
I'm not sure what this is asking but I tried, I hope this helps...
18 weeks: $4.26 per class
36 weeks: $3.70 per class
You save $0.56 per class. So the answer be A) less than 1$
Let
denote the given sequence.
has forward differences
{9 - 1, 36 - 9, 100 - 36, ...} = {8, 27, 64, ...} = {2^3, 3^3, 4^3, ...}
If we call the sequence of forward differences
, then for
,
![b_n=(n+1)^3](https://tex.z-dn.net/?f=b_n%3D%28n%2B1%29%5E3)
is defined in terms of
for all
by
![b_n=a_{n+1}-a_n](https://tex.z-dn.net/?f=b_n%3Da_%7Bn%2B1%7D-a_n)
and so
is defined recursively by
![a_n=\begin{cases}a_1=1\\a_{n+1}=a_n+(n+1)^3&\text{for }n\ge1\end{cases}](https://tex.z-dn.net/?f=a_n%3D%5Cbegin%7Bcases%7Da_1%3D1%5C%5Ca_%7Bn%2B1%7D%3Da_n%2B%28n%2B1%29%5E3%26%5Ctext%7Bfor%20%7Dn%5Cge1%5Cend%7Bcases%7D)
We can deduce a pattern for the general
-th term:
![a_2=a_1+2^3](https://tex.z-dn.net/?f=a_2%3Da_1%2B2%5E3)
![a_3=a_2+3^3=a_1+\displaystyle\sum_{i=1}^2(i+1)^3](https://tex.z-dn.net/?f=a_3%3Da_2%2B3%5E3%3Da_1%2B%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5E2%28i%2B1%29%5E3)
![a_4=a_3+4^3=a_1+\displaystyle\sum_{i=1}^3(i+1)^3](https://tex.z-dn.net/?f=a_4%3Da_3%2B4%5E3%3Da_1%2B%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5E3%28i%2B1%29%5E3)
and so on, up to
![a_n=a_1+\displaystyle\sum_{i=1}^{n-1}(i+1)^3](https://tex.z-dn.net/?f=a_n%3Da_1%2B%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5E%7Bn-1%7D%28i%2B1%29%5E3)
We can simplify the right hand side a bit, noticing that
matches
for
:
![a_n=\displaystyle\sum_{i=0}^{n-1}(i+1)^3](https://tex.z-dn.net/?f=a_n%3D%5Cdisplaystyle%5Csum_%7Bi%3D0%7D%5E%7Bn-1%7D%28i%2B1%29%5E3)
and to simplify things a bit more, we shift the index of summation:
![a_n=\displaystyle\sum_{i=1}^ni^3](https://tex.z-dn.net/?f=a_n%3D%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Eni%5E3)
You should know that the right side has a nice closed form (look up "Faulhaber's formula" if you don't):
![a_n=\dfrac{n^2(n+1)^2}4](https://tex.z-dn.net/?f=a_n%3D%5Cdfrac%7Bn%5E2%28n%2B1%29%5E2%7D4)
The answer is 29
hope this helps
Answer:
She will have stretched her neck 1 time, she will have stretched her legs 2 times, and she will have stretched her arms 4 times.
Step-by-step explanation:
This is because 1/2 can only go into 2/3 once, 1/3 can go into 2/3 twice, and 1/6 can go into 2/3 four times.