Answer: ![\bold{a_1=p+3,\quad d=2p+1,\quad a_n=(2p+1)\cdot a_{n-1}}](https://tex.z-dn.net/?f=%5Cbold%7Ba_1%3Dp%2B3%2C%5Cquad%20d%3D2p%2B1%2C%5Cquad%20a_n%3D%282p%2B1%29%5Ccdot%20a_%7Bn-1%7D%7D)
<u>Step-by-step explanation:</u>
p + 3, 3p + 4, 5p + 5, ... , 23p + 14
Notice that each p-term is increased by 2p.
Notice that each number is increased by 1
So, the difference (d) is: 2p + 1
![\text{The general form for the recursive rule of an arithmetic sequence is:}\\a_n=d\cdot a_{n-1}\quad \text{where d is the difference and}\ a_{n-1}\ \text{is the previous term}](https://tex.z-dn.net/?f=%5Ctext%7BThe%20general%20form%20for%20the%20recursive%20rule%20of%20an%20arithmetic%20sequence%20is%3A%7D%5C%5Ca_n%3Dd%5Ccdot%20a_%7Bn-1%7D%5Cquad%20%5Ctext%7Bwhere%20d%20is%20the%20difference%20and%7D%5C%20a_%7Bn-1%7D%5C%20%5Ctext%7Bis%20the%20previous%20term%7D)
![\text{So, the recursive rule with the information provided is:}\\a_n=(2p+1)\cdot a_{n-1}](https://tex.z-dn.net/?f=%5Ctext%7BSo%2C%20the%20recursive%20rule%20with%20the%20information%20provided%20is%3A%7D%5C%5Ca_n%3D%282p%2B1%29%5Ccdot%20a_%7Bn-1%7D)
Answer:
![(a)\ (x+6)^2 + (y-5)^2 = 25](https://tex.z-dn.net/?f=%28a%29%5C%20%28x%2B6%29%5E2%20%2B%20%28y-5%29%5E2%20%3D%2025)
![(b)\ Area = 16.75cm^2](https://tex.z-dn.net/?f=%28b%29%5C%20Area%20%3D%2016.75cm%5E2)
Step-by-step explanation:
Solving (a):
Given
![(a,b) = (-6,5)](https://tex.z-dn.net/?f=%28a%2Cb%29%20%3D%20%28-6%2C5%29)
![r = 5](https://tex.z-dn.net/?f=r%20%3D%205)
Required
The equation of the circle
This is calculated as:
![(x-a)^2 + (y-b)^2 = r^2](https://tex.z-dn.net/?f=%28x-a%29%5E2%20%2B%20%28y-b%29%5E2%20%3D%20r%5E2)
So, we have:
![(x--6)^2 + (y-5)^2 = 5^2](https://tex.z-dn.net/?f=%28x--6%29%5E2%20%2B%20%28y-5%29%5E2%20%3D%205%5E2)
![(x+6)^2 + (y-5)^2 = 25](https://tex.z-dn.net/?f=%28x%2B6%29%5E2%20%2B%20%28y-5%29%5E2%20%3D%2025)
Solving (b):
Given
![r = 8cm](https://tex.z-dn.net/?f=r%20%3D%208cm)
--- Missing from the question
Required
The area of the sector
This is calculated using:
![Area = \frac{\theta}{360} * \pi r^2](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B%5Ctheta%7D%7B360%7D%20%2A%20%5Cpi%20r%5E2)
So, we have:
![Area = \frac{30}{360} * 3.14 * 8^2](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B30%7D%7B360%7D%20%2A%203.14%20%2A%208%5E2)
![Area = \frac{1}{12} * 200.96](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B12%7D%20%2A%20200.96)
![Area = 16.75cm^2](https://tex.z-dn.net/?f=Area%20%3D%2016.75cm%5E2)
Answer:
3,489 + 8,617 + 1,240 – 564 x 6 = 9,962
There are 9,962 books left in the library
Hope so it helps cause it's also in my book
Answer:
I'm not sure what the answer is, but try Photo math. it helps me so much with my equations, and it'll even tell you the steps to get the answer.