1. Starting with 15, each successive term is obtained by multiplying by
![\dfrac15](https://tex.z-dn.net/?f=%5Cdfrac15)
. So the explicit rule for the sequence must be
![a(n)=15\left(\dfrac15\right)^{n-1}](https://tex.z-dn.net/?f=a%28n%29%3D15%5Cleft%28%5Cdfrac15%5Cright%29%5E%7Bn-1%7D)
2. Starting with 10, the next terms are obtained by multiplying by -8. So the recursive rule would be
![\begin{cases}a(1)=10\\a(n)=-8a(n-1)&\text{for }n\ge2\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Da%281%29%3D10%5C%5Ca%28n%29%3D-8a%28n-1%29%26%5Ctext%7Bfor%20%7Dn%5Cge2%5Cend%7Bcases%7D)
3. We're given the recursive rule,
![\begin{cases}a(1)=2\\a(n)=\dfrac13a(n-1)&\text{for }n\ge2\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Da%281%29%3D2%5C%5Ca%28n%29%3D%5Cdfrac13a%28n-1%29%26%5Ctext%7Bfor%20%7Dn%5Cge2%5Cend%7Bcases%7D)
We have
![a(n)=\dfrac13a(n-1)=\left(\dfrac13\right)^2a(n-2)=\left(\dfrac13\right)^3a(n-3)=\cdots=\left(\dfrac13\right)^{n-1}a(1)](https://tex.z-dn.net/?f=a%28n%29%3D%5Cdfrac13a%28n-1%29%3D%5Cleft%28%5Cdfrac13%5Cright%29%5E2a%28n-2%29%3D%5Cleft%28%5Cdfrac13%5Cright%29%5E3a%28n-3%29%3D%5Ccdots%3D%5Cleft%28%5Cdfrac13%5Cright%29%5E%7Bn-1%7Da%281%29)
so the explicit rule is
![a(n)=2\left(\dfrac13\right)^{n-1}](https://tex.z-dn.net/?f=a%28n%29%3D2%5Cleft%28%5Cdfrac13%5Cright%29%5E%7Bn-1%7D)
4. We're given the explicit rule
![a(n)=\dfrac12\left(\dfrac43\right)^{n-1}](https://tex.z-dn.net/?f=a%28n%29%3D%5Cdfrac12%5Cleft%28%5Cdfrac43%5Cright%29%5E%7Bn-1%7D)
When
![n=1](https://tex.z-dn.net/?f=n%3D1)
, we get the first term to be
![a(1)=\dfrac12](https://tex.z-dn.net/?f=a%281%29%3D%5Cdfrac12)
. For each successive term, we have to multiply by
![\dfrac43](https://tex.z-dn.net/?f=%5Cdfrac43)
. So the recursive rule is
Answer:
The hypotenuse is 7.62
Step-by-step explanation:
i just don't get what it means when it says "give answer as a decimal to 3 places"
Area of a triangle = (h × b) ÷ 2, where h is height and b is the base.
7.1 × 28 = 198.8
198.8 ÷ 2 = 99.4
The area of this triangle is 99.4 yd²
Answer:
Step-by-step explanation:
<u>Given:</u>
- Total number = 700
- Off grid class = 450
- Online class = 320
- Both = 275
<u>Based on the given we find the following</u>
1) <u>Off-grid class only:</u>
3) <u>Online class only:</u>
2) <u>None of the classes:</u>
- 700 - (175 + 275 + 45) = 205
4) <u>Not online:</u>
5) <u>Not off-grid:</u>
Answer:
There would be 8 red marbles and 47 purple marbles.
Step-by-step explanation:
In order to find this, we can first set the amount of red marbles as x. Once we do this, it is possible to model the number of purple marbles as 5x + 7. Knowing this, we can add the two together and set equal to 55.
x + 5x + 7 = 55
6x + 7 = 55
6x = 48
x = 8
With 8 red marbles, we know the rest must be purple (47)