Answer:
Explicit formula is
.
Recursive formula is ![h_n=0.85h_{n-1}](https://tex.z-dn.net/?f=h_n%3D0.85h_%7Bn-1%7D)
Step-by-step explanation:
Step 1
In this step we first find the explicit formula for the height of the ball.To find the explicit formula we use the fact that the bounces form a geometric sequence. A geometric sequence has the general formula ,
In this case the first term
, the common ratio
since the ball bounces back to 0.85 of it's previous height.
We can write the explicit formula as,
![h(n)=4(0.85)^{n-1}.](https://tex.z-dn.net/?f=h%28n%29%3D4%280.85%29%5E%7Bn-1%7D.)
Step 2
In this step we find the recursive formula for the height of the ball after each bounce. Since the ball bounces to 0.85 percent of it's previous height, we know that to get the next term in the sequence, we have to multiply the previous term by the common ratio. The general fomula for a geometric sequene is ![a_n=a_{n-1}\times r.](https://tex.z-dn.net/?f=a_n%3Da_%7Bn-1%7D%5Ctimes%20r.)
With the parameters given in this problem, we write the general term of the sequence as ,
![h(1)=4\\h(n)=h_{n-1}\times 0.85.](https://tex.z-dn.net/?f=h%281%29%3D4%5C%5Ch%28n%29%3Dh_%7Bn-1%7D%5Ctimes%200.85.)
Answer:
a estimate of 376
Step-by-step explanation:
I counted all the students and added
/ estimate
Using proportions, it is found that the total volume of the glass is of 216 cm³.
<h3>What is the missing information?</h3>
The problem is incomplete, but researching it on a search engine, it is found that:
- Initially, the glass is 1/3 full.
- After adding 63 cm³ of orange of juice, the glass is 5/8 full.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Considering the volume of the glass as x, and the information given in the problem, the following equation can be built:
![\frac{x}{3} + 63 = \frac{5x}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B3%7D%20%2B%2063%20%3D%20%5Cfrac%7B5x%7D%7B8%7D)
We solve for x to find the volume of the glass as follows:
![\frac{5x}{8} - \frac{x}{3} = 63](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B8%7D%20-%20%5Cfrac%7Bx%7D%7B3%7D%20%3D%2063)
![\frac{15x - 8x}{24} = 63](https://tex.z-dn.net/?f=%5Cfrac%7B15x%20-%208x%7D%7B24%7D%20%3D%2063)
Then, applying cross multiplication:
7x = 24 x 63
Simplifying by 7:
x = 24 x 9
x = 216 cm³.
The total volume of the glass is of 216 cm³.
More can be learned about proportions at brainly.com/question/24372153
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Answer:
1. 8:5
2. 4:7:9
3. 4:3
4. 1:7
Step-by-step explanation:
1. they both are in 7 times table
2. both in 8 times table
3. 15 times table
4. 10 times table