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: 47/100
Step-by-step explanation: I converted 2/10 to 20/100 and then i subtracted 20 from 67 and got 47 and my answer was 47/100.
A rotation 270° counterclockwise about the origin is the same as rotation 90° clockwise about the origin and has a rule:
(x,y)→(y,-x).
Then:
- D(−2,4)→D'(4,2)
- E(4,7)→E'(7,-4)
- F(10,3)→F'(3,-10)
- G(8,0)→G'(0,-8)
Answer: the coordinates of vertices of quadrilateral D′E′F′G′ are D'(4,2), E'(7,-4), F'(3,-10), G'(0,-8).
<h2>
Question Clarification:</h2>
I think there is some typing error with your question as searching it on google is showing me it is a "fill the blanks" type of question. I am attaching the actual question for clarification.
<h2>
Answer:</h2>
(1) Number
(2) Proportion
<h2>
Step-by-step explanation:</h2>
(1) A Frequency distribution is a tabular or graphical representation of number of observations within a given interval. The size of the intervals are determined by the nature of the data being analyzed and the objectives of the analyst. The intervals are collectively exhaustive and mutually exclusive.
(2) On the other hand, a relative frequency distribution, instead of numbers, shows the proportion (percentage) of the total number of observations that belong to a certain value or a class of values