1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivanshal [37]
1 year ago
10

A ball is thrown vertically upwards from the ground. It rises to a height of 10m and then falls and bounces. After each bounce,

it vertically 2/3 the height of which is fell.
i) Find the height to which the ball bounces after the nth impact
ii) Find the total distance travelled by the ball from the first throw to the nth impact with the ground​
Mathematics
1 answer:
Citrus2011 [14]1 year ago
4 0

{\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}

(i)

\sf{a_n = 20 \times  {( \frac{2}{3} )}^{n - 1} }

(ii)

\sf S_n = 60 \{1 -  { \frac{2}{3}}^{n}  \}

Step-by-step explanation:

\underline\red{\textsf{Given :-}}

height of ball (a) = 10m

fraction of height decreases by each bounce (r) = 2/3

\underline\pink{\textsf{Solution :-}}

<u>(</u><u>i</u><u>)</u><u> </u><u>We</u><u> </u><u>will</u><u> </u><u>use</u><u> </u><u>here</u><u> </u><u>geometric</u><u> </u><u>progression</u><u> </u><u>formula</u><u> </u><u>to</u><u> </u><u>find</u><u> </u><u>height</u><u> </u><u>an</u><u> </u><u>times</u>

{\blue{\sf{a_n = a {r}^{n - 1} }}} \\ \sf{a_n = 20 \times  { \frac{2}{3} }^{n - 1} }

(ii) <u>here</u><u> </u><u>we</u><u> </u><u>will</u><u> </u><u>use</u><u> </u><u>the</u><u> </u><u>sum</u><u> </u><u>formula</u><u> </u><u>of</u><u> </u><u>geometric</u><u> </u><u>progression</u><u> </u><u>for</u><u> </u><u>finding</u><u> </u><u>the</u><u> </u><u>total</u><u> </u><u>nth</u><u> </u><u>impact</u>

<u>\orange {\sf{S_n = a \times  \frac{(1 -  {r}^{n} )}{1 - r} }} \\  \sf S_n = 20 \times  \frac{1 -  ( { \frac{2}{3} })^{n}  }{1 -  \frac{2}{3} }  \\   \sf S_n = 20 \times  \frac{1 -  {( \frac{2}{3}) }^{n} }{ \frac{1}{3} }  \\  \sf S_n = 3 \times 20 \times  \{1 - ( { \frac{2}{3}) }^{n}  \} \\   \purple{\sf S_n = 60 \{1 -  { \frac{2}{3} }^{n}  \}}</u>

You might be interested in
What is the percent of increase from 106 miles to 122 miles?
Elis [28]

Answer:

15.094 %

Step-by-step explanation:

[(122 - 106) /106] 100

(16/106) 100

(0.15094)x100

15.094

8 0
3 years ago
Pencils are sold 9 to a package, and pens are sold 6 to a package. If an equal number of pencils and pens are purchased, what is
nalin [4]

Answer:

18

Step-by-step explanation:

You need to find the least common multiple of 9 and 6 - that is 18. In this case you buy 2 packages of pencils and 3 package of pens.

5 0
3 years ago
Read 2 more answers
-1/5y+7=7<br> What is the value of y?
liq [111]
The answer is y=0

See the attached photo for details

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

8 0
3 years ago
Is b = 6 a solution to the inequality b – 3 &gt; 5?
const2013 [10]

Answer:Hlello, my name is woods245.

So you have the problem b - 3>5 and is says that b=6.

So know the problem looks like this. 6 - 3>5.

Step-by-step explanation:

6 0
2 years ago
A scatter plot is made with the data shown below: Number of Bakers at a Cake Shop 5 6 7 8 9 10 11 12 13 Number of Cakes Baked 7
Alenkinab [10]
I think the correct answer would be the second option. Given the data above, the type of association that the scatter plot would show would be a positive linear association. It is best if you plot these points so you will see that there is an almost linear relation of the points. By doing linear regression, you can validate that the correlation of the data points would be linear. A positive linear association would mean that it changes linearly from the left increasing to the right. So, most likely, the graph would be sloping up to the right and it can be observed for the given data above.
8 0
3 years ago
Other questions:
  • Which is greater 0.75 or 0.9
    11·2 answers
  • CAN U PLEASE HELP AS FAST AS POSSIBLE
    12·2 answers
  • Two points sit on a line with the following coordinates p(2,2) and Q(3,7) which is the distance from p to q
    10·1 answer
  • The distance between x and 8 is less than 14
    14·1 answer
  • Negative magnitude rotation is
    6·1 answer
  • 18x + 9y use the distributive property to write an equivalent expression
    5·1 answer
  • What is the negative coterminal angle of 165 degrees ?
    9·2 answers
  • Samantha drives 4.2 miles each workday. How<br> far will Samantha drive after 18 workdays?
    10·1 answer
  • Is this right please hep
    7·2 answers
  • PLEASE PLEASE PLEASE HELP +30 POINTS!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!