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]
2 years 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]2 years 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
I don’t really understand this?
Serga [27]

You replace the p  in the given expression by -2 and the m by 3 and simplify

So its (-2)^ /  4 - 3

= 4/4 - 3

= 1 - 3   (note the division 4/4 is done first according to the order of operations rule)

= -2      answer

4 0
3 years ago
Read 2 more answers
1. If = 1, = −2 = −1 then find the value of the following
Mariana [72]

Answer:

hope its helpful......

5 0
3 years ago
0.001 in Standard form
horrorfan [7]
1*10<span>- 3 is the standard form of 0.001</span>
8 0
3 years ago
State the slope of the line perpendicular to the line -2x+5y=12
defon

Answer:

- 5/2

Step-by-step explanation:

Arrange this line equation into y = mx + b form   m = slope

 y = 2/5x + 12/5    

  then perpindicular line = - 1/m   = - 1/ (2/5) = - 5/2

5 0
2 years ago
To show how to do this step by step
Jet001 [13]

Answer:

to do it 5 x 10 x 4 x 5 x 6 x 7 x 3 x 2 3 x 4  x5

Step-by-step explanation:

x 3x 3x 3x3 x4 x4x4 x4x  to the power  of 5 million

3 0
3 years ago
Other questions:
  • ABCD is a rectangle. E is the midpoint of BC , F is the midpoint of AB and G is the point of intersection of AE and CF . If the
    14·1 answer
  • the spinner at the right is spun once.find the probability of each event.write each answer as a fraction, percent, and decimal
    7·1 answer
  • 4.025 x 10^3 in standard form
    12·2 answers
  • The price of 2 bananas are $1.00. How much would 7 bananas cost ?
    14·2 answers
  • [WILL MARK BRAINLIEST]
    7·1 answer
  • 6 7 8 9 10 TIME REMAINING 59:50 Two positive integers are 3 units apart on a number line. Their product is 108. Which equation c
    12·2 answers
  • PLLLLLLLEEEEEEEEEEEEEEASE ANSWER FAST MATH GENIUSES!!!!!!!
    14·2 answers
  • When a number x is multiplied by 6, the result is 3/8.
    10·2 answers
  • Create a word problem for 2x+10=30
    14·1 answer
  • Plz help me I’m so confused about this stuff
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!