Mathematics: Acertain ball is dropped from a height of x feet. it always bounces up to 2/3 x feet. suppose the ball is dropped from 10 feet and is stopped exactly when it touches the ground after 30th bounce. what is the total distance traveled by the ball ? express your answer in exponential notation.

oh I was helping to you (•‿•)...

Acertain ball is dropped from a height of x feet.

Ответ:

burritomadness

11.03.2022

Ok, so bouncing

when it bounces up, it bounces up
so we double the summation

but for the initial bounce, it only goes down
so we double the whole thing and minus the first bounce

the summation of the geometric sequence where the initial term is a_1

and the common ratio is r and the term is n is
$S_n=\frac{a_1(1-r^n)}{1-r}$

a_1=10

, $r=\frac{2}{3}$ and n=30

double and minus 10

$2S_{30}-10=2(\frac{10(1-(\frac{2}{3})^{30})}{1-\frac{2}{3})-10$

the total distance traveled is $\frac{20(1-(\frac{2}{3})^{30})}{\frac{1}{3}}$
it simplifies to $60(1-(\frac{2}{3})^{30})$
that's the answer is exponential notation

0,0(0 оценок)

Ответ:

yah57

16.01.2020

Mathematics

I was helping to you (•‿•)

0,0(0 оценок)

Acertain ball is dropped from a height of x feet. it always bounces up to 2/3 x feet. suppose the ball is dropped from 10 feet and is stopped exactly when it touches the ground after 30th bounce. what is the total distance traveled by the ball ? express your answer in exponential notation.

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question