calcules help needed

Calculus
Tutor: None Selected Time limit: 1 Day

Apr 28th, 2015

4. After the first fall from the height a the ball will go up by some height and down by the same height.

As follows: a, ra (up), ra (down), r*ra (up), r*ra (down) and so on.

We ought to compute the sum of this (infinite) series. Let's group the terms:

a + (r*a+r*a) + (r^2*a + r^2*a) + (r^3*a + r^3*a) + ... = 

= a + a*2*(r + r^2 + r^3 + ...). Again we see a geometric progression, its ratio r<1 and the first term is also r. It is convergent to the r/(1-r).

So the entire sum equals to a + 2*a*r/(1-r) = a*(1 + 2/(1-r)) = a*(1+r)/(1-r).


5. Denote the total area of a square as A.

Then at the first step we shade the area A0*4*(1/4)*(1/4) = A/4.
And the square that remains for shading at the second step also has area A/4.

At the second step we shade 1/4 of A/4 and leave for the third step A/(4^2).

And so on, on the n-th step we shade the area A/(4^n).

It is the sum of an infinite geometric progression with the first term A/4 and the ratio 1/4. So this sum is equal to A*(1/4)/(1-1/4) = A*(1/4)/(3/4) = A*(1/3).

So the answer 1s 1/3.

Apr 28th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Apr 28th, 2015
...
Apr 28th, 2015
May 26th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer