Solving for Total Distance on 9th Bounce: Help Needed!

[Mspike6]

I have always had problems with Swquences and sum :S

A basketball is dropped from a height of 15 m and bounces to 70% of the previous height. The total distance the ball travels when it hits the ground for the ninth time is (give answer to the nearest tenth)


i know we probably going to use sn=a(1-2ⁿ)/1-r somewhere.
and we going to use Tn-1 (0.70) ... but i really can't get it right.

 

[Mspike6]

Nvm, i think i got it..

sn=a(1-r^n)/1-r
sn=15(1-(0.70^9) / (1-0.70)

sn=48.0But there is anther one that am having troubles with

An oil well produces 25 000 barrels of oil during its first month of production. The oil company predicts its production will drop 7% each month thereafter. How many barrels of oil will this company produce in its first year? Round your answer to the nearest thousand.

Edit:
i could get that Tn= Tn-1 * 0.93

 

[HallsofIvy]

Nvm, i think i got it..

sn=a(1-r^n)/1-r
sn=15(1-(0.70^9) / (1-0.70)

sn=48.0


But there is anther one that am having troubles with

An oil well produces 25 000 barrels of oil during its first month of production. The oil company predicts its production will drop 7% each month thereafter. How many barrels of oil will this company produce in its first year? Round your answer to the nearest thousand.

Edit:
i could get that Tn= Tn-1 * 0.93

Yes, your sum is 25000+ 25000(.93)+ 2500(.93)^2+ ... which is
\sum_{n=0}^{11}25000 (.93)^n
(n goes up to 11 because there are 12 months in a year and we started the numbering at "0".)

That sum is, using the same formula you did before,
25000\frac{1- (.93)^{12}}{1- .93}

 

[Mspike6]

Thank you HallsofIvy

I got this new QUestion about Lim.

Lim(x-->0) Sinx/Tan X

I think it will go something like.

Lim(x-->0) Sinx / (Sinx/Cosx)

Lim(x-->0) Sinx * Cosx/Sinx

Then am stuck from here :P Thanks guysm, your help is REALLY appreciated.and btw. is there a good Tutorial on Treg. On general or Specificly on Treg Limits ?

 

[TheFurryGoat]

Thank you HallsofIvy

I got this new QUestion about Lim.

Lim(x-->0) Sinx/Tan X

I think it will go something like.

Lim(x-->0) Sinx / (Sinx/Cosx)

Lim(x-->0) Sinx * Cosx/Sinx

Then am stuck from here :P

You can now divide sin x by sin x which will leave you with 1*cos x. what happens when x-->0 now?

 

[Mspike6]

Thanks Furrygoat !..

It will be 1.

Thanks again :D

 

[HallsofIvy]

Thank you HallsofIvy

I got this new QUestion about Lim.

Lim(x-->0) Sinx/Tan X

I think it will go something like.

Lim(x-->0) Sinx / (Sinx/Cosx)

Lim(x-->0) Sinx * Cosx/Sinx

So it is like "(ab)/a". As long as a is not 0, you can cancel: (ab)/a= b.
As long as sin(x) is not 0 (that is, as long as x is not 0) sin(x)cos(x)/sin(x)= cos(x).

Important "law of limits" that is often overlooked: if f(x)= g(x) for all x except x= a then \lim_{x\to a} f(x)= \lim_{x\to a} g(x).

Then am stuck from here :P


Thanks guysm, your help is REALLY appreciated.


and btw. is there a good Tutorial on Treg. On general or Specificly on Treg Limits ?