ReCom.org
Portal Page Forum Wiki Social Groups Scholarship Holders Infobase Site Map About
Go Back   ReCom.org > Forum > ReCom Cafe > Education > SPM & STPM

SPM & STPM Post questions on SPM and STPM topics ONLY.

[STPM] Maths T needs help!!

Reply
 
Thread Tools
mitsukolyn Female
Member
 
mitsukolyn's Avatar
 
Join Date: Sep 2007
Posts: 341
  #1 Old 20-06-2008 Default [STPM] Maths T needs help!!

I need help on this question...

Question:

Find the set of values of x for the following inequalities.
b)e^x - 3e^-x ? 2 [hint: multiply both sides by e^x]
mitsukolyn is offline   Reply With Quote
ken_cck_kid Male
Super Junior Member
 
ken_cck_kid's Avatar
 
Join Date: Jun 2008
Posts: 30
  #2 Old 20-06-2008 Default just wanna help..

e^x - 3e^-x ? 2
e^x << 2 + 3e^-x
e^2x << 2e^x + 3 ( multiply by e^x)
e^2x-2e^x-3<<0 (a quadratic equation)
(e^x-3)(e^x+1) <<0

try to continue ya, tis should be the way la if i'm not mistaken..haha..
ken_cck_kid is offline   Reply With Quote
luke Male
KittyLover
Administrator
 
luke's Avatar
 
Join Date: Nov 2003
Posts: 1,878
  #3 Old 21-06-2008 Default

e^x - 3e^(-x) < 2
e^(2x) - 3 < 2e^x
e^(2x) - 2e^x - 3 < 0

let Z = e^x, therefore: Z^2 - 2Z - 3 < 0 (voila! normal quadratic inequality!)

after a bit of drawing the curve we figure out that, -1 < Z < 3

substitute back, -1 < e^x < 3
but e^x cannot be less than 0, thus 0 =< e^x < 3

ln 0 =< ln (e^x) < ln 3

negative infinity =< x < ln 3

simply means x < ln 3
__________________
luke is offline   Reply With Quote
mitsukolyn Female
Member
 
mitsukolyn's Avatar
 
Join Date: Sep 2007
Posts: 341
  #4 Old 22-06-2008 Default reply

Quote:
Originally Posted by luke View Post
e^x - 3e^(-x) < 2
e^(2x) - 3 < 2e^x
e^(2x) - 2e^x - 3 < 0

let Z = e^x, therefore: Z^2 - 2Z - 3 < 0 (voila! normal quadratic inequality!)

after a bit of drawing the curve we figure out that, -1 < Z < 3

substitute back, -1 < e^x < 3
but e^x cannot be less than 0, thus 0 =< e^x < 3

ln 0 =< ln (e^x) < ln 3

negative infinity =< x < ln 3

simply means x < ln 3
haha..im stuck in the half way thts y i turn to here...wow...ur so smart!!! but cn i knw wad's ln means and when to use it??
mitsukolyn is offline   Reply With Quote
chiunlin
Slightly Senior Member
 
chiunlin's Avatar
 
Join Date: Jan 2004
Posts: 705
  #5 Old 22-06-2008 Default

ln = log to the base e/natural log
__________________
知不知道饮酒和饮水有什么区别?酒越饮越暖,水越喝越寒。 你越想忘记一个人时,其实你越会记得他。人的烦恼就是记性太好,如果可以把所有事都忘掉,以后每一日都是个 新开始,你说多好
chiunlin is offline   Reply With Quote
The Following User Says Thank You to chiunlin For This Useful Post:
mitsukolyn Female
Member
 
mitsukolyn's Avatar
 
Join Date: Sep 2007
Posts: 341
  #6 Old 26-06-2008 Default

Quote:
Originally Posted by chiunlin View Post
ln = log to the base e/natural log
thanks!! i got it d...
mitsukolyn is offline   Reply With Quote
lonewolf5999
Super Junior Member
 
Join Date: Jul 2008
Posts: 44
  #7 Old 19-07-2008 Default

As in the hint, multiply both sides to obtain

e^2x - 3 < 2e^x

use the substitution u = e^x to get

u^2 -3 < 2u, which is easily solved

substitute back e^x, but note that e^x is always positive, so you will need to reject any answers contradicting this fact.
lonewolf5999 is offline   Reply With Quote
tomatoinc Male
Less Junior Member
 
Join Date: Jul 2004
Posts: 54
  #8 Old 29-07-2008 Default

luke is still da smart ass.

Quote:
Originally Posted by luke View Post
e^x - 3e^(-x) < 2
e^(2x) - 3 < 2e^x
e^(2x) - 2e^x - 3 < 0

let Z = e^x, therefore: Z^2 - 2Z - 3 < 0 (voila! normal quadratic inequality!)

after a bit of drawing the curve we figure out that, -1 < Z < 3

substitute back, -1 < e^x < 3
but e^x cannot be less than 0, thus 0 =< e^x < 3

ln 0 =< ln (e^x) < ln 3

negative infinity =< x < ln 3

simply means x < ln 3
tomatoinc is offline   Reply With Quote
Lance2 Male
Super Junior Member
 
Join Date: Feb 2010
Posts: 1
  #9 Old 21-02-2010 Default Re: [STPM] Maths T needs help!!

Nice post, Keep up the good work man.
__________________
jewelry designs and handbag reviews and digital camera models
Lance2 is offline   Reply With Quote
smallkid Male
Super Junior Member
 
Join Date: Feb 2010
Posts: 12
  #10 Old 11-03-2010 Default Re: [STPM] Maths T needs help!!

I found this question in fajar bakti ace ahead (volume 2)
Exam practise chapter 8
Q21.

Suppose the time T taken for a car wash is normally distributed with mean 6minutes and standard deviation 1.5 minutes.

c) If 1000 cars are washed, what is the probability that not more than one car takes more than 10.62 minutes.

Answer : 0.3399

Anyone knows how to do it?

I've tried poisson approximation, but i'm still no where near the solution

Last edited by smallkid; 11-03-2010 at 07:34 PM. Reason: Automerged Doublepost
smallkid is offline   Reply With Quote
Reply

Bookmarks

Tags
mathematics, stpm

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Similar Threads
Thread Thread Starter Forum Replies Last Post
Differences between the 3 maths subjects in STPM? infested_ysy Education 5 16-06-2009 08:48 PM
I need stpm 06,05 further maths answer.. Help me pls.... UlquiorraSchiffer SPM & STPM 0 09-09-2007 09:46 AM
Where to get latest STPM further maths book? qfeng Education 9 20-01-2007 09:21 AM
Further Maths lolilo Education 37 05-06-2005 04:45 AM
need help for maths project joebf86 Education 4 15-09-2004 07:04 AM


All times are GMT +8. The time now is 12:56 PM.


Powered by vBulletin® Version 3.7.6
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

ReCom stands for Reborn Community. It has no affiliation with other organizations that may share the same name. The views expressed in this website solely represent the authors point of view and do not necessarily reflect the views of ReCom Anchors and other ReCom users.


 

Page generated in 0.09726 seconds with 15 queries