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Archives for 2007

A-Math P & C Qn!

The no. of applicants for a job is 15. (i)Calculate the no. of ways in which 6 applicants can be selceted for the interview.

The six selected applicants on a particular day. (ii)Caluculate the no. of ways in which the order of the six interviews can be arranged.

Of the 6 applicants, 3 have backgrounds in business, 2 have backgrounds in education and 1 has a background in recreation. Calculate the number of ways in which the order of the 6 interviews can be arranged, when applicants having the same background are interviewed in succesion.

Who's up for this challenge?

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Of the 6 applicants, 3 have backgrounds in business, 2 have backgrounds in education and 1 has a background in recreation. Calculate the number of ways in which the order of the 6 interviews can be arranged, when applicants having the same background are interviewed in succesion.

BBB EE RSo there are 3 groups of people and there are 3! ways of arranging these 3 groups
Within BBB group, there are 3! ways of arrange these 3 B people, similar within EE group, there are 2! ways of arrange these 2E people
so Total = Arrange Big Groups * Arrange within each group = 3! * 3! * 2!

A-Math Qn Involving Ln / Log

Hi, i have an Additional Mathematics (A-Math) question which i can't solve it.

Qn: Peter deposited $540000 in a bank at the beginning of 1980, which gave a compound interest of 1.8% per annum, which pays directly into his bank account. After a period of t years, the amount of money that peter has in the bank was given by 540000( 1.018)^t. Find
a) the amount of money peter has at the beginning of 1993.
b) the year, in which he would have one million dollars.
If peter wants to have one million dollars in 20 years, he needs to find a bank that gives a compound interest of r% per annum. Find the value of r.

a) 1993-->1980 = 13
when t = 13, amount of $ he has = 540000( 1.018)^(13)

b)1,000 000 = 540000( 1.018)^t
1.85 = ( 1.018)^t
Either take Ln or Log on both sides of the equation ,

Ln1.85 = t Ln1.018
t=34.5 years = 35 years to have the 1 million dollars
1980 + 35 = 2015

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let r be the compound interest rate
1,000 000=540000(1+(r/100))^20
1.85= (1+(r/100))^20

Taking Ln on both sides,
Ln1.85= 20 Ln(1+(r/100))
Ln(1+(r/100))=0.0308
1+(r/100)=1.0313
r/100=0.0313
r=3.13%

When your unknown is located in the POWER, in order to bring it down, you can either Log or Ln both sides of the equations.

Drawing of Trigo Graphs

Can you give an example of a drawing of tangent graphs? For eg, 3tan2x + 1, what does each stand for and how do i go about drawing?

From the drawing, you see only 1 diagram instead of a few diagrams as what most people will have.

The secret is............ I drew my x and y axis LAST which is the reason why my diagram is so neat and it takes me less than 2 min to complete : )

Click on diagram to have an larger view

Differentiation of e

How to differentiate e^tanx?

first of all to differentiate e^anything = (Diff anything)*e^anything

so to differentiate e^tanx = (Diff tanx)*e^tanx = sec^2x*e^tanx

:)

btw, i couldn't remember what is Diff tanx = to, but i know how to sinx & cosx
so tanx=sinx/cosx Diff using quotient rule, get the ans within 30s :)

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