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Another question for O Level Additional Mathematics (A-Math).
On the same diagram, sketch the graphs of
y=sin 3x & y=cos2x,
for x between 0 degree and 180 degree
Hence state the number of soutions to the equation
sin 3x=cos 2x
in the interval 0 degree less than or equals to x which is less then or equals to 180 degree
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Another question from O Level Additional Mathematics (A-Math).
If 
, 
find sinx and cosx in terms of p.
Another question from O Level Additional Mathematics (A-Math).
How many even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated?
Conditions
#1: Even
#2: 5-digit number
#3: no digit is to be repeated
Case 1:When the first digit is odd (must be more than or equal to 5)
2C1 * 5P3 * 3C1
Logic & Reasoning:
first digit: either 5 or 7 so 2C1
last digit: either 2,4 or 6 so 3C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3Case 2:When the first digit is even
5P3 * 2C1
Logic & Reasoning:
first digit: 6 so no need to choose just put!
last digit: either 2 or 4 so 2C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3Total even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated = Case 1 + Case 2 = 480
:)
Qn2
A closed box with a square base of length x and height h, is to have a volume, F, of 150m^3. The material for the top and bottom of the box costs $2 per square metre, and the material for the sides of the box costs $1.50 per square metre. Fnd the value of x and h, correct to 3 decimal places, if the total cost of the materials, C is to be a minimum.
Qn3
A viscous liquid is poured onto a flat surface. It forms a circular patch which grows at a steady rate of 6cm^2/s. Find,
a) the radius r, in pie, of the patch 24 seconds after pouring has commenced.
b) the rate of increase of the radius at this instant, correct to 2 decimal places.
Done reading the qns? Do and see if your answers are correct!
:)
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I seem to have trouble now with integrating ln and e.
Haha, you are having trouble because you are learning sth you don't have to know at O'Level. You don't have to know how to Integrate Ln directly.
Having said this, you note that you must know how to Differentiate Ln, e and Integrate e
For more info on how to differentiate Ln and e, refer to this post >>
http://askalwayslovely.blogspot.com/2007/09/math-differentiation-with-ln.html
Okie how to Int e
Example
Int e^(2x+3) = e^(2x+3)/2 + c (since there are no limits given)
In short to Int e^(wadever) = e^(wadever) OVER (Differentiate wadever)
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!