A maths questions

bonkysleuth SG

I have some questions over here. I want to verify the answers because I do not have the answer sheet and I will be having my paper tomorrow. thanks.

I think there's a little bit of problem of this question.

2cos^y + 3 sin y = 0

you get sin y = -0.5 or sin y = 2

the range is between 0 and pi(in radians)

since y is in the 3rd/4th quadrant, the answer would surely exceed pi and we have to reject sin y =2 since it exceeds 1.

2. evaluate the coefficient of x^-1 in the expansion of ( 1-x)(2 + 2/x)^5. my answer's -160.

3. find the coefficient of x^-15 in the expansion of (x^3 - 1/2x^2)^10.. i got-5/256.

lastly, express in partial fractions.

4x^2 - 11x + 9 / (2x^2 -x -3)(x+5). i realise you can't solve this question using the long division nor any other methods. can someone suggest an alternative?

you do not have to answer all the questions. just do which you guys feel comfortable with... ^^

SexyChin SG

for the first question,

2cosy+3siny=0

siny=-2/3 cos y

tan y = -2/3

y = tan^-1 (-2/3)

angle in 2nd quad, so angle is pie minus tan^-1(2/3).

Mikethm SG

4x^2 - 11x + 9 / (2x^2 -x -3)(x+5)

=4x^2 - 11x + 9 / (2x-3)(x+1)(x+5)

Let 4x^2 - 11x + 9 / (2x-3)(x+)(x+5) = A/(2x-3) + B/(x+1) + C/(x+5)

4x^2 - 11x + 9 = A(x+1)(x+5) + B(2x-3)(x+5) + C(2x-3)(x+1)

Solve A, B and C by comparison or subsitution.

Ahm97sic SG

Hi bonkysleuth,

Alternatively, we can use the cover up method to solve this partial fraction question as the factors in the denominators are linear.

4x^2 - 11x + 9 / (2x^2 -x -3)(x+5)

= 4x^2 - 11x + 9 / (2x-3)(x+1)(x+5) = A/(2x-3) + B/(x+1) + C/(x+5)

[The cover up is done on the part in red]

Cover 2x - 3, substitute x = 3/2 into 4x^2 - 11x + 9 / (x+1)(x+5) to get A

Cover x + 1, substitute x = -1 into 4x^2 - 11x + 9 / (2x-3)(x+5) to get B

Cover x + 5, substitute x = -5 into 4x^2 - 11x + 9 / (2x-3)(x+1) to get C

Thank you for your kind attention.

Regards,

ahm97sic