Bunch of Maths Questions (1 Viewer)

[boongsta]

Hey can you guys show ALL your working out for me just so I learn

1. Factorise: 5x^2-9x-2

2. If 3 / (2(3)^1/2 - 5) =a (3)^1/2 + b, find the values of a and b

3. simplify 2/(2x^2-x-1) - 6/(4x^2-1)

4. Express 3x^2 - 5 in the form A(x-2)^2 + B(x-2) + C

5. If tan theater = -0.3 and sin theater > 0. Find the exact value of Cos theater.

6. Find the equation of the directrix for the parabola (x-2)^2=-4y

7. Sketch the region where y<=(4-x^2)^1/2 and y>x^2-9

8. Find the values of k for which kx^2- 8x+k is negative definite.

Thanks in advance guys any help is appreciated

 

[webby234]

1. (5x+1)(x-2)

2. 3/(2rt3-5)

= 3(2rt3+5)/-13

= -6rt3/13 - 15/13

a = -6
b =-15

3) 2/(2x^2-x-1) - 6/(4x^2-1)

= 2/[(2x+1)(x-1)] - 6/[(2x+1)(2x-1)]

= [2(2x-1) - 6(2x+1)]/[(2x+1)(2x-1)(x-1)]

= (4x-2-12x-6)/[(2x+1)(2x-1)(x-1)]

= -(8x+4)/[(2x+1)(2x-1)(x-1)]

= -4/([2x-1)(x-1)]

 

[webby234]

4. A(x-2)^2 + B(x-2) + C

=Ax^2 - 4Ax +4A +Bx - 2B +C

= Ax^2 - (4A+B)x + (c- 2B)

Equating coefficients

A = 3
4A + B = 0
B = -12
C-2B = -5
C = -29

5) tan is -ve and sin is positive so theta is in the second quadrant

tan = opp/adj = 3/10

hypotenuse = rt109

cos theta = adj/hyp = 10/rt109 = -10rt109/109

 

[webby234]

6. a = -1

Vertex at (2,0)

So directrix y = 3


8. kx^2- 8x+k

b^2 - 4ac < 0 and a is negative

64 - 4k^2 < 0

k^2 > 16

k < -4

 

[Mountain.Dew]

Hey can you guys show ALL your working out for me just so I learn

4. Express 3x^2 - 5 in the form A(x-2)^2 + B(x-2) + C

5. If tan theater = -0.3 and sin theater > 0. Find the exact value of Cos theater.

6. Find the equation of the directrix for the parabola (x-2)^2=-4y

7. Sketch the region where y<=(4-x^2)^1/2 and y>x^2-9

8. Find the values of k for which kx^2- 8x+k is negative definite.

Thanks in advance guys any help is appreciated

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

let x = 2 ==> equation 1
let x = 1 => equation 2
let x = 0 ==> equation 3

SOLVE SIMULTAENOUSLY

5) use right angled triangles. u will eventually get cos@ = - 10/sqrt(109)

6) ==> 4a = -4, a = -1

therefore, directrix is y = -a = -(-1) = 1, y = 1

7).....

8) the equation kx^2- 8x+k is negative definite IF k < 0 AND discriminant < 0. use that information to find k.

 

[boongsta]

Thanks guys its really helpful going over this stuff i really gotta learn it

 

[Riviet]

Hope that helps.

 

[boongsta]

Shizen man thanks for taking the time to do that ... but how did u get the values of y? did u just sub in x values over and over till u have enough points???

 

[Riviet]

how did u get the values of y? did u just sub in x values over and over till u have enough points???

I substituted x=+2 into the parabola y=x²-9 to find the points of intersection of the two curves, I knew it was x=+2 because that's where the regions intersect.

 

[pLuvia]

A little bit big isn't it

 

[Riviet]

A little bit big isn't it

Yeah I noticed that, it's better than too small. =P
Remember that cellulose dot point summary I posted up? - that one was enormous. XD

 

[pLuvia]

Yeah I noticed that, it's better than too small. =P
Remember that cellulose dot point summary I posted up? - that one was enormous. XD

I sure do