MATHS study thread. (1 Viewer)

[mitsui]

here I go~

exact value of tan (15degree)

 

[HamuTarou]

do u prefer the tan(a-b) or sin(a-b)/cos (a-b)

 

[mitsui]

i dont realli know wat it wants.. coz u cant realli express it as an exact number

mite as well put another one up.

make n the subject of S=n/2[2a + (n-1)d ]

 

[HamuTarou]

ok...u can rewrite tan15 as tan(45-30) or tan(60-45)..

the expansion for tan(A-B) is tanA-tanB/(1+tanAtanB)

so tan15=tan(45-30)=tan45-tan30/(1+tan45tan30)

exact values...solve the rest...cbb

 

[klaw]

i dont realli know wat it wants.. coz u cant realli express it as an exact number

mite as well put another one up.

make n the subject of S=n/2[2a + (n-1)d ]

that's just rearranging the equation....

 

[mitsui]

ok...u can rewrite tan15 as tan(45-30) or tan(60-45)..

the expansion for tan(A-B) is tanA-tanB/(1+tanAtanB)

so tan15=tan(45-30)=tan45-tan30/(1+tan45tan30)

exact values...solve the rest...cbb

i swear ineva see it in my life b4!!! O.O!

 

[klaw]

for that Q, you have to make sure you leave it in surd form

 

[drewgcn]

And you're coming 11th/82 in 3u maths?
What school do you go to?

(not trying to be insulting by the way)

 

[mitsui]

err.. cheltenham..
i think it is combined in a way
coz our adv and stand eng r.. xD

 

[insert-username]

Derive the following functions:

1. f(h) = h²

2. y = 4x³

3. f(x) = (x + 5)^6

4. y = (2x² + 3x) ÷ (4x - 7)

5. f(x) = (2x² - 6x)³(3x³ + x)^4

6. y = 1 ÷ √(x-4)³

7. f(w) = (5w - 2)(3w² + 4w)^-5


Fully factorise the following equations:

1. a - 4a + 4

2. a^4 - 16

3. (a+b)(a² - ab + b²)

4. a - 4a + 4 - 9b²


I_F

 

[Yip]

Theres also a nice way to solve tan 15 without using compound angle if anyones interested

from the diagram, tan15=1/root3+2

btw insert-username not to be piccy, but do u mean differentiate? if so, it shoudl be f(x) imo since h isnt anywhere in the equation. ALso, some of the equations to factorize actually look like they should either be expansions or just simple simplifications like a-4a+4=-3a+4 or (a+b)(a^2-ab+b^2)=a^3+b^3

 

[insert-username]

Whoopsie, I'll fix that error...

And the factorisations are meant to be "simple". They're straight off a few past papers I've done - that's what they ask, the perfect square, difference of two squares, sums/diffs of cubes, etc.


I_F

 

[klaw]

Derive the following functions:

1. f(h) = h²

2. y = 4x³

3. f(x) = (x + 5)^6

4. y = (2x² + 3x) ÷ (4x - 7)

5. f(x) = (2x² - 6x)³(3x³ + x)^4

6. y = 1 ÷ √(x-4)³

7. f(w) = (5w - 2)(3w² + 4w)^-5


Fully factorise the following equations:

1. a - 4a + 4

2. a^4 - 16

3. (a+b)(a² - ab + b²)

4. a - 4a + 4 - 9b²


I_F

Derive the following functions? you mean differentiate?

 

[pLuvia]

yeh i was confused as well.....

 

[klaw]

1. f'(h)=2h
2. y'=12x²
3. f'(x)=6(x+5)⁵
4. y'=[4x(4x-7)-9x²(2x² + 3x)]/(2x² + 3x)² (then you simplify it but I cbb)
5. f'(x)=12x(3x³ + x)⁴+108x²(2x²-6x)³
6.y=(x-4)^-3/2
y'=-(3x-4^-5/2)/2
7. f'(w)=(-30w+20)(3w²+4w)(5w-2)^-6+5(3w² + 4w)^-5

 

[Yip]

For the cubic polynomial, 6x^3+6x^2-12x+3=0, where a, b and c represent the roots,
find
(a) a+b+c
(b) 1/a+1/b+1/c
(c) a^2+b^2+c^2
(d) a^3+b^3+c^3

 

[klaw]

For the cubic polynomial, 6x^3+6x^2-12x+3=0, where a, b and c represent the roots,
find
(a) a+b+c
(b) 1/a+1/b+1/c
(c) a^2+b^2+c^2
(d) a^3+b^3+c^3

a)-b/a=-6/6=-1
b)1/a+1/b+1/c=(bc+ac+cb)/abc=(c/a)/(-d/a)
=-2/-.5
=4

 

[HamuTarou]

Derive the following functions:

Fully factorise the following equations:

1. a - 4a + 4

2. a^4 - 16

3. (a+b)(a² - ab + b²)

4. a - 4a + 4 - 9b²


I_F

factorise and simplify?

1 -3a+4 (WTF? cant factorise mate)
2 (a²+4)(a-2)(a+2)
3 (a+b)(a²-ab+b²) <-> (a³+b³) (cant factorise here either)
4 -3a+4-9b² (ok...i'm lost)

weird Q's u have there :S

 

[klaw]

Derive the following functions:

1. f(h) = h²

2. y = 4x³

3. f(x) = (x + 5)^6

4. y = (2x² + 3x) ÷ (4x - 7)

5. f(x) = (2x² - 6x)³(3x³ + x)^4

6. y = 1 ÷ √(x-4)³

7. f(w) = (5w - 2)(3w² + 4w)^-5


Fully factorise the following equations:

1. a - 4a + 4

2. a^4 - 16

3. (a+b)(a² - ab + b²)

4. a - 4a + 4 - 9b²


I_F

1.a²-4a+4=(a-2)²
2.a⁴-16=(a²+4)(a²-4)=(a²+4)(a+2)(a-2)
3.(a+b)(a² - ab + b²)=(a+b)³
4.a² - 4a + 4 - 9b²=(a-2)²-9b²=(a-2+3b)(a-2-3b)

 

[klaw]

factorise and simplify?

1 -3a+4 (WTF? cant factorise mate)
2 (a²+4)(a-2)(a+2)
3 (a+b)(a²-ab+b²) <-> (a³+b³) (cant factorise here either)
4 -3a+4-9b² (ok...i'm lost)

weird Q's u have there :S

I think he meant a²