Preliminary mathematics marathon (1 Viewer)

[ohexploitable]

3/m+1****

lol yar, I typed it wrong -.-

 

[ohexploitable]

Post some questions that I can answer!

Haven't done any of this stuff yet >.< Haha.

Factorise:

4x⁴ - 2x³y - 3xy³ - 9y⁴

 

[Gussy Booo]

Well, how far can you go =/

4x^3-2x^3y-3xy^3-9y^4
=4x^3-9y^4-2x^3y-3xy^3
=(2x^2+3y^2)(2x^2-3y^2)-xy(2x^2+3y^2)
= 2x^2+3y^2(2x^2-3y^2-xy)
= (2x^2+3y^2)(2x-3y)(x+y)

 

[Gussy Booo]

I'll give you cute prelims 2 nice questions,

Here's a warm up

1)

a^2 = a+2
a^3 = ?

Express a^3 in linear form.

This one is more fun.

2)

If 2^x = 5^y = 10^z, show that z = xy/x+y

 

[hscishard]

I'll give you cute prelims 2 nice questions,

Here's a warm up

1)

a^2 = a+2
a^3 = ?

1.Confusing. Is it (a+2)root(a+2)?<---- not even linear

The second one is weird.

 

[mirakon]

I'll give you cute prelims 2 nice questions,

Here's a warm up

1)

a^2 = a+2
a^3 = ?

Express a^3 in linear form.

This one is more fun.

2)

If 2^x = 5^y = 10^z, show that z = xy/x+y

a^3= 8 or -1 I assume? It's a simple matter of solving the first for a and then subbing into the latter equation

is Q2 an application of log laws? I think it is but too be honest cannot be screwed to do it here as it's too hard to type without latex and I don't know how to use it

 

[untouchablecuz]

I'll give you cute prelims 2 nice questions,

Here's a warm up

1)

a^2 = a+2
a^3 = ?

Express a^3 in linear form.

This one is more fun.

seeing as you guys arent getting this

a²=a+2
a³=a(a+2)=a²+2a=a+2+2a=3a+2

 

[mirakon]

seeing as you guys arent getting this

a²=a+2
a³=a(a+2)=a²+2a=a+2+2a=3a+2

just asking is linear form in exact value form as well? Like the above?

 

[AAEldar]

Well, how far can you go =/

4x^3-2x^3y-3xy^3-9y^4
=4x^3-9y^4-2x^3y-3xy^3
=(2x^2+3y^2)(2x^2-3y^2)-xy(2x^2+3y^2)
= 2x^2+3y^2(2x^2-3y^2-xy)
= (2x^2+3y^2)(2x-3y)(x+y)

I'd say that's about as far as you can go...

 

[Gussy Booo]

seeing as you guys arent getting this

a²=a+2
a³=a(a+2)=a²+2a=a+2+2a=3a+2

Well done. .
Question was testing more than just knowledge.
3a+2 is in linear form. The highest degree of a, is one.

 

[ohexploitable]

New Question:

Simplify:

 

[Gussy Booo]

A clue for the second question.
NOTE: Does not require logs. It's just a harder application of your normal algebra.

If 2^x = 5^y = 10^z, show that z = xy/x+y

2x5 = 10. Hopefully that gets you somewhere.

 

[Gussy Booo]

New Question:

Simplify:

=sin(-)/1+cos(-) + 1+cos(-)/sin(-)
=sin(-)^2 + (1+2cos(-)+cos(-)^2)/sin(-)(1+cos(-))
=sin(-)^2+1+2cos(-)+(1-sin^2(-))/sin(-)(1+cos(-))
=2+2cos(-)/sin(-)(1+cos(-))
=2(1+cos(-))/sin(-)(1+cos(-))
=2/sin(-)
=2cosec(-)

 

[ohexploitable]

lol no fair, you've done all this before!

New Question:

 

[Gussy Booo]

Do my question:

If 2^x = 5^y = 10^z, show that z = xy/x+y

 

[hscishard]

Someone do mine on page 1. Lol.

 

[mirakon]

Well done. .
Question was testing more than just knowledge.
3a+2 is in linear form. The highest degree of a, is one.

Hi, I was just wondering if this solution is entirely correct.

Doesn't this imply that for any value for 'a' that the answer is '3a+2'? However doesn't this violate the first condition as a^2=a+2 only has two solutions?

 

[hello-there]

New question:

A cubic curve has a minimum point at point (-2,-15), a maximum point at (1,12)
and it cuts the y axis at 5. What is the equation of the cubic?

A good question

is the answer x^3+1.5x^2+4.5x+5

 

[shaon0]

is the answer x^3+1.5x^2+4.5x+5

No, I believe the answer is: P(x)=-2x^3-3x^2+12x+5. But i could be wrong.

 

[hscishard]

No, I believe the answer is: P(x)=-2x^3-3x^2+12x+5. But i could be wrong.

No, that's correct.