Some questions from the Moriah College trial... (1 Viewer)

[lychnobity]

Thanks in advance

 

[gurmies]

For a conic to be an ellipse, it needs to be more or less in the form of x^2/a^2 + y^2/b^2 = 1.

In other words, lambda has to satisfy both >23 and <5, which is impossible, meaning the ellipse cannot exist.

 

[shaon0]

Thanks in advance

for 1) Use demoivre's on z^n+conj. z^n where z=cis@
And;
e^z+e^(/z)
=e^cos@(e^isin@+e^-isin@)

 

[gurmies]

EDIT: Alternatively I could have actually used my brain and let z = x+iy for the exponential one...simplifying things immensely.

 

[untouchablecuz]

...

there may be some issues with taking the logarithm of the presumably complex number, but then thats all uni math crap

 

[untouchablecuz]

no euler in hsc

can we use euler's formula in the HSC?

 

[gurmies]

Provided we derive it, it would be stupid not to be allowed to use it. However, there is the issue of proving that complex numbers can be integrated the same way as real numbers or something along those lines...? Be careful when you take the natural log of both sides:

y = a + b

lny = ln(a+b) and NOT lna + lnb

 

[shaon0]

...

there may be some issues with taking the logarithm of the presumably complex number, but then thats all uni math crap

there maybe a problem with your solution for 1)

 

[untouchablecuz]

there maybe a problem with your solution for 1)

oo yes, there is

thanks for that (you and gurmies)

 

[shaon0]

oo yes, there is

thanks for that (you and gurmies)

Ok nw. btw, 1) has been solved by Gurmies.

 

[gurmies]

Ok nw. btw, 1) has been solved by Gurmies.

Not quite - I cheated

 

[Trebla]

For 3c)
x! + y! = x(x - 1)! + y!
> (y + 1)(x - 1)! + y! (since x > y + 1)
= y(x - 1)! + (x - 1)! + y!
> y.y! + (x - 1)! + y! (since x - 1 > y => (x - 1)! > y!)
= (y + 1)y! + (x - 1)!
= (x - 1)! + (y + 1)!
.: x! + y! > (x - 1)! + (y + 1)!

 

[lychnobity]

A big sincere thank you to all who contributed.