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Ships A and B leave port P at the same time. Ship A sails 4km on a bearing of 40 degrees , then a further 6km on a bearing of 155 degrees to reach destination D. Ship B sails directly from P to the the destination D. In which direction does Ship B sail? I solved this in two ways (sine...

thanks, what if its x^x=sqrt(27/8)?

Is the answer to x^(2/3)=4 a) 8 b) 8 or -8?

Hi guys, for those who sat the 2014 AMC, could someone please enlighten me on the last 2 questions. Especially the last question...i dont see any pattern for the primes...

Re: HSC 2014 4U Marathon Go http://community.boredofstudies.org/14/mathematics-extension-2/243515/complex-locus-help.html

Re: HSC 2014 4U Marathon We're looking for a geometrical approach without using algebra. So no solving equations(at least not simultaneous equations) if that makes sense

Re: HSC 2014 4U Marathon

Re: HSC 2014 4U Marathon Without letting z=x+iy, explain why the locus of arg(z-3-4i)-arg(z-2+2i)=\frac{\pi}{3} is the major arc of a circle. Find the centre of this circle without letting z=x+iy.

Re: HSC 2014 4U Marathon $Given$\ x,y,z \geq 0\ ,\\ $R.T.P.$\ (x^2+1)(y^2+1)(z^2+1)-(x+y+z- xyz)^2 \geq 0\\ $LHS$=x^2y^2+x^2z^2+y^2z^2-2xy-2xz-2yz+2x^2yz+2xy^2z+2xyz^2+1\\ $But$\ (xy+xz+yz)^2=(x^2y^2+x^2z^2+y^2z^2)+2x^2yz+2xy^2z+2xyz^2\\ \therefore \...

In circle geometry, when we say an angle is standing on an arc, do we mean it stands on the major arc or the minor arc?

Thanks and yes i see what you are saying. But what i am saying is: If we have zw=r_1 r_2 cis(\theta_1+\theta_2), then we can say z^2=r^2cis(\theta+\theta), and it is true that z^n=r(multiply itself n times) X cis(\theta(adding itself n times))=r^n cis(n \theta). Is that not proving DMT for...

I'm confused...MUST you use induction to prove De Moivre's theorem(by the way how do you prove De moivre's theorem for negative integers?)? I mean, isnt zw=r_1 r_2 cis(theta_1+theta_2)? then isnt it obvious that z^n=(r^n)cis(n theta)? so why induction?

does it have something to do with principal argument in this case?

yeah that gives me -pi/4< arg(z) < pi/4 but on wolfram alpha it gave me something weird, try typing "arg(z(1+i))< pi/2" and see the plot that wolfram alpha returns

sorry had a few issues with typeset

How do one sketch 0< arg(z(1+i)) < pi/2

Please help

Re: MX2 Integration Marathon Ok, it's by parts twice, letting primitive be e^x in both times.too much tex to type...

ok...so does anyone else have a copy?

Why is limit as x -> infinity that y goes to 0? How do you explain this without using l'hopital's rule?