Search results

Uhh, beg to differ with this sentiment. I don't think it is easier for competent arts/comm students to get a high wam than it is for competent science students (I know less about engineering, but I doubt it is harder to get consistently high marks than it typically is in arts). It might be...

Re: HSC 2015 4U Marathon Of course. I suspect it could well be true for this function with that condition, but you certainly can't phrase it as an injectivity type argument as he/the tutor did. Injectivity is precisely what you need to prove to draw that conclusion!

Re: HSC 2015 4U Marathon Lol, his tutor really shouldn't be tutoring then. Is he really not convinced? Ask him how the situation in his question differs from that in my example. It seems his claim is that for an arbitrary function f(x,y), that if f(x,y)=f(y,x) then x=y. Ask him if he thinks...

Re: HSC 2015 4U Marathon a might be forced to equal b (not going to check this myself right now), but the reasoning is not. Eg x+y = y+x for all x and y whatsoever, but this does not tell us that x=y.

Dropping down to general is prioritising the short term over the long term if you want to do a sciencey degree. If all you want is to get as good grades in HS as you can and you think this will do it then okay, but if you actually want to understand any real science you really shouldn't drop.

Re: HSC 2015 4U Marathon So an approach similar to Sy's in spirit works here. Recall from my previous post that a complex polynomial p such that p(x) is real for all real x must in fact be a real polynomial. q(x):=p(x)\overline{p}(x)=p(x)\overline{p(x)}\in \mathbb{R} \quad \forall...

ut99 was/is amazing. also played tacops back in the day!

Re: HSC 2015 4U Marathon Nice :). My way was essentially the same: $For $P(z)=\sum_{k=0}^na_k z^k$, we define the real polynomials $\Re(P)(z)=\sum_{k=0}^n \Re(a_k)z^k$, $\Im(P)(z)=\sum_{k=0}^n \Im(a_k)z^k$, and the conjugate polynomial $\overline{P}(z)=\sum_{k=0}^n \overline{a_k}z^k.$ \\ \\...

Re: HSC 2015 4U Marathon .

LHS=\frac{d}{dx}((1+x)^n)|_{x=1}=n(1+x)^{n-1}|_{x=1}=RHS.

Re: HSC 2015 4U Marathon Two more polynomial questions: Let p be a degree n polynomial with complex coefficients. 1. If the roots of p form an equilateral n-gon, show that p' has a single root of multiplicity (n-1), located at the centroid of this n-gon. 2. Given that p(ix) is real for every...

Re: HSC 2015 4U Marathon Given that every degree n polynomial with real coefficients has exactly n complex roots (counting multiplicity), show that the same is true of every degree n polynomial with complex coefficients. (Obviously, you may not assume the fundamental theorem of algebra for...

47. Largely depends on what you have learned / what definition of determinant you are working from. Since you are just talking about square row echelon matrices (which are necessarily upper triangular), you can probably just use the fact that the determinant of an upper triangular square matrix...

I walk to think about problems. Change of environment definitely helps creative thought.

A grad student and still yes.

Re: HSC 2015 4U Marathon - Advanced Level This is only necessarily true if: a) The polynomial has real coefficients. (Otherwise any three different complex numbers with the same imaginary part can be non-real roots of a polynomial with positive \Delta.) b) The polynomial has distinct roots...

(Not created by me.) Cheryl Welcome, Albert and Bernard, to my birthday party, and I thank you for your gifts. To return the favor, as you entered my party, I privately made known to each of you a rational number of the form n-1/2^k-1/2^{k+r}, where n and k are positive integers and r is a...

Re: MX2 2015 Integration Marathon Or if you want real quadratic factors: x^4+1=(x^2+1)^2-(\sqrt{2} x)^2=(x^2+\sqrt{2} x+1)(x^2-\sqrt{2} x+1).

Re: HSC 2015 4U Marathon - Advanced Level Do you understand the definition of a convex set in the first sentence? Then the second sentence is just asking: If we have a finite collection of convex sets in the plane such that any three sets from this collection share a common point, then show...

Haha I can't wait to get 4-stocked by mango in friendlies next month. Do you play? There's a skype group of people who play online from around Aus. Depending on distance/connection, the input lag isn't TOO bad. Ps if anyone would like to improve at smash, particularly melee, PM and 64, hit...