Search results

Re: HSC 2013 4U Marathon $Prove that$ 1+ \frac{1}{2^2} + \frac{1}{3^2} + \dots + \frac{1}{n^2} < 2 - \frac{1}{n}

Re: HSC 2013 3U Marathon Thread Yep and \int_{\pi}^{2\pi} \sin x = - 1 So the answer should be 2 :P

Re: HSC 2013 3U Marathon Thread Nope the absolute value needs to be there, and you did the right thing by splitting into 4 integrals (only 2 is needed though). \int_{\pi}^{2\pi} |\sin x| \ dx \neq \int_{\pi}^{2\pi} \sin x \ dx

Re: HSC 2013 4U Marathon $A projectile is fired in a medium of no air resistance, and lands on an inclined plane of angle$ \ \ \alpha $It is fired with some velocity, at$ \ \ \theta \ \ $to the horizontal, the projectile is fired from the start of the inclined plane$ $The projectile lands...

Re: MX2 Integration Marathon \int \frac{x^{-\frac{1}{2}}}{1+x^{\frac{1}{3}}} \ dx

Re: HSC 2013 3U Marathon Thread \int_0^{2\pi} \sqrt{1-\cos^2 x} \ dx

re: HSC Physics Marathon Archive $A black hole is a body that light cannot escape$ $Hence its a body where the escape velocity is greater than the speed of light$ $Knowing that escape velocity is given by$ v_e = \sqrt{\frac{2GM}{r}} $We have to find$ \ \ r \ \ $such that$ \ \ v_e = c...

re: HSC Physics Marathon Archive I'm doing Astrophyiscs.

re: HSC Physics Marathon Archive $i) How much energy does a 500g energy drink contain?$ $ii) It is impractical to extract this energy from the mass, the only way to convert energy from mass is a collision of matter and anti-matter$ e^{+} + e^{- } \rightarrow 2\gamma $Is the collision...

Re: HSC 2013 4U Marathon $Someone swings a rock of mass$ \ \ m \ \ $attached to a string, in a vertical circle in uniform circular motion$ $By considering Tension in the string, show that IF the rock makes a full revolution, then the velocity$ \ \ v \ \ $must be$ v > \sqrt{gr} \ \ \...

$Step 1: \ \ n=1$ 1 \leq \frac{1(7)}{6} \ \ $True$ $Step 2:$ \ \ n=k $Assume true$ \ \ \sqrt{1} + \dots + \sqrt{k} \leq \frac{\sqrt{k} (4k+3)}{6} \ \ \ \ \fbox{1} $Step 3:$ \ \ n=k+1 $Prove true that$ \ \ \sqrt{1} + \dots + \sqrt{k+1} \leq \frac{\sqrt{k+1} (4k+7)}{6} $From$ \ \...

re: HSC Physics Marathon Archive $If it were possible to squash the Earth into a smaller sphere without losing any mass$ $How much would you have to squash the Earth, so that the Earth becomes a black hole?$

2-\frac{1+x}{6} = 2x By making a common denominator. \Rightarrow \frac{12-(1+x)}{6} = \frac{12x}{6} Then multiplying 6 to both sides of the equation, to eliminate the fraction (or cross multiply, same thing). 12-(1+x) = 12x Expand the minus in: 12 - 1- x = 12x Collect like terms...

Re: HSC 2013 4U Marathon Allowing x to be the distance to the point on the circular table to the actual ball, then we have a triangle of sides, d (the distance), x and 1, with angle theta. (I am assuming constant speed for the ball) So by the cosine rule: d= \sqrt{x^2-2x\cos \theta + 1}...

Re: HSC 2013 4U Marathon Yep I get it. I'll see what I can do with this though.

Re: HSC 2013 4U Marathon Why do we need to integrate with respect to something that changes at a constant rate?

1. \ \ y=4^x + 1 = e^{\ln(4^x)} + 1 = e^{x \ln 4} + 1 You can do the rest, using \frac{d}{dx} e^{f(x)} = f'(x) e^{f(x)} 2. \ \ y= \log_3 x = \frac{\ln x}{\ln 3}= \frac{1}{\ln 3} \ln x \ \ \ $Since$ \ \ \log_b a = \frac{\log_c a}{\log_c b} \ \ $(logarithm law)$ The rest is just...

Well its a private school so it can implement these policies if it wants, mine has it too and it makes absolute sense. Why should an advantage be given to people who choose not to come to school just so they can study?

Re: HSC 2013 4U Marathon I'll leave the previous question to someone else. Here are my answers to this one: $Max$ = 1 $Min$ = \sin \theta $Average$ = \sin \theta \cdot \ln \left |\frac{1+\cos \theta}{1-\cos \theta} \right | $If the ball undergoes a 'period', whereby it hits the same...

I'm not supposed to do your assignment for you, make your own, its not hard. Nah this thread is intended for people to give praise for silly teaching method OP has, instead of giving helpful criticisms and suggestions, because after all forums aren't used for the latter, right?