Search results

1. 1-cos(2x) = 2sin^{2}(x) \therefore 1 - cos(2x) = 1 + cos(2x) cos(2x) = 0 $ Then use the fundamental formula for cosine 2. $ Consider, $ cos(2x) - 2sin^{2}(x) + 1 $ = cos(2x) - (1 - cos(2x)) + 1 = 2cos2x For 0 < x < \frac{\pi}{4} 0 < 2x < \frac{\pi}{2} $ Drawing...

Re: MX2 2015 Integration Marathon q2 is an even function

Re: MX2 2015 Integration Marathon factorise (x^6 - 1) and you'll eventually get int (dx/(x^2 + x+1)(x^3 + 1)) and then partial Idk if there's an easier way

For 1, draw up the two graphs, and integrate with borders making sure to put absolute values wherever, the area goes under the x-axis. For 2, note that : \frac{d}{dx} (-cotx) = (cscx)^{2} So by integrating both sides \int \frac{d}{dx} (-cotx) = \int (cscx)^{2} dx -cotx + C= \int (cscx)^2...

~96

Re: HSC 2015 4U Marathon Unless the question says that it's a vertical motion question right?

Why is it more suitable? In both cases, you're differentiating with respect to displacement. Integrating vdv = v^2 / 2

Re: HSC 2015 4U Marathon Shouldn't the first step be something like F_{net} = ma F_{net} = F - kv^{2} ma = F - kv^{2} \frac{dv}{dt} = \frac{1}{m} [F - kv^{2}] Do we need to assume mg acts on it?

Yes, use dv/dt to find velocity as a function of time and d(1/2 v^2)/dx to find velocity as a function of displacement. In 4 unit, it's more common to use vdv/dx to find velocity as a function of displacement.

it's essentially the changeof base law and multiplying both top and bottom by 'n'

Re: MX2 2015 Integration Marathon How did you get those expressions for the integral in the first line ?

Probably not but you should still check with your teacher. I've never seen that used before. When would there be a good time?

thanks guys. anyone else?

Connect O to midpt of chord AB and also to chord CD. This will both be perpendicular (radii bisecting chord is at right angles). Then connect O to P. You can prove congruency in the two triangles and hence prove AB = CD

will English bring me down a lot? Cohort is weak

Comm at Macquarie

92.6

School rank: Around 300 to 400 English Advanced: 26/71 Maths 3u: 4/31 Maths 4u: 2/11 Chemistry: 2/37 Physics: 5/49