Search results

You can use the product of intercepts of intersecting chords theorem. Basically, CE*EF=AE*EB. Since CD bisects AB, AE=EB=7.5. Hence, CE*2=7.5^2 --> CE=7.5^2/2 = 28.125 cm

Haven't done any work since last year :(

nah stop lying mate

nice

Me three

yeh its most likely acidic environment

Another possible method: Since it's parallel to that line, the tangent is in the form of y=-2x/3 + b Now sub this into the equation of the ellipse to get a quadratic in x. Since the line is a tangent, there is only 1 point of intersection, so there are only 1 solution (1 value of x) thus ∆=0. By...

hsc marks releasing tomorrow right? Well good luck all haha

$\noindent$ $ Normal at P: $x+py=ap^3+2ap \\ $ Normal at Q: $ x+qy=aq^3+2aq. \\$ To find the intersection of these normals, solve them simultaneously. You can subtract them to eliminate $x. \\ \therefore py-qy=ap^3-aq^3+2ap-2aq. \\y(p-q)=a(p^3-q^3)+2a(p-q)$ factorise the difference of cubes...

Re: HSC 4U Integration Marathon 2017 I=\int \frac{(3+4\cos x)}{(4+3\cos x)^2}$ d$x\\ $ Let $t =\tan \left ( \frac{x}{2} \right )\\ $ d$t=\frac{1}{2}\sec^2\left ( \frac{x}{2} \right )$ d$x\\\Rightarrow $ d$x=\frac{2}{1+t^2}$ d$t \\I= 2\int \frac{\left...

dw cause you're gonna be the dux anyway

Ye for that question, but doesn't have to be true for any other Qs. even if it starts at 0m off the ground, it could end up landing on a 200m cliff. The only time where you can double the time of max height to find the time of flight is when the change in y displacement is 0. ie, the projectile...

So I was just notified by my school that im eligible for this scholarship from western Sydney university. It's valued at $20000 while also getting a guaranteed entry into WSU and a vip meeting (or something like that idk). The problem is that, I was originally thinking of doing Bachelor of...

For part ii) Turn the mod arg form into x+iy and simplify to get 4z-4=z(1+root3i). Rearrange to get 3z-z√3 i =4. z(3-√3 i)=4. Now make z the subject z=4/(3-√3 i) realising this, we get Z= (4(3+ √3i))/(9+3). Simplify, then Z=(3+root 3i)/3 Typing on phone so soz if it's messy

oh man thats genius

you can write that infinite sum as Im(cisx+cis2x+cis3x+...+cisnx) = Im(cisx+cis^2(x)+cis^3 (x) + ...+ cis^n (x) [DMT]. This is a geometric series, and so you use the formula for the sum of geometric series; Sn=(a(r^n-1)/(r-1)). They have basically written that in terms of t. So both the common...

If you simultaneously try to solve the equation of the parabola and chord of contact equation, (note that a=1) then you'll end up with a quadratic in x. The roots of this quadratics are the x coordinate of M and Q. So to find the midpoint of it, youll do (x1+x2)/2= sum of roots/2. Now the sum of...

Re: HSC 4U Integration Marathon 2017 started ages ago, from watching vids and looking at other peoples working out on marathons. (thats partially how i grasped integration by substitution lol, by looking at people making dx the subject etc). Then participating in marathons strengthens the...

Re: HSC 4U Integration Marathon 2017 lmao no way, I shouldn't be even compared to him

Re: HSC 4U Integration Marathon 2017 $\noindent$I= \int \frac{1-a^2}{1-2a \cos x + a^2}$ d$x \\ = (1-a^2)\int\frac{1}{1+a^2-2a(2\cos^2(\frac{x}{2})-1)} $ d$x \\(1-a^2) \int \frac{1}{(1+a)^2-4a \cos^2 \frac{x}{2}}$ d$x\\\\ $Let $t=\tan \frac{x}{2}\Rightarrow $ d$t=\frac{1}{2}\sec...