HSC Mathematics Marathon (3 Viewers)

hscishard

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Use basic geometry. The locus is a circle, contruct a triangle joining the centre, (0,1) and (0,-1) and make a chocolate cake. The length of the base is obvious (2), the angle subtended at the centre is twice the angle at the circumference (pi/2). Now find the height of the circle to get the coordinates of the centre then find the radius. The cake is a lie.
You need to restrict the range too if you're going to show it algebraically
 

blackops23

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Use basic geometry. The locus is a circle, contruct a triangle joining the centre, (0,1) and (0,-1) and make a chocolate cake. The length of the base is obvious (2), the angle subtended at the centre is twice the angle at the circumference (pi/2). Now find the height of the circle to get the coordinates of the centre then find the radius. The cake is a lie.
I see...
 

rawrence

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rawrence - looks like you are ahead of the pack; most have not done this topic yet. Have you already done this question?


a)












b)







Correct!

And yes, I have done it, my school's putting everything except mechanics and probability from harder 3 unit

D :
 

ZachBC_94

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Slightly unrelated, but ohexploitable, is your avatar from Gossip Girl?

Also, as we have an absence of questions:

If In = (Integral from 1 to 0) x^n tan(inverse)x dx, n = 0, 1, 2, ...
Show that In = 1/(n+1) * π/2 - 1/[n(n+1)] - (n-1)/(n+1) * I(n-2), n = 2, 3, 4, ...

Sorry, don't know latex
 

ZachBC_94

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why thank you. I'm only new at it, that's why all the fractions are still in x/y form for instance
 

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