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How would you sketch this? It's a HSC question.
2016 HSC (Accelerated)
// 2 Unit Maths // Studies of Religion 1 //
2017 HSC
// Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //
2016 Preliminary
Maths Extension • English Advanced • Biology • Legal Studies • Physics • PDHPE
2017 HSC
Maths Extension 2 • English Advanced • Biology • Physics • PDHPE
Atar aim: 97
Desired Course: Physiotherapy
2016 Preliminary
Maths Extension • English Advanced • Biology • Legal Studies • Physics • PDHPE
2017 HSC
Maths Extension 2 • English Advanced • Biology • Physics • PDHPE
Atar aim: 97
Desired Course: Physiotherapy
That's just hazy high school science definitions. There are various precise definitions of lines/curves of best fit (regression analysis, interpolating polynomials etc), and whenever such an object is named a line it is definitely a line in the usual sense of the word (at least as far as I have seen).
Is there a way to expand it so the cis2kpi/5's cancel out, leaving only the z^5-1?
Quick question: When we are finding the roots of unity (or any complex number) and leaving it in mod-arg form do we have to change the argument to the principle range or just leave it as it as (e.g. for k=5 arg = 15pi/8). The answers in past papers leave it as it is...so not sure what to do.
2016 Preliminary
Maths Extension • English Advanced • Biology • Legal Studies • Physics • PDHPE
2017 HSC
Maths Extension 2 • English Advanced • Biology • Physics • PDHPE
Atar aim: 97
Desired Course: Physiotherapy
2016 HSC (Accelerated)
// 2 Unit Maths // Studies of Religion 1 //
2017 HSC
// Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //
Last edited by InteGrand; 6 Dec 2016 at 8:27 PM.
This is probably a vague explanation but...
In the case where both roots are real.
The sum of roots = -b/a, which is negative if a,b are either both positive or both negative. This implies that at least one of the roots is negative.
Product of roots = c/a, if the roots are both negative, then the product must be positive therefore a,c must be both positive or both negative.
If the roots are complex, they must be in conjugate pairs due to real coefficients, this means that the real parts must be the same.
So if the real part is negative, then the sum of roots must be negative, and the product of roots must be positive.
“Smart people learn from their mistakes. But the real sharp ones learn from the mistakes of others.”
― Brandon Mull
This geometry question doesn't involve any advanced knowledge but requires a bit of creativity.
ABCD is a quadrilateral with three equal sides AB,BC and CD. Show that the mid-point of AD lies on a circle with diameter BC if and only if the area of ABCD is a quarter of the product of its diagonals.
A question posted in the 2016 MX2 marathon by Paradoxica that wasn't answered:
Mathematics Extension 2 - Physics - Chemistry - Economics - English Advanced
MX2 - ADV - ECO - BUS
Suppose you have n points on a circle such that no three distinct chords coincide at any single point.
How many regions do the nC2 chords divide the interior of the circle into?
(You don't have to provide rigorous proof for this question if you can guess the answer correctly).
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