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13C6 + 13C5 = 13!/6!7! + 13!/5!8! = (8(13!) + 6(13!))/8!6! =14!/8!6! =14!/8!(14-8)! or 14!/6!(14-6)! =14C8 or 14C6 or =15!/8!6!(5x3) =15!/5!(3x3x2x5x8!) =15!/5!(8!x9x10) =15!/5!10! =15C10 or 15C5 or =3003 =3003C1 or 3003C3002 or...

Just so the x^2 doesn't have 0.25 as a coefficient, just makes the function look nicer really. Can multiply both numerator and demonitator by 4 because it's really just multiplying the function by 4/4, which is one and doesn't change the function.

Multiplied both numerator and denominator by 4.

The mistake is in your second step, where you have multiplied -0.5x by 2, then squaring. The order of operations requires for the -0.5x to be squared first, as indices come before multiplication and the entire -0.5x is in parentheses, hence it is all included. Squaring -0.5x first will give...

NESA has a sample HSC paper, including all topics in the new syllabus. AceHSC (website) has a sample 3D vectors exam in its resources section. The VCE has included 3D vectors in its highest level of maths (Specialist Mathematics) in previous years, so it is worth looking at the past papers and...

The general equation for displacement in respect to time for SHM is x = acos(nt+b), a>0, n>0 The particle starts from rest (hence t=0) 10 metres to the right of its centre of oscillation (origin). Note that the particle starts from rest, so this point would be a turning point on its cos graph...