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In circle geometry, to prove three points are collinear, say A,B,C, do you have to prove that AB and BC are part of a cyclic quad? Then you prove AB and BC are supplementary. Or can you just prove directly that AB and BC are supplementary

Two chords AB and CD bisect each other at X. Show that this is not possible unless X is the center. NO idea how to approach this one as well. Also Show that in a circle, a shorter chord is always further from the centre than a longer chord.

AB, CD and XY are chords in a circle with centre O. XY cuts AB and CD in L and M, which are the midpoints of AB and CD. Prove that XY is greater than either AB or CD. I hav no idea how to approach this problem

P(x) = x^4 + cx^2 + e, where c and e are real If sqrt3 + i is a root, determine c and e, then factor into quadratic factors with linear factors Here's my attempt: Since c and e are real, then sqrt3 - i is a root (complex conjugates theorem) Also P(-x) = P(x) therefore P(x) is even...

When I intergrated: 1/sqrt(x)sqrt(1-x) = I, Ive got sinh sqrtx. This i used a subsitution x=u^2 However, expanding the bottom; I = 1/sqrt(x-x^2), then chaging the denominator to a perfect square: I = 1/sqrt (1/4 - (1/2-x)^2), then using the same sin inverse identity, i got a complete different...

Do we have to know all the speeches or just select a few?

How do you do middle of sequence questions? They kill me and takes a very long time to do. Help?

In this question Deduce cos4a = 8(cosa)^4 - 8(cosa)^2 + 1 hence solve 8x^4 - 8x^2 +1 = 0 Ive done all except this part: Deduce exact values of cos(pi/8) and cos (5pi/8) Im using sum and product of roots and im getting cos^2(5pi/8)cos^2(pi/8) = 1 and cos^2(5pi/8) + cos^2(pi/8) = 1 But i...

To all the employees/managers out there of retail stores have you had any experience with corporate sponsorship of schools? I am not talking about anything big, but just some small support for the school, like sporting equipment per say. Who would I contact in such a situation? If I am...

Could someone perhaps enlighten me on the difference between these two concepts? For it is thoroughly confusing.

When considering hyperbola via parametrics, how come the angle (a) for the RHB is limited to pi/2 - -pi/2 whilst on the LHB, (a) is limited to -pi/2 - -pi and pi-2 - pi

When integrating by parts, such as integral arccosx why cant we use let x=cos a

I am just interested to know when the syllabus specifies environment affecting phenotype, do they mean that the environment triggers a change in the genotype, i.e. signaling the switch on/off of a gene, OR do they mean the environment affecting the phenotype, without affecting the genotype.

If a, b ,c, d are the coefficent of any four consecutive terms in the expansion of (1+x)^n, prove that: \frac{a}{a+b} + \frac{c}{c+d} = \frac {2b}{b+c}

A vessel is being filled at a variable rate and the volume of liquid in the vessel at any time t is given by: V=A(1-e^-kt) b) If one quarter of the vessel is filled in 5 minutes, what fraction is filled in the next five minutes.

Find the speed and direction of a particle which , when projected form a point 15m above the horizontal ground, just clears the top of a wall 26.25 m and 30m away.

For SHM say this Q A particle executes SHM with n =pi/4 a =10 Find v and aceleration at x=6 When finding v v^2 = (pi/4)^2(64) How do we take the sign from here on? Also for max acceleration i argued that it occurs at x=0 but acceleration then = -3pi^2/8 So what reasoning is used to say...

If w is a compelx cube root of 1, form a cubic with root (a+b)^-1, (aw+b)^-1, (aw^2 + b)^-1

Solve the differential equation a (d2x/dt2) + 16x = 0 (SHM) Also, when solving strait line motion equations. How do we take the signs. For example A particle moves in a straight line so that at any time t, its displacement from a fixed origin is x and its velocity is v. If acceleration is...

Parabola x=2at, y=at^2 has parameters p, q etc.. M is mid point of chord PQ, T is point on parrabola where tangent is parrallel to PQ and I is point where the tangents at P and Q intersect M,T,I lie on a vertical line, with T the mid point of MI The tangent at T bisects tangents PI and QI What...