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1. Colinear Points

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
2. Circle Geometry: Trivial Question on Chords?

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.
3. Circle Geometry: Shortest 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
4. Complex Roots of Polynomial

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...
5. Integration Help?

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...
6. Speeches

Do we have to know all the speeches or just select a few?
7. Umat: S3

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

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...
10. Texual Format Vs Medium of Production

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

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
12. Integration by parts

When integrating by parts, such as integral arccosx why cant we use let x=cos a
13. Environment Affecting Phenotype

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.
14. Binomial

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}
15. Volume Question - dN/dt = k(N-P)

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.
16. Projectile Motion

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.
17. SHM - Sign Taking

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...
18. Polynomials

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

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...
20. Locus Help

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...