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In 5 it says it sits on a bowl. Wherever it sits, the normal acts perpendicular to the surface, ie perp to the tangent. Similarly in 6 the force is perpendicular to the surface, which is the table.

In 5 its perpendicular to the tangent to the point of contact on the hemisphere. In 6 its perpendicular to the table, that is straight up.

It is always perpendicular. In example 8 the slant of the surface at that point is the tangent, so the normal force is perpendicular to it.

5^n = (3+2)^n = 3^n + 3^n-1.2 + ..... + 2^n > 3^n + 2^n, for n>1

The locus where the product of distances from two points is a constant is a Cassini's oval, but what the hell is that?

Usyd has a new combined science/MB BS/ PhD program lasting 10 years.

Then you're probably looking at mb bs, then phd, and working as a clinician/researcher.

http://medicalsciences.med.unsw.edu.au/medsciences.nsf/RI-All/7401145?OpenDocument Are you looking for something along these lines?

Go check the state rankings for last year for Laurie Field, and count all the units he was ranked in.

A medical science degree maybe, or advanced science?

Deleted posts.

Draw 1/sqrt(x+1). Draw vertical lines on each integer. Complete the rectangles so their areas are 1/sqrt2, 1/sqrt3, etc up to 1/sqrtn. Integrate from 0 to n-1. Hence as the rectangles have a greater area than the integral, ( 1/sqrt(2) ) + ( 1/sqrt(3) ) + ... + ( 1/sqrt(n) ) > int 1/srt(x+1)...

So In = 1/(n+1)(n+2) Similarly work out In-1 = 1/n(n+1) So In = n/(n+2) In-1

Substitute n - 1 for n into that integration result and you can prove the reduction formula as well.

You can find that by 3u volumes. Equation of semicircle is y = sqrt (a^2 - x^2). Revolve around x axis and find volume: pi S y^2 from -a to a.

Very nice and elegant. Why is it induction? I guess if you really want to prove it that way, write X = 4n + 7m. Then X + 1 = 4n + 7m + 1 and peel off 4s and 7s, eg 4(1 + p) etc. and then factorise.

Do you mean 18 cents and any multiple of 18 cents?

Ha. It's true though. In 3u trials I lost a few marks for Newton's method, and some other things in questions 4 and 5. In 4u trials I got 13 for q8, but lost marks in 1,2 and 3 for stuff like integration. In 4u hsc I reckon I lost most marks in the probability question, which was in 4 i think...

Comment: 1/8 is not greater than 1/4. The proof is wrong because ln (1/2) is negative.

The lines are very long, and they keep on running out of stuff.