a) An odd function is defined by f(x) = -f(-x).
At x = 0, f(0) = -f(-0)
f(0) + f(0) = 0 (since f(0) = f(-0))
2f(0) = 0
f(0) = 0, as required.
b) Take any odd polynomial P(x).
By the remainder theorem, P(x) is divisible by (x + 0) if P(0) = 0.
From (a), we know that for all odd...
Enjambment is pretty much whenever there isn't a punctuation mark (comma or full stop) at the end of a line.
Eg The wind rose high
As if a thousand eagles were sailing through
Enjambment: the sentence continues onto the next line
Here's how it works if you have 4 equations 1, 2, 3 and 4:
Use equations 1 and 2 to make equation 5 (3 unknowns)
Use equations 3 and 4 to make equation 6 (the SAME 3 unknowns)
Use either 1 and 3 or 2 and 4 to make equation 7 (the SAME 3 unknowns).
Now you have 3 equations 5, 6 and 7.
Use 5 and...
Insertion and Selection sort both require the 'shift' manoeuvre (when you insert an item into the array and 'shift' the rest down). This means they are quite inefficient on large amounts of data and are better done using 2 arrays (one for the unsorted pile, one for the sorted). Bubble sort is...
A and B mean you are in the same reference frame as the spaceship. C and D mean you're on Neptune, E means you're on Uranus.
"L is the length observed by an observer in relative motion with respect to the object", that means travelling in any direction.
so in A you're moving TOWARDS...
English Adv - 95
Maths 2u - 95 (08)
Maths Ext 1 - 97
Maths Ext 2 - 94
IPT - 92 (08)
SDD - 96 (08)
Economics - 91
Physics - 91
16 units of band 6... Pretty set :D
God, I really underestimated myself this year... I'm so happy for myself and all my friends :)
Aww wow... Thanks :) Everyone on here seems so clever though... But I haven't been browsing for all that long.
Oh, and I forgot to mention something! 4u and 3u get doubled to 2 units or something... So it still counts as 4 units of maths, even though my 2u mark is rejected... Can't remember...
Errm... I'm new to this site and I've never done this before, so...
Here are some of my marks, hopefully they can give an idea of how I'm going:
Last year (HSC marks and overall internal ranks)
IPT - 92, rank 1/12
SDD - 97, rank 1/4
Maths - 95, rank 1/61
This year (Trial marks and...