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#176 Re: Exercises » Integration by Substitution » 2009-08-14 02:57:44

Nice solution rzaidan, but I think the step of multiplying by (secx + tanx) requires a big leap of faith whereas u-substitution does not.

#179 Re: Puzzles and Games » Sum of fractions which equals 1 » 2009-08-11 18:41:45

So could this problem be solved theoretically?

#180 Re: Puzzles and Games » Sum of fractions which equals 1 » 2009-08-10 23:34:23

Just wondering, are there number theory problems for which there is a proof that a solution cannot be reached without brute force?

#181 Re: Dark Discussions at Cafe Infinity » VCE mid-year results » 2009-08-03 03:22:30

Congratulations glenn!
Have you been to vcenotes.com? There's a great community there to discuss vce!

#183 Re: Help Me ! » Number of roots of a number » 2009-08-01 03:44:30

But who's to say

is 'more' positive than
?

After all, aren't they off the real-number line?

#185 Re: Help Me ! » Number of roots of a number » 2009-07-31 04:08:02

I don't see how it makes a difference? If you multiply the right equation by -1 you still get

,

#187 Help Me ! » complex log (basic) » 2009-07-31 01:31:10

Identity
Replies: 2

Let

Show that

is a logarithm of

#188 Help Me ! » Number of roots of a number » 2009-07-31 00:57:34

Identity
Replies: 11

This issue came to my attention while doing a practice exam paper. The question is to find

. The solution goes:

So I tried extending this to real roots:

Suppose

for some number a.

I always learnt in school that

implies the positive root though! What is correct??

Also, is the story the same for

?

#189 Re: Maths Is Fun - Suggestions and Comments » Dividing by Zero » 2009-07-29 21:57:42

For centuries it has been undefined, but today...

...I define it to be equal to be 42!!!

#190 Re: Help Me ! » simplify to cosh(x) » 2009-07-20 18:04:07

Thankyou anyway, it is always good to see more approaches to a problem smile

#191 Re: Help Me ! » A Kinematics Question » 2009-07-18 16:55:32

LOL oh no

I was meant to do

!!

aaaah thanks ricky

#192 Help Me ! » A Kinematics Question » 2009-07-18 15:44:08

Identity
Replies: 3

If a = 2-v and v = 0 when x = 0, find x when v = -2

thanks!!

#193 Re: Help Me ! » simplify to cosh(x) » 2009-07-18 15:41:18

I'm wondering how it is equivalent though, I mean like...

If you had

, and you wanted to find x in terms of t, you could solve for x with soroban's answer, but how can you do it with bobbym's?

#196 Help Me ! » simplify to cosh(x) » 2009-07-17 18:54:05

Identity
Replies: 10

Can someone explain how

simplifies to

thankyou



also another question

how do you find

!

#197 Re: Jokes » That's Mathematics! » 2009-07-17 15:48:27

Tom Lehrer is fantastic!

#198 Re: Help Me ! » Average acceleration » 2009-07-15 22:36:51

Thanks, maybe the book was wrong

#199 Help Me ! » Average acceleration » 2009-07-15 00:50:40

Identity
Replies: 5

A particle moves in a line with velocity

given by
. The object starts from the origin. Find the average acceleration over the third second.

The answer is

but no matter what I try I can't seem to get it.

If t=0 to t=1 is the first second, then t = 2 to t = 3 should be the third second, but I've found v(3)-v(2) and it's still not right!

#200 Re: Dark Discussions at Cafe Infinity » Name a species... » 2009-07-12 07:40:03

Yeah, that's exactly what I get. Even raising the temperature by 1 degree would require

nukes, which is ridiculous, seeing as we only have 23000 nukes in the world.

The nuclear winter would be more catastrophic however, it could plunge the whole world into a possible ice age. Humans would likely not survive. But an ice age has occurred before, and those lucky enough to be adapted to it will survive. In particular, I've heard that co.ckroaches are specially adapted to survive nuclear fallout.

I don't know which species would survive, but an ice age has occurred before, and obviously certain species did survive.

I think suicidal bombardment is the 'best' way humans could try to eradicate another species. They would succeed with most species, but not with all.

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