HSC 2013 Maths Marathon (archive) (1 Viewer)

Status
Not open for further replies.

Youi_

Member
Joined
Mar 13, 2013
Messages
67
Gender
Male
HSC
2013
Re: HSC 2013 2U Marathon

I guessed the decimals, and yes I do work out a little bit thanks for noticing.
One day you will be truly funny but keep trying you get better with practice.... Have you ever said these jokes to yourself before posting them online and do they ever seem funny to you :p

Edit: I wasn't even talking to you
 

andybandy

Member
Joined
Sep 1, 2012
Messages
294
Gender
Male
HSC
2013
Re: HSC 2013 2U Marathon

Working out? Or did you just guess the decimals by some random stroke of luck
<a href="http://www.codecogs.com/eqnedit.php?latex=\textup{Let&space;}&space;t&space;=&space;1" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\textup{Let&space;}&space;t&space;=&space;1" title="\textup{Let } t = 1" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=P&space;=&space;100(1.23)^{1}&space;\therefore&space;P&space;=&space;123" target="_blank"><img src="http://latex.codecogs.com/gif.latex?P&space;=&space;100(1.23)^{1}&space;\therefore&space;P&space;=&space;123" title="P = 100(1.23)^{1} \therefore P = 123" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=123&space;=&space;100e^{x1}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?123&space;=&space;100e^{x1}" title="123 = 100e^{x1}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\ln&space;\frac{123}{100}}{1}&space;=&space;x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\ln&space;\frac{123}{100}}{1}&space;=&space;x" title="\frac{\ln \frac{123}{100}}{1} = x" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=x&space;=&space;0.207614169" target="_blank"><img src="http://latex.codecogs.com/gif.latex?x&space;=&space;0.207614169" title="x = 0.207614169" /></a>
 

spanky125

Just waitin' for a mate
Joined
Sep 7, 2012
Messages
285
Location
Classified
Gender
Male
HSC
2013
Re: HSC 2013 2U Marathon

One day you will be truly funny but keep trying you get better with practice.... Have you ever said these jokes to yourself before posting them online and do they ever seem funny to you :p

Edit: I wasn't even talking to you
I give myself a little giggle.
 

andybandy

Member
Joined
Sep 1, 2012
Messages
294
Gender
Male
HSC
2013
Re: HSC 2013 2U Marathon

<a href="http://www.codecogs.com/eqnedit.php?latex=a&space;=&space;1&space;\textup{&space;r&space;}&space;=&space;\sin^{2}x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?a&space;=&space;1&space;\textup{&space;r&space;}&space;=&space;\sin^{2}x" title="a = 1 \textup{ r } = \sin^{2}x" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=S\underset{\infty&space;}{\rightarrow}&space;=&space;\frac{1}{1-\sin^{2}x}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?S\underset{\infty&space;}{\rightarrow}&space;=&space;\frac{1}{1-\sin^{2}x}" title="S\underset{\infty }{\rightarrow} = \frac{1}{1-\sin^{2}x}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==&space;\sec&space;^{2}x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=&space;\sec&space;^{2}x" title="= \sec ^{2}x" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\int_{0}^{\pi/4}\sec&space;^{2}x.dx&space;=&space;[\tan&space;x]&space;=&space;\tan&space;\frac{\pi}{4}&space;-&space;\tan&space;0" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\int_{0}^{\pi/4}\sec&space;^{2}x.dx&space;=&space;[\tan&space;x]&space;=&space;\tan&space;\frac{\pi}{4}&space;-&space;\tan&space;0" title="\int_{0}^{\pi/4}\sec ^{2}x.dx = [\tan x] = \tan \frac{\pi}{4} - \tan 0" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==&space;1" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=&space;1" title="= 1" /></a>
 
Last edited:
Joined
Mar 10, 2013
Messages
105
Gender
Male
HSC
2014
Re: HSC 2013 2U Marathon

1 + (sinx)^2 + (sinx)^4 + (sinx)^6 +... = 1/(1-(sinx)^2) = 1/(cosx)^2 = (secx)^2

Therefore, the integral of "1 + (sinx)^2 + (sinx)^4 + (sinx)^6 +..." = the integral of (secx)^2 = tanx

Therefore the answer is tan(π/4) - tan(0) = 1
 

leesh95

Member
Joined
Nov 7, 2011
Messages
487
Gender
Undisclosed
HSC
2013
Re: HSC 2013 2U Marathon

<a href="http://www.codecogs.com/eqnedit.php?latex=\textup{Find&space;the&space;derivative&space;of&space;}&space;5^{x}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\textup{Find&space;the&space;derivative&space;of&space;}&space;5^{x}" title="\textup{Find the derivative of } 5^{x}" /></a>
Is the answer 5^x ln5?

Do you take log of both sides and then differentiate them?
 

leesh95

Member
Joined
Nov 7, 2011
Messages
487
Gender
Undisclosed
HSC
2013
Re: HSC 2013 2U Marathon

Lol, thats what i thought at first. But the answer says it 2/11.
Since you know at least one dice is definitely a 5, the total possible outcomes are : 1,5 2,5 3,5 4,5 5,5 and 5,1 5,2 5,3 5,4 (dont count 5,5 again)
Since only 2 outcomes are favourable the probability is 2/11
So it is a biased dice??
 

andybandy

Member
Joined
Sep 1, 2012
Messages
294
Gender
Male
HSC
2013
Re: HSC 2013 2U Marathon

Is the answer 5^x ln5?

Do you take log of both sides and then differentiate them?
Yes, you got to get it a base of e, but im sure you got it, i have the full solution on the same page
 

Menomaths

Exaı̸̸̸̸̸̸̸̸lted Member
Joined
Jul 9, 2013
Messages
2,373
Gender
Male
HSC
2013
Re: HSC 2013 2U Marathon

So it is a biased dice??
No, it's know a 5 is rolled so it could've been either die 1 or die 2, thus two possible combinations can give a total of 8.
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top