HSC 2013 Maths Marathon (archive) (2 Viewers)

[Youi_]

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

Edit: I wasn't even talking to you

 

[Sy123]

Re: HSC 2013 2U Marathon

 

[andybandy]

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>

 

[Menomaths]

Re: HSC 2013 2U Marathon

Sy has joined the marathon

Menomaths has left the marathon

 

[spanky125]

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

Edit: I wasn't even talking to you

I give myself a little giggle.

 

[Shazer2]

Re: HSC 2013 2U Marathon

 

[Youi_]

Re: HSC 2013 2U Marathon

Sy has joined the marathon

Menomaths has left the marathon

Your not the only one who feels the same way

 

[Menomaths]

Re: HSC 2013 2U Marathon

Your not the only one who feels the same way

Sy has joned the marathon

The marathon has left the Sy

 

[andybandy]

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>

 

[anthony_wheels]

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

 

[ColdLipstick]

Re: HSC 2013 2U Marathon

Another Q I wrote ^.^

Bumping for more exposure in case anyone didn't see.

 

[Sy123]

Re: HSC 2013 2U Marathon

 

[leesh95]

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]

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]

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

 

[anthony_wheels]

Re: HSC 2013 2U Marathon

Is the answer 5^x ln5?

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

Yeah, the answer is 5^x.ln5... There are a few ways which you can do it.

 

[Menomaths]

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.

 

[leesh95]

Re: HSC 2013 2U Marathon

Is the answer ln 1.23? I don't have a calculator on me to find the decimal form right now.

 

[Youi_]

Re: HSC 2013 2U Marathon

 

[Youi_]

Re: HSC 2013 2U Marathon

Is the answer ln 1.23? I don't have a calculator on me to find the decimal form right now.

Yeah