HSC 2013 Maths Marathon (archive) (4 Viewers)

[Menomaths]

Re: HSC 2013 2U Marathon

 

[andybandy]

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>

 

[spanky125]

Re: HSC 2013 2U Marathon

uv'+u'v

x.3sec^2(3x)+tan(3x)

= 3xsec^2(3x)+tan(3x)

Tan3x + 3xsec^2(3x)

Correct.

 

[spanky125]

Re: HSC 2013 2U Marathon

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\partial&space;}{\partial&space;x}[xtan3x]&space;=&space;x.3sec^{2}3x+1.tan3x&space;=&space;xsec^{2}3x+tan3x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\partial&space;}{\partial&space;x}[xtan3x]&space;=&space;x.3sec^{2}3x+1.tan3x&space;=&space;xsec^{2}3x+tan3x" title="\frac{\partial }{\partial x}[xtan3x] = x.3sec^{2}3x+1.tan3x = xsec^{2}3x+tan3x" /></a>

You left a 3 off at the start of your answer.

 

[Menomaths]

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>

I don't think this is in 2U?

 

[andybandy]

Re: HSC 2013 2U Marathon

<a href="http://www.codecogs.com/eqnedit.php?latex=Area&space;=&space;\frac{\pi&space;r^{2}}{4}&space;&plus;&space;\frac{1}{2}.b.h&space;&plus;&space;l.h" target="_blank"><img src="http://latex.codecogs.com/gif.latex?Area&space;=&space;\frac{\pi&space;r^{2}}{4}&space;&plus;&space;\frac{1}{2}.b.h&space;&plus;&space;l.h" title="Area = \frac{\pi r^{2}}{4} + \frac{1}{2}.b.h + l.h" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==&space;\frac{\pi&space;1^{2}}{4}&space;&plus;&space;\frac{1}{2}.1.1&space;&plus;&space;3.1&space;=&space;\frac{\pi&space;&plus;2&space;&plus;&space;12}{4}&space;=&space;\frac{\pi&space;&plus;&space;14}{4}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=&space;\frac{\pi&space;1^{2}}{4}&space;&plus;&space;\frac{1}{2}.1.1&space;&plus;&space;3.1&space;=&space;\frac{\pi&space;&plus;2&space;&plus;&space;12}{4}&space;=&space;\frac{\pi&space;&plus;&space;14}{4}" title="= \frac{\pi 1^{2}}{4} + \frac{1}{2}.1.1 + 3.1 = \frac{\pi +2 + 12}{4} = \frac{\pi + 14}{4}" /></a>


question 2 im stuck

 

[andybandy]

Re: HSC 2013 2U Marathon

woops!

 

[andybandy]

Re: HSC 2013 2U Marathon

I don't think this is in 2U?

It is.. hint: you have to use log laws to change to a base of e

 

[spanky125]

Re: HSC 2013 2U Marathon

A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung?

 

[Menomaths]

Re: HSC 2013 2U Marathon

<a href="http://www.codecogs.com/eqnedit.php?latex=Area&space;=&space;\frac{\pi&space;r^{2}}{4}&space;+&space;\frac{1}{2}.b.h&space;+&space;l.h" target="_blank"><img src="http://latex.codecogs.com/gif.latex?Area&space;=&space;\frac{\pi&space;r^{2}}{4}&space;+&space;\frac{1}{2}.b.h&space;+&space;l.h" title="Area = \frac{\pi r^{2}}{4} + \frac{1}{2}.b.h + l.h" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==&space;\frac{\pi&space;1^{2}}{4}&space;+&space;\frac{1}{2}.1.1&space;+&space;3.1&space;=&space;\frac{\pi&space;+2&space;+&space;12}{4}&space;=&space;\frac{\pi&space;+&space;14}{4}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=&space;\frac{\pi&space;1^{2}}{4}&space;+&space;\frac{1}{2}.1.1&space;+&space;3.1&space;=&space;\frac{\pi&space;+2&space;+&space;12}{4}&space;=&space;\frac{\pi&space;+&space;14}{4}" title="= \frac{\pi 1^{2}}{4} + \frac{1}{2}.1.1 + 3.1 = \frac{\pi +2 + 12}{4} = \frac{\pi + 14}{4}" /></a>


question 2 im stuck

Hint: To find the area you integrate the function (from my understanding) so when you're integrating that function, you should end up with the area that function contains.

 

[andybandy]

Re: HSC 2013 2U Marathon

derivate of 5^x = 1/xlogx

nope thats not it

 

[andybandy]

Re: HSC 2013 2U Marathon

Hint: To find the area you integrate the function (from my understanding) so when you're integrating that function, you should end up with the area that function contains.

is the function pi +14/4 though, the thing we just proved?

 

[Menomaths]

Re: HSC 2013 2U Marathon

is the function pi +14/4 though, the thing we just proved?

I don't think so

 

[andybandy]

Re: HSC 2013 2U Marathon

I don't think so

im completely stuck -.-

 

[andybandy]

Re: HSC 2013 2U Marathon

ok, 1/5^x * log5

still not it

 

[RealiseNothing]

Re: HSC 2013 2U Marathon

You found the positive area under the curve. When you integrate, anything below the x-axis becomes negative

 

[girlworld_club]

Re: HSC 2013 2U Marathon

A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung?

is it in the 10th hour? i'm so bad at visualising.

Can someone help me with this question:

Find the exact area enclosed by the curve y=sinx and the line y=1/2 for 0 < x < 2pi

 

[Menomaths]

Re: HSC 2013 2U Marathon

You found the positive area under the curve. When you integrate, anything below the x-axis becomes negative

Yeah, that's pretty much the answer

 

[Menomaths]

Re: HSC 2013 2U Marathon

is it in the 10th hour? i'm so bad at visualising.

Can someone help me with this question:

Find the exact area enclosed by the curve y=sinx and the line y=1/2 for 0<x<2pi

you must leave spaces between '<' for it to show

 

[RealiseNothing]

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>