Login

Welcome, Guest. Please login or register.

March 28, 2024, 08:50:52 pm

Author Topic: Mathematics Question Thread  (Read 1296645 times)  Share 

0 Members and 7 Guests are viewing this topic.

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #660 on: October 20, 2016, 12:08:05 pm »
0
@BPunjabi

How i solve these ( which may not be correct, Rui may correct me after if im wrong)

Equation is Sin(2x+pi/3)

To find the where it crosses the x axis
let 2x+pi/3=0
2x = -pi/3
x = -pi/6

Therefore when we inspect A,B,C,D
A and B are eliminated
And between C and D , D is -pi/6

Again, not sure if this is the best way to do it but that is how ive always done it and it has worked for me

Good method Deng! I'd personally suggest a more intuitive approach based on rules that you can find here, once you get the hang of doing it this way, purely for speed! ;D

@SimplyNikhil ( not sure how to tag your post )

But to find the area it would be top curve - bottom curve
ln2x-lnx
By index laws that would become ln2
Since ln2 is a constant you can integrate it to xln2 and you just simply sub in b and a to solve

Hope i answered your question

This is also correct, and extremely clever, well done Deng ;D
« Last Edit: October 20, 2016, 12:12:56 pm by jamonwindeyer »

Deng

  • Trendsetter
  • **
  • Posts: 136
  • Respect: 0
Re: Mathematics Question Thread
« Reply #661 on: October 20, 2016, 12:12:28 pm »
0
At Rui for the area under the curve integral question

Would this not give the correct working

Area = integrate between e and 1 for ln2x-ln2
= ln 2 + ln x - ln x
= ln2 ( constant there is no x, therefore integratable )
Therefore, it becomes xln2 between e and 1
eln2 - ln2
= ln2 ( e - 1 )

I'm not sure if the method you provided gave same answer because i dont understand it
English Advanced -89
Legal Studies - 90
Business Studies -92
Economics - 92
Mathematics - 88

BPunjabi

  • Forum Obsessive
  • ***
  • Posts: 262
  • So... Hows life?
  • Respect: 0
Re: Mathematics Question Thread
« Reply #662 on: October 20, 2016, 12:13:39 pm »
0
Good method Deng! I'd personally suggest a more intuitive approach based on rules that you can find here, once you get the hang of doing it this way, purely for speed! ;D

So Jamon, we are basically looking at (Bx+C)
Did HSC in 2016 and was first person to get 100. Aeronautical engineering for me now :P
  <-- CLICK ME

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #663 on: October 20, 2016, 12:14:15 pm »
0
Following from my mistake

I oversimplified it. You actually have to analyse THREE regions, not just TWO. I have labelled them in the diagram for reference.



Jamon please double check

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #664 on: October 20, 2016, 12:15:03 pm »
0
At Rui for the area under the curve integral question
Would this not give the correct working
...
I'm not sure if the method you provided gave same answer because i dont understand it

Jamon please double check

Yeah to reiterate above, Rui's method is overkill in this case (though I think correct), Deng your answer is definitely correct ;D

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #665 on: October 20, 2016, 12:15:42 pm »
+1
At Rui for the area under the curve integral question

Would this not give the correct working

Area = integrate between e and 1 for ln2x-ln2
= ln 2 + ln x - ln x
= ln2 ( constant there is no x, therefore integratable )
Therefore, it becomes xln2 between e and 1
eln2 - ln2
= ln2 ( e - 1 )

I'm not sure if the method you provided gave same answer because i dont understand it
Ah. I missed the logarithm law.

BPunjabi

  • Forum Obsessive
  • ***
  • Posts: 262
  • So... Hows life?
  • Respect: 0
Re: Mathematics Question Thread
« Reply #666 on: October 20, 2016, 12:16:21 pm »
0
anyone know how to do this?
Did HSC in 2016 and was first person to get 100. Aeronautical engineering for me now :P
  <-- CLICK ME

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #667 on: October 20, 2016, 12:16:34 pm »
0
So Jamon, we are basically looking at (Bx+C)

Yeah precisely! ;D

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #668 on: October 20, 2016, 12:17:45 pm »
0
Hey guys, i was wondering on how i would identify the second derivative for this q

The first derivative would be f'(a) < 0 since the gradient is negative
I just cant picture in my head what the second derivate would look like ( some reason i picture a horizontal line since f(x) looks like a parabola to me
Do not picture the second derivative in your head. Use definitions.

The first derivative tells us whether it is increasing or decreasing. Since it is decreasing, f'(a) < 0

The second derivative tells us its concavity. Since it is concave up, f"(a) > 0

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #669 on: October 20, 2016, 12:18:55 pm »
0
anyone know how to do this?
(Image removed from quote.)

Edit: Woops, dictation error

The denominator of a function cannot be zero, so:



But also we can't square root a negative number:



Put these together to obtain \(x>-3\) ;D

Deng

  • Trendsetter
  • **
  • Posts: 136
  • Respect: 0
Re: Mathematics Question Thread
« Reply #670 on: October 20, 2016, 12:37:07 pm »
0
For this question, if i did the maths right, the x value where it is increasing is 2/3 and 2, but how would i know if its 2/3<x<2 or if its split
I've been told to draw a parabola but i dont particularly understand this method and just want more clarification

Thanks
English Advanced -89
Legal Studies - 90
Business Studies -92
Economics - 92
Mathematics - 88

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #671 on: October 20, 2016, 12:39:05 pm »
0
For this question, if i did the maths right, the x value where it is increasing is 2/3 and 2, but how would i know if its 2/3<x<2 or if its split
I've been told to draw a parabola but i dont particularly understand this method and just want more clarification

Thanks



BPunjabi

  • Forum Obsessive
  • ***
  • Posts: 262
  • So... Hows life?
  • Respect: 0
Re: Mathematics Question Thread
« Reply #672 on: October 20, 2016, 12:42:23 pm »
0
Edit: Woops, dictation error

The denominator of a function cannot be zero, so:



But also we can't square root a negative number:



Put these together to obtain \(x>-3\) ;D

Thanks Jamon but the answer says a?
Did HSC in 2016 and was first person to get 100. Aeronautical engineering for me now :P
  <-- CLICK ME

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #673 on: October 20, 2016, 12:43:46 pm »
0
Thanks Jamon but the answer says a?
That's what he got. He said in the last line that hence the answer is x > -3

rinagee12

  • Trailblazer
  • *
  • Posts: 25
  • Respect: 0
Re: Mathematics Question Thread
« Reply #674 on: October 20, 2016, 12:44:59 pm »
0
Hey I'm stuck on this question:

For what values of k will the equation 2x^2 + 8kx - (1-k) = 0
have roots that differ by 2?

My first thought was to use the formula
α+β=-b/a
and αβ=c/a

I tried to replace 'β' with (α-2) but I'm not sure if I'm doing the right thing, I can't seem to get the answer
ATAR: 95.10

HSC 2016: English (Advanced) | English Ext 1 | Mathematics | Legal Studies |
Business Studies | Ancient History

2017: B Commerce / B Science @ UNSW