Login

Welcome, Guest. Please login or register.

March 29, 2024, 08:22:06 am

Author Topic: Mathematics Question Thread  (Read 1296910 times)  Share 

0 Members and 1 Guest are viewing this topic.

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 #615 on: October 18, 2016, 11:19:25 pm »
+1
2007, Q10: having trouble understanding the answer.
(Image removed from quote.)
Thanks :P

______________


______________







fizzy.123

  • Forum Regular
  • **
  • Posts: 72
  • Respect: 0
Re: Mathematics Question Thread
« Reply #616 on: October 19, 2016, 12:18:09 am »
0
How do we solve these sort of questions??

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #617 on: October 19, 2016, 12:22:35 am »
0
How do we solve these sort of questions??

Hey Fizzy! This one is a bit of intuition, a bit of Trial and Error, you are looking for a value of x on either side of the origin that puts as much area above the x-axis as below! This way, the areas cancel each other out and you get zero ;D

1 to -1: 2 square units above, 0 square units below
2 to -2: 3.5 square units above, 0 square units below
3 to -3: 3.75 square units above, 0.75 square units below
4 to 0 -4: 3.75 square units above, 2.75 square units below

And I'll let you think about the value we'd need to have them match ;) note that I am finding these areas using basic area formula for rectangles and triangles! ;D

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575

fizzy.123

  • Forum Regular
  • **
  • Posts: 72
  • Respect: 0
Re: Mathematics Question Thread
« Reply #619 on: October 19, 2016, 01:00:39 am »
0
thank you both! Also, another question.
how many solutions of the equation (sinx -1)(tanx +2) = 0 lie between 0 & 2pi
How do we solve these sort of questions?

ml125

  • Trailblazer
  • *
  • Posts: 47
  • Respect: 0
Re: Mathematics Question Thread
« Reply #620 on: October 19, 2016, 04:06:25 am »
0
thank you both! Also, another question.
how many solutions of the equation (sinx -1)(tanx +2) = 0 lie between 0 & 2pi
How do we solve these sort of questions?









Rui edit: Just fixed up some LaTeX for ya
« Last Edit: October 19, 2016, 09:18:01 pm by RuiAce »
HSC 2016: EE2 | MX1 | Chemistry | Physics
GOAL 2017: Combined Advanced Science/Engineering @ UNSW

smile123

  • Trailblazer
  • *
  • Posts: 25
  • Respect: 0
  • School: cerdon college
  • School Grad Year: 2016
Re: Mathematics Question Thread
« Reply #621 on: October 19, 2016, 09:07:26 am »
0
Hey  :)
I was wondering if some one can help with this question part (iii)

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 #622 on: October 19, 2016, 09:18:45 am »
0
Hey  :)
I was wondering if some one can help with this question part (iii)



smile123

  • Trailblazer
  • *
  • Posts: 25
  • Respect: 0
  • School: cerdon college
  • School Grad Year: 2016
Re: Mathematics Question Thread
« Reply #623 on: October 19, 2016, 09:33:18 am »
0
thanks RuiAce  :) that made things easier

kimmie

  • Forum Regular
  • **
  • Posts: 50
  • Respect: 0
  • School: St Marys Senior High School
  • School Grad Year: 2016
Re: Mathematics Question Thread
« Reply #624 on: October 19, 2016, 12:24:26 pm »
0
soz for barging in but can you explain why tanx= -2 has two solutions? im confused about that










jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #625 on: October 19, 2016, 12:31:28 pm »
0
soz for barging in but can you explain why tanx= -2 has two solutions? im confused about that

No worries if you look at a graph of tanx like the one here, we can see that from 0 to \(2\pi\), there are two locations where \(\tan{x}=-2\) ;D it's a graphical approach that we take here (or you can use your ASTC rules to find the values exactly, if you want to) ;D
« Last Edit: October 19, 2016, 12:33:01 pm by jamonwindeyer »

rinagee12

  • Trailblazer
  • *
  • Posts: 25
  • Respect: 0
Re: Mathematics Question Thread
« Reply #626 on: October 19, 2016, 03:54:49 pm »
0
Would someone please be able to help me with this question?  :) Just with the last part, (iv).

ATAR: 95.10

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

2017: B Commerce / B Science @ UNSW

jakesilove

  • HSC Lecturer
  • Honorary Moderator
  • Part of the furniture
  • *******
  • Posts: 1941
  • "Synergising your ATAR potential"
  • Respect: +196
Re: Mathematics Question Thread
« Reply #627 on: October 19, 2016, 04:01:41 pm »
0
Would someone please be able to help me with this question?  :) Just with the last part, (iv).

Hey! To find the total distance traveled, you would usually just think to integrate, right? However, you need to think about different sections separately. We already found that velocity equals zero at Pi/3. Before that, the velocity is negative, and after that, the velocity is positive. Therefore, it is travelling in opposite directions in these two sectors.

To answer the question, just integrate between 0 and Pi/3, and the Pi/3 to Pi. Absolute value both solutions, and add them together! Let me know if you want a fully worked solution.

Jake
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

FallonXay

  • Trendsetter
  • **
  • Posts: 165
  • Respect: +6
Re: Mathematics Question Thread
« Reply #628 on: October 19, 2016, 04:14:33 pm »
0
2014 Q7: How many solutions of the equation (sin x – 1)(tan x + 2) = 0 lie between 0 and 2π ?

The answers say 2, but shouldn't it be 3???
HSC (2016): English Advanced || Mathematics || Mathematics: Extension 1 || Physics || Design and Technology || Japanese Beginners

University: B Science (Computer Science) @UNSW

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 #629 on: October 19, 2016, 04:35:03 pm »
0
2014 Q7: How many solutions of the equation (sin x – 1)(tan x + 2) = 0 lie between 0 and 2π ?

The answers say 2, but shouldn't it be 3???

That was the trap in that question.
« Last Edit: October 19, 2016, 04:38:07 pm by RuiAce »