Welcome, Guest. Please login or register.

August 26, 2019, 10:32:19 am

Author Topic: VCE Specialist 3/4 Question Thread!  (Read 1084187 times)  Share 

0 Members and 2 Guests are viewing this topic.

dc302

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1030
  • Respect: +52
  • School: Melbourne High School
  • School Grad Year: 2009
Re: Specialist 3/4 Question Thread!
« Reply #30 on: December 05, 2011, 08:19:03 pm »
+2
yeahh thats right haha,
hence 'im stuck' :p

I know i shouldnt have even gone there..., so do you think it was something to do with not converting tanx to sin/cos ?
or just some arithmetic?

Cancelling is a big nono ;)
2012-2015 - Doctor of Medicine (MD) @ UniMelb
2010-2011 - Bachelor of Science (BSc) majoring in Pure Mathematics @ UniMelb
2009 - VCE [99.70] -- Eng [43] - Methods [44] - Chem [44] - JapSL [45] - Spesh [45] - MUEP Jap [5.5]

Bhootnike

  • Chief Curry Officer
  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1332
  • Biggest Sharabi
  • Respect: +74
  • School Grad Year: 2012
Re: Specialist 3/4 Question Thread!
« Reply #31 on: December 05, 2011, 08:21:29 pm »
0
move everytihng to the one side then used null factor law.

4tan(x)-4tan3(x)-12tan(x)=0
take tan(x) as a factor
tan(x)(-8-4tan2(x))=0
tan(x)=0 or -8-4tan2(x)=0
x=0 or tan2(x)=2
x=0, or   or no solution

So x=0, ,

EDIT: forgot sols

legend! thanks bro!

just ah... wouldnt:
 -8-4tan2(x)=0
 -4tan2(x)=0 +8
 tan2(x)= 8 /-4
tan2(x)=-2 ?

so yeah no solution because u cant take the sq.root of a negative number anyways!


And thanks alot guys, will remember this for next time! :D
+1

2011: Biol - 42
2012: Spesh |Methods |Chemistry |English Language| Physics
2014: Physiotherapy
khuda ne jab tujhe banaya hoga, ek suroor uske dil mein aaya hoga, socha hoga kya doonga tohfe mein tujhe.... tab ja ke usne mujhe banaya hoga

b^3

  • Honorary Moderator
  • ATAR Notes Legend
  • *******
  • Posts: 3530
  • Overloading, just don't do it.
  • Respect: +627
  • School: Western Suburbs Area
  • School Grad Year: 2011
Re: Specialist 3/4 Question Thread!
« Reply #32 on: December 05, 2011, 08:24:32 pm »
+1
move everytihng to the one side then used null factor law.

4tan(x)-4tan3(x)-12tan(x)=0
take tan(x) as a factor
tan(x)(-8-4tan2(x))=0
tan(x)=0 or -8-4tan2(x)=0
x=0 or tan2(x)=2
x=0, or   or no solution

So x=0, ,

EDIT: forgot sols

legend! thanks bro!

just ah... wouldnt:
 -8-4tan2(x)=0
 -4tan2(x)=0 +8
 tan2(x)= 8 /-4
tan2(x)=-2 ?

so yeah no solution because u cant take the sq.root of a negative number anyways!


And thanks alot guys, will remember this for next time! :D
+1


YES! I did it in my head, and didn't type it, I've lost it already :(. Stupid holidays :|
2012-2016: Aerospace Engineering/Science (Double Major in Applied Mathematics - Monash Uni)
TI-NSPIRE GUIDES: METH, SPESH

Co-Authored AtarNotes' Maths Study Guides


I'm starting to get too old for this... May be on here or irc from time to time.

Bhootnike

  • Chief Curry Officer
  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1332
  • Biggest Sharabi
  • Respect: +74
  • School Grad Year: 2012
Re: Specialist 3/4 Question Thread!
« Reply #33 on: December 05, 2011, 08:26:27 pm »
0
ok sweet, atleast im getting something right ahaha... yaya.

thanks again guyss
2011: Biol - 42
2012: Spesh |Methods |Chemistry |English Language| Physics
2014: Physiotherapy
khuda ne jab tujhe banaya hoga, ek suroor uske dil mein aaya hoga, socha hoga kya doonga tohfe mein tujhe.... tab ja ke usne mujhe banaya hoga

Bhootnike

  • Chief Curry Officer
  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1332
  • Biggest Sharabi
  • Respect: +74
  • School Grad Year: 2012
Re: Specialist 3/4 Question Thread!
« Reply #34 on: December 06, 2011, 07:43:41 pm »
0
Was wondering what other people's approach to this question is :

Use vector methods to prove that the midpoint of the hypotenuse of a right-angled triangle
is equidistant from all vertices.
2011: Biol - 42
2012: Spesh |Methods |Chemistry |English Language| Physics
2014: Physiotherapy
khuda ne jab tujhe banaya hoga, ek suroor uske dil mein aaya hoga, socha hoga kya doonga tohfe mein tujhe.... tab ja ke usne mujhe banaya hoga

TrueTears

  • TT
  • Honorary Moderator
  • It's Over 9000!!
  • *******
  • Posts: 16358
  • Respect: +653
Re: Specialist 3/4 Question Thread!
« Reply #35 on: December 06, 2011, 07:48:53 pm »
+1
let one side (adjacent to the right angle) be denoted by vector b, other side (the other side which is adjacent to the right angle) be denoted vector a, the hypotenuse is given by a-b, half of this vector is given by 1/2(a-b), from the right angle vertex to the midpoint; this vector is given by b+1/2(a-b) = 1/2(a+b)

compute the magnitude, the magnitude are also the same hence equidistant.
« Last Edit: December 06, 2011, 10:31:21 pm by TrueTears »

kamil9876

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1945
  • Respect: +109
Re: Specialist 3/4 Question Thread!
« Reply #36 on: December 06, 2011, 10:10:07 pm »
+1
TT, . Your attempt doesn't use the fact that it's a right angle triangle so that alerted me.

What you should now do is compute the length:



Likewise we can show that

Hence the magnitudes are indeed the same (notice this is false for certain triangles that are not right angled e.g: an iscosceles triangle with two very long equal sides and one very short side, this is a good way to check your proof, does it use all the assumptions?)
« Last Edit: December 06, 2011, 10:12:04 pm by kamil9876 »
Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

TrueTears

  • TT
  • Honorary Moderator
  • It's Over 9000!!
  • *******
  • Posts: 16358
  • Respect: +653
Re: Specialist 3/4 Question Thread!
« Reply #37 on: December 06, 2011, 10:28:54 pm »
0
TT, . Your attempt doesn't use the fact that it's a right angle triangle so that alerted me.

What you should now do is compute the length:



Likewise we can show that

Hence the magnitudes are indeed the same (notice this is false for certain triangles that are not right angled e.g: an iscosceles triangle with two very long equal sides and one very short side, this is a good way to check your proof, does it use all the assumptions?)
thats right, i got lazy and didnt end up computing the lengths lol but yeah in my head using a.b = 0 was quite obvious from the start ;)
« Last Edit: December 06, 2011, 10:32:11 pm by TrueTears »

Bhootnike

  • Chief Curry Officer
  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1332
  • Biggest Sharabi
  • Respect: +74
  • School Grad Year: 2012
Re: Specialist 3/4 Question Thread!
« Reply #38 on: December 06, 2011, 11:00:35 pm »
0
I don't get why the hypotenuse is a-b? 
2011: Biol - 42
2012: Spesh |Methods |Chemistry |English Language| Physics
2014: Physiotherapy
khuda ne jab tujhe banaya hoga, ek suroor uske dil mein aaya hoga, socha hoga kya doonga tohfe mein tujhe.... tab ja ke usne mujhe banaya hoga

dc302

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1030
  • Respect: +52
  • School: Melbourne High School
  • School Grad Year: 2009
Re: Specialist 3/4 Question Thread!
« Reply #39 on: December 06, 2011, 11:41:24 pm »
+1
I don't get why the hypotenuse is a-b? 

It's just a matter of 'how' you draw the triangle. I think the triangle is supposed to use the positive x, y axes, with the hypotenuse slanting down from the positive y axis to the positive x axis. Here I'm only saying x and y axes for illustrative purposes.

edit: actually a better visualisation: if vector b goes from origin to point B, and vector a goes from origin to point A, and AOB is the right angle, then the hypotenuse is from B to A, which is given by a-b. Draw it!
« Last Edit: December 06, 2011, 11:43:37 pm by dc302 »
2012-2015 - Doctor of Medicine (MD) @ UniMelb
2010-2011 - Bachelor of Science (BSc) majoring in Pure Mathematics @ UniMelb
2009 - VCE [99.70] -- Eng [43] - Methods [44] - Chem [44] - JapSL [45] - Spesh [45] - MUEP Jap [5.5]

Planck's constant

  • Victorian
  • Forum Leader
  • ****
  • Posts: 752
  • Respect: +52
Re: Specialist 3/4 Question Thread!
« Reply #40 on: December 06, 2011, 11:57:47 pm »
+1
Easier to see why the hypotenuse = a - b, if you imagine the vertex corresponding to the right angle as the origin, O.
Therefore, the other two vertices will be represented by their position vectors,

OA = a
OB = b

And the hypotenuse, AB becomes,

BO + OA =
(-OB) + OA =
-b + a =
a - b

 

Bhootnike

  • Chief Curry Officer
  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1332
  • Biggest Sharabi
  • Respect: +74
  • School Grad Year: 2012
Re: Specialist 3/4 Question Thread!
« Reply #41 on: December 07, 2011, 12:16:33 am »
0
Thanks dc302,  making sense :)

Thanks to you too argonaut! Just checking, if you're going by the same diagram as dc302,  you've said ab = a-b,  but isn't that ba?  Ab would be - a + b wouldn't it?

Which leads me to asking,  the hypotenuse could be a-b or b-a yes?
2011: Biol - 42
2012: Spesh |Methods |Chemistry |English Language| Physics
2014: Physiotherapy
khuda ne jab tujhe banaya hoga, ek suroor uske dil mein aaya hoga, socha hoga kya doonga tohfe mein tujhe.... tab ja ke usne mujhe banaya hoga

TrueTears

  • TT
  • Honorary Moderator
  • It's Over 9000!!
  • *******
  • Posts: 16358
  • Respect: +653
Re: Specialist 3/4 Question Thread!
« Reply #42 on: December 07, 2011, 12:20:24 am »
0
Which leads me to asking,  the hypotenuse could be a-b or b-a yes?
yeh doesnt matter, but then the vector expression for the vector starting at the right angle vertex to the midpoint would also change, the final result is the same

Planck's constant

  • Victorian
  • Forum Leader
  • ****
  • Posts: 752
  • Respect: +52
Re: Specialist 3/4 Question Thread!
« Reply #43 on: December 07, 2011, 12:25:31 am »
0
Which leads me to asking,  the hypotenuse could be a-b or b-a yes?


Indeed it can be either.
But for the purposes of the (correct) solution posted by kamil, in order to find the relevant magnitudes, you end up forming the dot product,

(a - b) . (a - b)

which is equivalent to

(b - a) . (b - a)



Bhootnike

  • Chief Curry Officer
  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1332
  • Biggest Sharabi
  • Respect: +74
  • School Grad Year: 2012
Re: Specialist 3/4 Question Thread!
« Reply #44 on: December 07, 2011, 07:34:33 am »
0
Alright then!  Thanks again :)  and woops forgot to thank you before TT! 
2011: Biol - 42
2012: Spesh |Methods |Chemistry |English Language| Physics
2014: Physiotherapy
khuda ne jab tujhe banaya hoga, ek suroor uske dil mein aaya hoga, socha hoga kya doonga tohfe mein tujhe.... tab ja ke usne mujhe banaya hoga