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March 29, 2024, 08:32:43 pm

Author Topic: VCE Specialist 3/4 Question Thread!  (Read 2164611 times)  Share 

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Bhootnike

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Re: Specialist 3/4 Question Thread!
« Reply #105 on: January 01, 2012, 12:44:07 pm »
0
Given that cis 3θ = (cos^3 θ − 3 cos θ sin^2 θ) + i (3 cos^2 θ sin θ − sin^3 θ), it follows that cos 3θ
is equal to:
A cos^3θ
B 4 cos θ − 3 cos^3 θ
C 3 cos^2 θ − sin^3 θ
D 4 cos^3 θ − 3 cos θ
E −(2 cos^3 θ + 3 cos θ)

Ans. =D

Could someone plz go through this one?!
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brightsky

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Re: Specialist 3/4 Question Thread!
« Reply #106 on: January 01, 2012, 01:03:46 pm »
+2
cos(3x) = cos^3(x) - 3cos(x)sin^2(x)
= cos^3(x) - 3cos(x)(1-cos^2(x))
= cos^3(x) - 3cos(x) + 3cos^3(x)
= 4 cos^3(x) - 3cos(x)
so D.
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tony3272

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Re: Specialist 3/4 Question Thread!
« Reply #107 on: January 01, 2012, 01:07:01 pm »
+2


So you only need the cosine component to do this question



  once you have simplified it down
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Re: Specialist 3/4 Question Thread!
« Reply #108 on: January 01, 2012, 01:09:45 pm »
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silly me, i even wrote it out and still didn't realise it was 'sin^2' !!!!

thanks haha ;D
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Special At Specialist

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Re: Specialist 3/4 Question Thread!
« Reply #109 on: January 01, 2012, 01:45:45 pm »
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This is such an easy question, yet I keep getting the wrong answer :(

The radius of a spherical ball is and its volume is increasing at a rate of . At what rate is the radius increasing with respect to time?

My attempt was this:







But I got the answer wrong. I suspect that my flaw might have been in the part, but I'm not completely sure.
Please help me!
« Last Edit: January 01, 2012, 02:23:30 pm by Special At Specialist »
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Special At Specialist

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Re: Specialist 3/4 Question Thread!
« Reply #110 on: January 01, 2012, 02:04:09 pm »
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It says the answer is:
(approximation, not exact value).
Someone please tell me where I went wrong.
« Last Edit: January 01, 2012, 02:06:30 pm by Special At Specialist »
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Re: Specialist 3/4 Question Thread!
« Reply #111 on: January 01, 2012, 02:11:18 pm »
+2
Plug in the value of r (2.5m) as this is the radius at the point in time that you are looking for. Then you get dr/dt=0.00127m/min.

Also dont forget to put the \ in front of the "pi" in your LaTeX code (also leave a space between the \pi and the r) so that you get .
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butene

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Re: Specialist 3/4 Question Thread!
« Reply #112 on: January 01, 2012, 02:16:49 pm »
+1
This is such an easy question, yet I keep getting the wrong answer :(

The radius of a spherical ball is and its volume is increasing at a rate of . At what rate is the radius increasing with respect to time?

My attempt was this:







But I got the answer wrong. I suspect that my flaw might have been in the part, but I'm not completely sure.
Please help me!

dr/dt = 0.1/(4pir^2)
= 0.1/(4pi(2.5)^2) = 0.00127m/min

sorry i cant use latex LOL
« Last Edit: January 01, 2012, 02:23:04 pm by butene »

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Re: Specialist 3/4 Question Thread!
« Reply #113 on: January 01, 2012, 02:18:15 pm »
0
Plug in the value of r (2.5m) as this is the radius at the point in time that you are looking for. Then you get dr/dt=0.00127m/min.

Also dont forget to put the \ in front of the "pi" in your LaTeX code (also leave a space between the \pi and the r) so that you get .
+1.

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Re: Specialist 3/4 Question Thread!
« Reply #114 on: January 01, 2012, 02:24:59 pm »
0
Plug in the value of r (2.5m) as this is the radius at the point in time that you are looking for. Then you get dr/dt=0.00127m/min.

Also dont forget to put the \ in front of the "pi" in your LaTeX code (also leave a space between the \pi and the r) so that you get .

Oh so I got it all right I just didn't plug in the value.
Thank you!
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Re: Specialist 3/4 Question Thread!
« Reply #115 on: January 01, 2012, 02:37:45 pm »
+1
So if I then wanted to work out the rate of change of surface area to time, would I say:







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Re: Specialist 3/4 Question Thread!
« Reply #116 on: January 01, 2012, 03:27:24 pm »
+1
Looks good to me.
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jaydee

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Re: Specialist 3/4 Question Thread!
« Reply #117 on: January 01, 2012, 07:13:00 pm »
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can someone please explain linear independence and dependence? the maths quest book uses a=mb+nc whereas the essential book uses c=ma+nb. Im confused :(
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Re: Specialist 3/4 Question Thread!
« Reply #118 on: January 01, 2012, 07:39:25 pm »
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i'm a bit iffy about the geometric significance of linear dependence/independence myself. however, all you really need to know is that the vectors a, b and c are linearly dependent if there exists non-zero constants p, q, r such that pa + qb + rc = 0 (the letters don't matter, all you need to know is the idea). if a set of vectors aren't linearly dependent, then they're linearly independent. the a = mb + mc, etc. are merely 'shortcuts' that you can take.

the explanation below given by wikipedia represents my current understanding of linear dependence:

"A geographic example may help to clarify the concept of linear independence. A person describing the location of a certain place might say, "It is 5 miles north and 6 miles east of here." This is sufficient information to describe the location, because the geographic coordinate system may be considered as a 2-dimensional vector space (ignoring altitude). The person might add, "The place is 7.81 miles northeast of here." Although this last statement is true, it is not necessary.

In this example the "5 miles north" vector and the "6 miles east" vector are linearly independent. That is to say, the north vector cannot be described in terms of the east vector, and vice versa. The third "7.81 miles northeast" vector is a linear combination of the other two vectors, and it makes the set of vectors linearly dependent, that is, one of the three vectors is unnecessary.

Also note that if altitude is not ignored, it becomes necessary to add a third vector to the linearly independent set. In general, n linearly independent vectors are required to describe any location in n-dimensional space."
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Re: Specialist 3/4 Question Thread!
« Reply #119 on: January 01, 2012, 08:03:08 pm »
+1
if you guys wanna really understand linear independence etc formally, check out elementary linear algebra by anton, uploaded here http://ifile.it/0k9e8i/__Elementary_Linear_Algebra_with_Applications_9_edition.l_72x2j2n5nx4tx41.pdf

pg 370, section 5.3 a whole section on linear independence/dependence etc
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