VCE Specialist 3/4 Question Thread!

[humblepie]

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Thanks so much RuiAce!

[geminii]

Hi everyone!

I'm really confused on this question (screenshot attached). The solution in the textbook (the 2nd screenshot attached) says to solve pv=1500 for p, but I've solved for v. Looking at my solution and the textbook's solution, I don't feel like mine is illogical yet I got the wrong answer. I've attached a picture of my working out.

Could someone please let me know where I've gone wrong? And why didn't it worked when I solved for v instead of p like the textbook?

[RuiAce]

Hi everyone!

I'm really confused on this question (screenshot attached). The solution in the textbook (the 2nd screenshot attached) says to solve pv=1500 for p, but I've solved for v. Looking at my solution and the textbook's solution, I don't feel like mine is illogical yet I got the wrong answer. I've attached a picture of my working out.

Could someone please let me know where I've gone wrong? And why didn't it worked when I solved for v instead of p like the textbook?

Not sure why you subbed in the reciprocal of this expression.

[geminii]

Oh, thanks heaps! I think I meant to sub in dp/dv into the first line of working out as dp/dv is the reciprocal of dv/dp, but after rearranging I should have subbed in the original, not the reciprocal.

Thanks again!!

[Rieko Ioane]

Hello,

Could I have some help for this https://imgur.com/a/pP2LA
Q4a) the answer started off with dN/dt = kN(2000-N), isn't this sort of like cheating? I thought to prove these D.E you need to prove it with dN/dt in - dN/dt out?

c) the question starts with "dN/dt is max at N=1000”, the question gave no working for this. I'm not sure how they got to this conclusion?

[Eric11267]

Hello,

Could I have some help for this https://imgur.com/a/pP2LA
Q4a) the answer started off with dN/dt = kN(2000-N), isn't this sort of like cheating? I thought to prove these D.E you need to prove it with dN/dt in - dN/dt out?

c) the question starts with "dN/dt is max at N=1000”, the question gave no working for this. I'm not sure how they got to this conclusion?

4a) You can't use the standard in and out for the differential equation because the question makes no mention of any rabbits dying. Since the question says the growth varies with N and 2000-N, you can infer that that dN/dt =kN(2000-N)

c) Looking at the equation provided in part a you'll notice that the equation described is a parabola with intercepts at N=0 and N=2000. Because it is a parabola, the turning point occurs in the middle of the intercepts which is at N=1000.

[humblepie]

Hi! Could someone please explain to me why the graph isn't one straight line? (solutions attached)

Thanks in advance!

[Eric11267]

Hi! Could someone please explain to me why the graph isn't one straight line? (solutions attached)

Thanks in advance!

The question specifies that the principle argument must be less than pi/2. Therefore the section of the line between pi/2 and pi is not included

[Rieko Ioane]

4a) You can't use the standard in and out for the differential equation because the question makes no mention of any rabbits dying. Since the question says the growth varies with N and 2000-N, you can infer that that dN/dt =kN(2000-N)

c) Looking at the equation provided in part a you'll notice that the equation described is a parabola with intercepts at N=0 and N=2000. Because it is a parabola, the turning point occurs in the middle of the intercepts which is at N=1000.

Thanks a lot!

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Need some help again...https://imgur.com/a/33o0H

Q5b) I'm solving Pr(|A-B| < 5) = Pr(A-B <5) + Pr(A-B > -5) but I'm not getting the correct answer of 0.275. I have E(A-B) = -8 and sd(A-B) = sqrt(2265)/10 which were correct. Am I doing something wrong?

also, for complex numbers when you solve something like z^4 = sqrt(3)z^2 -1. I got cis(+-pi/12). How would I proceed to find the other 2 solutions?

My teacher says all 4 solutions are equally spaced around the complex plane which seems to be wrong as the other 2 solutions are cis(+-11pi/12).

[Eric11267]

Thanks a lot!

---
Need some help again...https://imgur.com/a/33o0H

Q5b) I'm solving Pr(|A-B| < 5) = Pr(A-B <5) + Pr(A-B > -5) but I'm not getting the correct answer of 0.275. I have E(A-B) = -8 and sd(A-B) = sqrt(2265)/10 which were correct. Am I doing something wrong?

also, for complex numbers when you solve something like z^4 = sqrt(3)z^2 -1. I got cis(+-pi/12). How would I proceed to find the other 2 solutions?

My teacher says all 4 solutions are equally spaced around the complex plane which seems to be wrong as the other 2 solutions are cis(+-11pi/12).

It seems you must have the wrong standard deviation. The sd should be sqrt(2.7²+4.4²). That should give you the right answer.

As for the second question
I would first sub u=z²
Giving you u²-sqrt(3)u+1=0
This should give you u=1/2(sqrt(3)±i)
so z²=cis(±π/6+2πk), kϵZ
Then you would solve this and get all four solutions

Your teacher was wrong about having four equally spaced solutions because its in the form of a quadratic equation

[Rieko Ioane]

It seems you must have the wrong standard deviation. The sd should be sqrt(2.7²+4.4²). That should give you the right answer.

As for the second question
I would first sub u=z²
Giving you u²-sqrt(3)u+1=0
This should give you u=1/2(sqrt(3)±i)
so z²=cis(±π/6+2πk), kϵZ
Then you would solve this and get all four solutions

Your teacher was wrong about having four equally spaced solutions because its in the form of a quadratic equation

Thanks again.

With that probability question, I'm now getting 0.258677 with normCdf(-5,5,-8,sqrt(2206)/10). Not sure what else I could've screwed up?

And when are the solutions for a complex equation equally spaced? What are the conditions for this to occur?

[RuiAce]

And when are the solutions for a complex equation equally spaced? What are the conditions for this to occur?

[Eric11267]

Thanks again.

With that probability question, I'm now getting 0.258677 with normCdf(-5,5,-8,sqrt(2206)/10). Not sure what else I could've screwed up?

And when are the solutions for a complex equation equally spaced? What are the conditions for this to occur?

I'm not sure how you are getting sqrt(2206)/10. The standard deviation should be sqrt(4.4²+2.7²) which is sqrt(2665)/10

[Willba99]

hello plz help. my understanding of this question is like a solid 2/10

[Eric11267]

hello plz help. my understanding of this question is like a solid 2/10

Alright so we have Arg(z³)ϵ(π/2+2πk,π+2πk)
Thus, by Demoivres theorem we have
Arg(z)ϵ(π/6+2/3πk,π/3+2/3πk)
Subbing in values of k gives you
Arg(z)ϵ(π/6,π/3)U(-π/2,-π/3)