VCE Specialist 3/4 Question Thread!

[Max Kawasakii]

Hey guys, I'm having trouble with Q11 of the NHT Specialist Exam 1 (question below). Can someone please help me 

Find the length of the curve specified parametrically by x = aθ – asin(θ), y = a – acos(θ) from θ = 2π/3 to θ = 2π, where a ∈ R+. Give your answer in terms of a.

Thanks in advance

From here sub into the formula on the formula sheet for Arc Length and integrate

[justsomerandom]

From here sub into the formula on the formula sheet for Arc Length and integrate

Wouldn't the a's cancel each other out if I did this?

[Max Kawasakii]

Wouldn't the a's cancel each other out if I did this?

Indeed they would, in that case, taking the x equation, solve for a then sub that into the y equation. You now have y in terms of theta and a, hence diff that in terms of theta. You will have an 'a' in your answer and can evaluate the length in terms of a. Answer should yield 6a.

[justsomerandom]

Indeed they would, in that case, taking the x equation, solve for a then sub that into the y equation. You now have y in terms of theta and a, hence diff that in terms of theta. You will have an 'a' in your answer and can evaluate the length in terms of a. Answer should yield 6a.

Ah nevermind, I managed to do it like this using the parametric form of the arc length formula (on the formula sheet):

Spoiler

And just worked it out from there, which isn't too difficult. I'm not really sure if this is the best way to do it though.

[shiba woof woof]

Hey Guys...

can you guys please explain to me how to do this question? Thanks a lot !!

[LifeisaConstantStruggle]

Hey Guys...

can you guys please explain to me how to do this question? Thanks a lot !!

The unit vector of b is literally just the unit vector of the first vector resolute (4i-3j+2k) and the unit vector perpendicular to b is actually (a-vector resolute parallel to b) so from there you can find a.
eg: a-(4i-3j+2k)=3i+j-k

[shiba woof woof]

The unit vector of b is literally just the unit vector of the first vector resolute (4i-3j+2k) and the unit vector perpendicular to b is actually (a-vector resolute parallel to b) so from there you can find a.
eg: a-(4i-3j+2k)=3i+j-k

OHH right, completely forgot about that.

Thanks for always helping me man 

[keltingmeith]

Hey Guys...

can you guys please explain to me how to do this question? Thanks a lot !!

For part a, the vector resolute of a in the direction of b is in the direction of b - so the unit vector of that resolute is the same as the unit vector of b.

For part b, a=parallel + perpendicular components.

[atar.notes.user]

can someone help me with q6 exam1 vcaa 2016
how do u go from 1+x^2(x^2+2) to (x^2+1)^2?

[LifeisaConstantStruggle]

can someone help me with q6 exam1 vcaa 2016
how do u go from 1+x^2(x^2+2) to (x^2+1)^2?

1+x²(x²+2)=1+x⁴+2x²

Rearrange it so it looks like

x⁴+2x²+1 which is a perfect square of (x²+1)²

[atar.notes.user]

1+x²(x²+2)=1+x⁴+2x²

Rearrange it so it looks like

x⁴+2x²+1 which is a perfect square of (x²+1)²

thank you
also q10 from the same exam, im getting my c as -pi/4

[keltingmeith]

can someone help me with q6 exam1 vcaa 2016
how do u go from 1+x^2(x^2+2) to (x^2+1)^2?

Erm, what does that have to do with question 6? O.o

[LifeisaConstantStruggle]

thank you
also q10 from the same exam, im getting my c as -pi/4

You CAN get c as -pi/4, which depends on where you put the c, if you insert it in the left after you've done the respective integration (after you have separated the variables), you would get -pi/4, what is important tho is how you rearrange your terms so you get the answer.

[LifeisaConstantStruggle]

Erm, what does that have to do with question 6? O.o

Probably referring to question 7?

[Ahmad_A_1999]

Could someone please explain Qs 3 c from the iTute Spesh Exam 1
Exam: http://www.itute.com/wp-content/uploads/2017-Specialist-Mathematics-Trial-Exam-1-update-1.pdf
Answers: http://www.itute.com/wp-content/uploads/2017-Specialist-Mathematics-Trial-Exam-1-Solutions-update-1.pdf

I don't understand how multiplying by 'i' in the complex plane has an effect on 'z', how do these transformations work?