VCE Specialist 3/4 Question Thread!

[Stick]

I actually saw that, but I thought it was wrong and didn't do it. Thanks for the help!

[Homer]

How would I convert 3 degrees per hour to degrees per second?

[sin0001]

How would I convert 3 degrees per hour to degrees per second?

divide by 3600

[pi]

How would I convert 3 degrees per hour to degrees per second?

Is this a serious spesh question..?

For future reference, use the units:
deg/1hour = deg/60mins = deg/(60*60)s = deg/3600s

Hence, multiply by 1/3600 or divide by 3600 to make the conversion.

[dim_sim]

If we're given a vector proof with a shape that already has vectors defined in the question, are we allowed to define new ones? I don't know if I make sense, but here's an example: Consider the quadrilateral OABC where OA=a and OB=b. Prove... etc. Can I then make OC=c then use it in my proof or will I lose marks as I'm supposed to use a and b?

[Jenny_2108]

If we're given a vector proof with a shape that already has vectors defined in the question, are we allowed to define new ones? I don't know if I make sense, but here's an example: Consider the quadrilateral OABC where OA=a and OB=b. Prove... etc. Can I then make OC=c then use it in my proof or will I lose marks as I'm supposed to use a and b?

Its okay to let OC=c but you need to write c in term of a and b so that in the end you can sub it back into your proof to get the answer  (as your proof will contain c while question requires the proof in term of a and b only)

[jono88]

Find all real values of r for which ri is a solution of the equation z^4-2z^3+11z^2-18z+18=0
(z^2+ri)(z^2-ri)
=z^2+r^2
therefore (z^2+r^2)(az^2+bz+c)=the equation in question
so far ive solved a=1
b=-2
what do i to find c?

[BubbleWrapMan]

You should be subbing z = ri into the polynomial equation. You then get real and imaginary parts, which both need to equal zero. You need to find the values of r for which both of them are zero simultaneously.

[Jaswinder]

How would I anti differentiate x^2/(x^2+4)

[polar]

How would I anti differentiate x^2/(x^2+4)

hence,

the rest of the question

[Jaswinder]

Woah you are one smart cookie polar

[~T]

Chapter 2E, question 18:
Coplanar points A, B, C, D, and E have position vectors a, b, c, d, and e respectively to a relative origin O. A is the midpoint of OB and E divides AC in the ratio 1:2. If e = d, show that OCDB is a parallelogram.

I've drawn a diagram, but it hasn't really helped. I know I need to show that OC and BD are equal (or CD and OB).

The Worked solutions say the following:


However, between the second and third lines of the working for OC, they change DC to -b, which is using the fact that it is a parallelogram (what we're trying to prove) to show that it is a parallelogram, isn't it?

[507]

^^ Had the same problem with that question :L

Just stuck on part c for this one.

[polar]

^^ Had the same problem with that question :L

Just stuck on part c for this one.

picture AB with MN intersecting it - lets call the point of intersection X. X cuts AB and also MN so:

firstly, there must exist a such that



similarly, there must exist a such that



now, equate these two expressions (I'll use matrices because they're easier to do on latex, use i-j-k notation here if you want)



now, write out simultaneous equations and solve them. this gives
hence, substitute into any expression for . for example

[507]

Nice one, thanks.