VCE Specialist 3/4 Question Thread!

[keltingmeith]

Fact - methods and specialist are two different subjects, and doing well in one does not dictate how you will do in the other. While it is true that there's a lot of overlap, it is still very possible to get under 30 in one and still get over 40 in the other. In fact, I know someone who matched my methods score, but was quite a bit below me in specialist. Similarly, I know someone who was quite a bit above me in methods, but not so much for specialist. Don't assume that a score of x in methods means you'll get a score of y in specialist.

To do well in specialist takes as much as it does in any other subject - you must understand the material, and be able to apply to any given situation. You don't have to understand the material the moment you've learned it - as long as you understand it by the time you walk into your SAC/exam. I didn't understand curvilinear motion and couldn't do any related questions until about a week before my final exam - still got full marks for mechanics. It doesn't matter if you don't understand things immediately, because barely anybody understands everything immediately. As long as you've got a handle on it when push comes to shove.

[Mieow]

where did the 1/k come from when it was anti-differentiated?

[nhmn0301]

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where did the 1/k come from when it was anti-differentiated?

You have ln|kp-1000| and then multiply it by the reciprocal of the derivative of the inside function which is "1/k"

[kinslayer]

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where did the 1/k come from when it was anti-differentiated?

Like nhmn0301 said, try differentiating the result with respect to and you will see why the 1/k is needed. Alternatively, make a change of variables in the integral by substituting and see what you get.

[nhmn0301]

Hey can someone assist me?

Pure oxygen is pumped into a 100L tank of natural air at a rate of 5L/minute. Natural air contains 21% oxygen. The oxygen is mixed well in the tank with the mixture in the tank then being drawn out at 5L/minute.

Write a differential equation, involving Q (the amount of oxygen, litres) at time, t.

This is a MAV question and it's incredibly ambigous. Can anyone help?

Answer:
dq/dt = 5- q/20

They used the chain rule somehow which perplexes me. (someone please show me a way without using chain rule?)

Inflow/outflow questions are based on chain rules so I really don't know how to do it without applying them , but maybe I can show you the thought process behind it so you can understand why we need each step?

After getting 5 - q/20, just get the whole equation under the same denominator and take reciprocal. Then integrate it with respect to Q. Our initial condition is when t = 0, Q=21 (since the tank contains 21% of Oxygen), use that to find c.

[Edward Elric]

Find all other solutions to z^3-(root5-i)z^2 +4Z -4root5 + 4i if root5-i is a solution. Help pls

[Conic]

As the polynomial is 0 when , is a factor of the polynomial. So you can divide the polynomial by . This gives , so the polynomial is . The polynomial is 0 when or when , so the solutions are .

[Brunette15]

Hi everyone,
Can someone please help me with the following question for vectors:

Determine the value of p if a, b, and c are linearly independent where
a= 6i -4j -3k
b= -4i +pj -2k
c= 5i +2j -4k

Thanks 

[allusionx]

Please help me with part c and d.

Thanks. 

[Edward Elric]

As the polynomial is 0 when , is a factor of the polynomial. So you can divide the polynomial by . This gives , so the polynomial is . The polynomial is 0 when or when , so the solutions are .

Thanks so much

[yang_dong]

can someone please explain this question, i get the magnitude bit, but how dont get the opposite direction bit, do i just put a negative in front of the vector?

[brightsky]

indeed you do.

unit vector of i - 2j + 2k is 1/3(i - 2j + 2k). hence a vector of magnitude 6 which points in the direction of i - 2j + 2k is 6/3(i - 2j + 2k) = 2(i - 2j + 2k). we want our vector to be in the opposite direction, so we add a negative sign: -2(i - 2j + 2k) = -2i + 4j - 4k. D looks pretty good to me.

[yang_dong]

thank you brightsky

how did you get: unit vector of i - 2j + 2k is 1/3(i - 2j + 2k), what there like a formula for that, it seems familiar but I cant remember, why did you divide by 1/3

and the you multiplied it by 6 shouldn't I be sqroot(the square of each coefficient of each individual component) and making sure that equals 6m in order to have a magnitude of 6?

sorry, can you please explain further
thank you

[RKTR]

unit vector = vector / magnitude

for i-2j+2k , magnitude =root ( 1^2 +(-2)^2+ 2^2)
                                     =3

[keltingmeith]

and the you multiplied it by 6 shouldn't I be sqroot(the square of each coefficient of each individual component) and making sure that equals 6m in order to have a magnitude of 6?

A unit vector is a vector of length 1 - if you multiply any number by 1, you're going to get that number out.

So, it follows that if you multiply a unit vector by a length a, the resulting vector will have length a. This means that if want our vector to be of length 6, we multiply the unit vector that brightsky found by 6.

If you ever need to find a vector of a specific length in the direction of a given vector, the easiest thing to do is to take the given vector, turn it into a unit vector (divide by its magnitude) and then multiply by the specific length you need it to be.