VCE Methods Question Thread!

[psyxwar]

Thanks
What would would be the implied domain in terms of these questions.
Like what values of x would not be permitted into these equations

60-4x>0 and 4x>0, so each piece of wire is greater than 0 (ie. you can't just have a circle and no square or a square and no circle, since the question tells you the wire is cut into 2 pieces)

=> 60>4x and 4x>0
=> 15>x and x>0
=> 0<x<15

[knightrider]

60-4x>0 and 4x>0, so each piece of wire is greater than 0 (ie. you can't just have a circle and no square or a square and no circle, since the question tells you the wire is cut into 2 pieces)

=> 60>4x and 4x>0
=> 15>x and x>0
=> 0<x<15

Thanks psyxwar

[knightrider]

For this question
The velocity of a train starting from 2 km to left of the
origin is given by v(t) = 10 − 4t, where t is in hours and v(t) is in
kilometres per hour for t ∈ [0, 3].

a)How far is it from the starting point when t = 3? For this question i got the answer but was unsure whether the answer should be in metres or kilometres
c )When and where is the train when it stops? For this question i am unsure whether time should be in hours or seconds
d How far does it travel in the first 3 s?For this question i was unsure whether the answer should be in metres or kilometres

[LiquidPaperz]

can someone tell me how to do this question. and also the last step where its +0.05 , shouldnt it be - Pr ( A' union B) (which i dont know how to figure out)

Thanks

[kinslayer]

P(A) = 0.3
P(B) = 0.4
P(A union B) = 0.65

We know that P(A union B) = P(A) + P(A) - P(A intersection B)

So P(A intersection B) = 0.3 + 0.4 - 0.65 = 0.05

P(A \ B) = P(A) - P(A intersection B) = 0.25. Likewise, P(B \ A)  = 0.35.

Also,  P(complement of (A union B)) = 1 - 0.65 = 0.35.

Now that you have the entire Venn diagram, the last part should follow immediately (it's everything except the part of A that isn't in B, so 1 - 0.25 = 0.75).

[kinslayer]

For this question
The velocity of a train starting from 2 km to left of the
origin is given by v(t) = 10 − 4t, where t is in hours and v(t) is in
kilometres per hour for t ∈ [0, 3].

a)How far is it from the starting point when t = 3? For this question i got the answer but was unsure whether the answer should be in metres or kilometres
c )When and where is the train when it stops? For this question i am unsure whether time should be in hours or seconds
d How far does it travel in the first 3 s?For this question i was unsure whether the answer should be in metres or kilometres

v(t) = 10 - 4t

x(t) = 10t - 2t^2 + C

x(0) = -2 -> C = -2

So x(t) = -2t^2 + 10t - 2

a) x(3) = -2*9 + 30 - 2 = 10, so the train is 10 km away from the starting point when t = 3 s

b) v(t) = 0 -> 10 = 4t -> t = 2.2 s

x(2.2) = 15.60

So the train is 15.6 km away from the starting point when it stops

You can put the answer in whatever units you want, so long as it represents the correct distance. Just remember x(t) is in kilometres, so if you get x(3) = 10, then that means 10 kilometres, 10 000 metres, 1.05702341 × 10^(-12) lightyears, etc etc. If the distance were small, say less than 100 metres, I would use a different unit, but here just stick to kilometres.

[M_BONG]

I think I am right, but answer says otherwise. Can someone explain.

The answer says "E". I chose "D" because a is a real constant, and "b" is negative so D. But it seems too silly a mistake for MAV to be making?

[nhmn0301]

I think I am right, but answer says otherwise. Can someone explain.

The answer says "E". I chose "D" because a is a real constant, and "b" is negative so D. But it seems too silly a mistake for MAV to be making?

I think I would choose E. Reason is "b" in this question itself is already negative. Say I let b=-2. Then put -b will turn it into a +2. Hence, I think it should be (x-b).

[lzxnl]

I think I am right, but answer says otherwise. Can someone explain.

The answer says "E". I chose "D" because a is a real constant, and "b" is negative so D. But it seems too silly a mistake for MAV to be making?

Yeah, regardless of if b is positive or negative, if at x=b the polynomial is zero, the polynomial has a factor (x-b)
You're getting b confused with the absolute value of b

[Zealous]

I think I am right, but answer says otherwise. Can someone explain.

The answer says "E". I chose "D" because a is a real constant, and "b" is negative so D. But it seems too silly a mistake for MAV to be making?

Nope, the answer is E.

The x-intercepts will occur when x=b, x=0 and x=c given the graph they've shown. Given option D and letting it equal 0 for intercepts:
-ax²(x+b)(x-c)=0
x=-b, x=0 or x=c
This gives us an x-intercept of x=-b which is not an intercept. So option D can't be the right answer.

Using option E:
-ax²(x-b)(x-c)=0
x=b, x=0 or x=c

So option E provides the right intercepts. Remember that "b" is a negative number, so when you put it into intercept form, you'll get (x+(-b))=(x-b). In other words, when x=b, x-b=0.

edit: beaten by lzxnl!
edit2: I was also beaten by nhmn, wow I'm slow today.

[LiquidPaperz]

when doing matrix questions like q3, when do you know - when writing out the matrix - that you make it like
[21 35 9]
[...........]
[...        ]   and not the normal

[21......]
[35......]
[9........]

what do you allign which way when writing it out. hope that makes sense.

Thanks
                                                                             

[silverpixeli]

you need to know about how the actual matrix multiplication works, the first matrix in a matrix product has its rows multiplied by the columns in the second matrix. In this case, M is the first matrix and the Cost matrix is the second one. For example for the first calculation in this product it makes sense to multiply 21 (F num) by 6.7 (F cost), 35 (B num) by 18.0 (B cost) and 9 (P num) by 29.5 (P cost) which means 21, 35 and 9 the first row of M, not column.
If you did it the other way the first calculation would be 21 (F num) * 6.7 (F cost), 12 (F num) * 6.7 (B cost) and 7 (F num) * 29.5 (P cost) which doesn't make sense in this problem's context.

[M-D]

Hi,

Could some help with the following question:

What is the value of ?

The question does not allow the use of a calculator and I would greatly appreciate if you could please explain it using the symmetry of the unit circle method.

Thanks

[LiquidPaperz]

P(A) = 0.3
P(B) = 0.4
P(A union B) = 0.65

We know that P(A union B) = P(A) + P(A) - P(A intersection B)

So P(A intersection B) = 0.3 + 0.4 - 0.65 = 0.05

P(A \ B) = P(A) - P(A intersection B) = 0.25. Likewise, P(B \ A)  = 0.35.

Also,  P(complement of (A union B)) = 1 - 0.65 = 0.35.

Now that you have the entire Venn diagram, the last part should follow immediately (it's everything except the part of A that isn't in B, so 1 - 0.25 = 0.75).

with the second last part, ALSO,,,.....

doesnt Pr (A' union B) mean B and not A, which i counted to be 0.35+0.35-0.05 = 0.65 whats this 1- 0.65??

thanks

[knightrider]

v(t) = 10 - 4t

x(t) = 10t - 2t^2 + C

x(0) = -2 -> C = -2

So x(t) = -2t^2 + 10t - 2

a) x(3) = -2*9 + 30 - 2 = 10, so the train is 10 km away from the starting point when t = 3 s

b) v(t) = 0 -> 10 = 4t -> t = 2.2 s

x(2.2) = 15.60

So the train is 15.6 km away from the starting point when it stops

You can put the answer in whatever units you want, so long as it represents the correct distance. Just remember x(t) is in kilometres, so if you get x(3) = 10, then that means 10 kilometres, 10 000 metres, 1.05702341 × 10^(-12) lightyears, etc etc. If the distance were small, say less than 100 metres, I would use a different unit, but here just stick to kilometres.

thanks kinslayer