Questions

[Rosie]

ok so your saying that if x and y have a number greater than 0, there will be a unique solution

[shinny]

Urgent question!!!

MATRICES
Q. How many of the following five sets of simultaneous linear equations have a unique solution?

1. 4x + 2y = 10
    2x + y = 5

2. x = 0
    x + y = 6

3. x - y = 3
   x + y = 3

4. 2x + y = 5
    2x + y = 10

5. x = 8
    y = 2

Answer choices
A. 1
B. 2
C. 3
D. 4
E. 5

How do i work out the answer especially the ones that dont have an equation, like x = 0, x = 8 etc.

Well for 1, the two equations are actually the same if you multiply the second one by two (and hence there is only one equation for 2 variables), and thus there are an infinite number of solutions. For 2, Mao's proved that already. 3, since there's two different equations, there will be a unique solution (x=3, y=0). For 4, since you have the same equation equal to two different numbers, there cannot be any possible solution, and thus there are no unique solutions. For 5, you don't need to solve anything; it's already given. So thus, C: 3

EDIT: and no, thats not what he's saying. Simultaneous equations will have a unique solution when there are as many unique equations as there are variables. i.e. in this case, you need two unique equations to solve for two variables, x and y. A unique solution just means that there is only one set of x and corresponding y values that can satisfy both equations to be true. For example in one, since both equations mean that 2x+y=5, you could have x=5 and y=-5, or x=3 and y=-1 and so on; there are an infinite number of possibilities. However in 4, there are no values that would satisfy both equations as 2x+y can equal both 5 and 10, which makes no sense at all.

[rayray_t]

A simpler way to solve that problem is to just write out the 'left hand side' of the equation in matrix form and work out the determinant. Any determinant that is equal to 0 will not have a unique solution.

[Rosie]

I just did the 2007 exam 1 vcaa paper and i am really stuck on Q7 of NUMBER PATTERNS. The answer is E but i am really sure that it is B. Can anyone help.   

[Rosie]

In addition to this question, i am having trouble with getting the answers to two other questions.

Q. A closed cubic box of side length 36cm is to contain a thin straight metal rod. The maximum possible length of the rod is closest to :
A. 36cm
B. 51cm
C. 62cm
D. 108cm
E. 216cm
 
i thought that the possible length of the rod can fit diagonal in the box and i get B. But the answer is c. any help

[cara.mel]

sqrt(36^2 + 36^2 + 36^2) = 62.4 => is C

It would be B if it was 2D (you were putting the rod in a square)

so for 3 dimensions you add all 3 sides (same for any number). I can visualise this in my head, but if you can't, don't worry about it

[Rosie]

I just did the 2007 exam 1 vcaa paper and i am really stuck on Q7 of NUMBER PATTERNS. The answer is E but i am really sure that it is B. Can anyone help.  

help needed with this question please

[Odette.]

I just did the 2007 exam 1 vcaa paper and i am really stuck on Q7 of NUMBER PATTERNS. The answer is E but i am really sure that it is B. Can anyone help.  

help needed with this question please

Rosie, if it were B, the common ratio would have had to be between 0 and 1, however in the question it was stated that the common ratio was negative, hence E is the correct answer as it shows a graph that has a negative common ratio. If you need further explanation on this question, just ask. 

Oh and another thing, you should have model graphs in your notes to help you, as in when r is >1, 0<r<1, -1< r<0 and r< -1

[Rosie]

can the Heron's formula only be used if we are given 3 sides of a triangle and not if we have found a side as this would lead to rounding errors. is that right?

[Noblesse]

Well I thought, usually if you have worked out a side and rounded it to the question specification (eg. to 2 decimal places). You are allowed to use that rounded answer in subsequent calculations. Anyone else heard this?

Generally, I prefer to use the 1/2*1side*2side*sin(x) instead, because that is all that is required to work out the other side, so you could use that instead. (unless of course you used SAA form to find the opposite side.)

[vce01]

is it possible to graph a residual plot without finding the regression line guys? or do you HAVE to find it first before you can plot it? (just a tricky ques for me i wanted to clarify)

[Noblesse]

Fairly sure you have to find the regression line, although the calculator can do it without the regression and simply use the StatPlot function.

[Mikey123]

Need a formular of effective interest guys.

[Noblesse]

[vce01]

^ thats from the essential book right? are you going to use that for your bound reference?