VCE Methods Question Thread!

[Daenerys Targaryen]

Go to the forum or place you want to make one. and on the rightish there is new topic. click that and yeah

[jono88]

If 3log2 x  -  7log2 (x-1) = 2+ log2 y, then y is equal to:
My working out
log2 x^3 - log2 (x-1)^7 = 2+log2 y
log2 (x^3/(x-1)^7) = 2+log2 y

What do i do next? Do i change everything to a base of 2? Or is that wrong?
If so i get (x^3/(x-1)^7) = 2^2+y
y= (x^3/(x-1)^7) -4  which isn't correct (MC question)

[Jeggz]

You can change into and this equals .
Then you can just solve for for y  I hope that's the right answer!

[b^3]

When you have a constant, you need to turn it into a log of the same base, so we need to find a log that has base 2 and equals 1. So we can se , which makes (you can only equate things inside the logs when you have the same bases everywhere).


 
EDIT: Beaten

[jono88]

Changing 2 to just 2log2(2) LOL can't believe i missed that! Thanks guys

[Planck's constant]

When you have a constant, you need to turn it into a log of the same base, so we need to find a log that has base 2 and equals 1. So we can se , which makes (you can only equate things inside the logs when you have the same bases everywhere).


 
EDIT: Beaten

That's the way.

With, x > 1 at the end

[justsoundslikeaworn-outcliche]

Hey I'd just love some explanations on how to approach/work out the following questions.
sketch the graph of f:R/{-3/5}--->R,2x+1/5x+3
How do i find the inverse and domain and range?? whilst also the x-inter so I can sketch the graph? And how does "f:R/{-3/5}" come into play?

And how would I find the value of h in terms of x, of a cuboid(made of 640m of wire) that has the dimensions x metres in width, h metres in height and 5x metres in length?
Thanks in advance!!!

[clıppy]

How would i go about finding the implied domain of this function?

[Conic]

How would i go about finding the implied domain of this function?

Remember, since you have the square root, can't be negative, and since it's a fraction you can't divide by 0.

[vashappenin]

Can someone please help me with this?
Thanks

[justsoundslikeaworn-outcliche]

Hey I'd just love some explanations on how to approach/work out the following questions.
sketch the graph of f:R/{-3/5}--->R,2x+1/5x+3
How do i find the inverse and domain and range?? whilst also the x-inter so I can sketch the graph? And how does "f:R/{-3/5}" come into play?

And how would I find the value of h in terms of x, of a cuboid(made of 640m of wire) that has the dimensions x metres in width, h metres in height and 5x metres in length?
Thanks in advance!!!

can someone pls help me with this kinda urgent

[Lasercookie]

Can someone please help me with this?
Thanks

So we have two linear equations (equations of the y = mx + c), and we're told that we have infinite solutions. Lets say we had the equations and A solution to a linear system are whatever values of 'x' we need to satisfy the equations. What does it mean for two linear equations to have infinite solutions?

If they had a unique solution, then they would intersect once. If they had no solutions, they'd intersect never. But for infinite solutions, that means for every x, the two lines intersect. So for all x, or in other words: they are actually the same line.

If they're the same line, then they have the same gradient, and the same y-intercept. So one way of solving this is to find the gradients, and y-intercepts of both equations and equate them together. To find your values, solve for n. Once you've done that, don't forget to double check the values you get to make sure that they actually will give you infinite solutions - you might often end up having to reject one of the values you get.

There's other methods of doing these type of questions too, e.g. using matrices

[Conic]

Beaten, but will post anyway.

Find out when the gradients are the same:











or

Sub both of them in. One will have infinite and one will have none.

n=8:

1:

2:

These have no solutions since they have the same gradient but different y intercepts (The LHS of 2 is the LHS of 1 multiplied by , but the RHS of 2 is not the RHS of 1 multiplied by ).

n=-3:

1:

2:

These have infinite solutions since they're the same line (2 is 1 multiplied by -1).

[e^1]

Hey I'd just love some explanations on how to approach/work out the following questions.
sketch the graph of f:R/{-3/5}--->R,2x+1/5x+3
How do i find the inverse and domain and range?? whilst also the x-inter so I can sketch the graph? And how does "f:R/{-3/5}" come into play?

And how would I find the value of h in terms of x, of a cuboid(made of 640m of wire) that has the dimensions x metres in width, h metres in height and 5x metres in length?
Thanks in advance!!!

To simplify the function, you may use polynomial long division.

Sketching function.

Doing it correctly gives

To explain why the domain of this function excludes , the denominator of the second term cannot equal zero.
Hence solving , this explains why the domain excludes this value.

Furthermore, simplifying the equation more gives . Take note that this function is a hyperbola. From there I'm sure you can do the rest.

And just to be sure about your cuboid question, is it 640 m, 640 m^2 or something else?

[Stick]

Can someone please help me with this?
Thanks

I'd put those equations in matrices, solve the determinant equal to zero and trial each solution in the equations. Remember that if the determinant is equal to zero, it means their either infinite or zero solutions exist, so you must trial each value.