VCE Methods Question Thread!

[Cogglesnatch Cuttlefish]

Can someone help with:



Thank you in advance!

Take out a factor of 2e^2x from the numerator and 5e^x from the denominator
Then the numerator and denominator should simplify to -2e^x/5

Im sorry If I couldn't explain it properly; cant be bothered using the tex thingy and it would be too messy without it   

[knightrider]

How would you do this question?

A sand timer consists of two cones joined at the apex. Each cone has height h, radius r and an angle at the apex of 60°.

Express the radius of the top cone in terms of its height. Give your answer in exact form.

[Floatzel98]

I need help with d) ii). Are we supposed to look at the graphs or equate and solve the two equations? I'm kind of lost with it.

Anyone?

[Eiffel]

this is a property of even functions: f(-x)=f(x)
it means that: the y value of an x value is equal to the y value of -x
for y=(x-h)^2+k to be symmetrical, h can only be 0 because if it is shifted left or right, f(-x)=f(x) is not true

Even functions mean that f(x) = f (-x). Therefore, they are concerned with reflection in the y axis.

Think about it, what is the only value of x will always be true for x = -x... 0!

1 =/= -1
2 =/= -2
etc...

But 0 = -0
0 = 0

Therefore, if your function is to be even, then x can have no horizontal translation.

X - h can only be equal to -(x-h) if the value of h is 0.

Hope that made sense.

Edit: Oh and K can be any real number because symmetry around the y-axis is not affected by vertical translations.

sorry, i still dont understand.

i do understand the property

[Cosec]

Anyone?

What question in particular? Or the whole thing?

[Floatzel98]

What question in particular? Or the whole thing?

I need help with d)ii). The very last part of question 6

[knightrider]

How would you do this question?

A sand timer consists of two cones joined at the apex. Each cone has height h, radius r and an angle at the apex of 60°.

Express the radius of the top cone in terms of its height. Give your answer in exact form.

Question?can someone answer this?

[kinslayer]

sorry, i still dont understand.

i do understand the property

f(x) = (x-h)^2 + k

Assume f(x) is even. Then:

f(x) = f(-x)

(x-h)^2 + k = (-x - h)^2 + k

(x-h)^2 = (-(x+h))^2

(x-h)^2 = (x+h)^2

x^2 - 2h + h^2 = x^2 + 2h + h^2

-2h = 2h

-4h = 0

h = 0

[kinslayer]

Question?can someone answer this?

Draw a diagram. You are looking for a right-angled triangle with opposite and adjacent sides h and r, respectively. (The apex angle will give you the angle, you will need to use symmetry). Then trigonometry tells us that tan(pi/3) = h/r.

[cosine]

Draw a diagram. You are looking for a right-angled triangle with opposite and adjacent sides h and r, respectively. (The apex angle will give you the angle, you will need to use symmetry). Then trigonometry tells us that tan(pi/3) = h/r.

Can someone give me a quick run down on how to solve equations using matrices? Apparently its on my sac tomorrow, i didnt know

[dankfrank420]

Can someone give me a quick run down on how to solve equations using matrices? Apparently its on my sac tomorrow, i didnt know

Transformations? Or just equations?

[cosine]

Transformations? Or just equations?

Equations man, thanks :3

[knightrider]

How would you do 0.06 divided 12 by hand?

[dankfrank420]

Equations man, thanks :3

It's pretty basic, but inverse/matrix multiplication can be tricky at the start.

Try Khan Academy?

[keltingmeith]

Equations man, thanks :3

Consider the following transformations:

-Dilation from x-axis by 1/3
-Reflection in the y-axis
-Translate left 5 units
-Translate up 2 units.

So, consider the mappings
x to x'
y to y'

Well, x and y will both have a relationship with this transformed variables. So first, dilation from the x-axis:

y'=y/3

Next, reflection in the y-axis:

x'=-x

Now, the translations:

x'=-x-5
y'=y/3+2

Now, solving for x and y, we get:

x=-x'-5
y=3y'-6

We can put this into the following matrix equation:



Basically, just write out the transformations, change into a matrix equation (you should be able to go from a set of linear equations into a matrix equation for methods - becomes even more important for Markov Chains later on)

EDIT: Wait, just realised how wrong I read that LOL. Ah well, still here if people need help with matrix transformations. dankfrank420's on the ball with this one.

How would you do 0.06 divided 12 by hand?

It's 0.06/12.
Done. Exact form. (of course, normally we take out the decimals, so I'd multiply top and bottom by 100)