VCE Methods Question Thread!

[~V]

sin 2pi/12 =sin pi/6 =1/2

Thought so... Oh shit i looked at the answer being 19pi/12.

[alchemy]

Distance D after t hours is given by the equation: D(t)=10+3sin(pi*t/6), 0<=t<=24. Find the value of t for which D(t)>=8.5.
Is it a must to sketch the graph first (although I have)? Non-CAS question.

[IndefatigableLover]

Distance D after t hours is given by the equation: D(t)=10+3sin(pi*t/6), 0<=t<=24. Find the value of t for which D(t)>=8.5.
Is it a must to sketch the graph first (although I have)? Non-CAS question.

It's not really a 'must' sketch the graph first question unless you don't know how many intersections it has when you draw a line where D(t)>=8.5





Because it's a negative value you know that it'll appear in Quadrants 3&4
Also since it intersects the graph four times, we just double up (the period that is)









I think it's enough there since you're only finding the value of 't' but you should also state the domain (not the right word I know) that 't' is in... you'll know what I mean if you draw the graph (actually maybe you do need to draw the graph LOL)

D(t) >=8.5

= {t: 0<=t<=7}U{t:11<=t<=19}U{t:23<=t<=24}

(Hope that makes sense)!

[soNasty]

if

[rhinwarr]

*Sorry for my weird looking graphs*

From the graphs you can see that the positive solutions for f(x)=0 are at x=3/2 and x=2. To dilate the graph from the y axis so that both of these solutions are between 0 and 1, you will need dilate them by a factor of 1/2 or less. This is because the largest number you can multiply with 2 (the larger solution to f(x)=0) to get a number between 0 and 1 is 1/2.
Therefore, 0<m<=1/2

[alchemy]

*Sorry for my weird looking graphs*

From the graphs you can see that the positive solutions for f(x)=0 are at x=3/2 and x=2. To dilate the graph from the y axis so that both of these solutions are between 0 and 1, you will need dilate them by a factor of 1/2 or less. This is because the largest number you can multiply with 2 (the larger solution to f(x)=0) to get a number between 0 and 1 is 1/2.
Therefore, 0<m<=1/2

You could use https://www.desmos.com/ (and share the link) if you like (:

[soNasty]

how would i solve the following question for:
0<f(|x|)<k ?

[knightrider]

how do you draw a function when there is an unknown factor?

For example f(x)=k(x-2)^2+3

[alchemy]

how do you draw a function when there is an unknown factor?

For example f(x)=k(x-2)^2+3

Well, I suppose you could translate the graph of f(x)=x^2 2 units to the right and 3 units up. Since k hasn't been specified, you can't do so much about dilation though.

[Rishi97]

Could I pls have help me q 2 from pg101 of the Maths QUEST textbook?
Its about composite functions and functional equations
thanks in advance

[Lizzy7]

Could I pls have help me q 2 from pg101 of the Maths QUEST textbook?
Its about composite functions and functional equations
thanks in advance

Try and look at example 30, it's basically using the same principles If it doesn't help then here is my attempt at an explanation:
2/x + 2/y
------------    = x+y   (Make the LHS have the same denominator of xy)
2/xy

2y/xy  +2x/xy
----------------   =x+y (Then now simplify by multiplying by the reciprocal)    --> 2y+2x
2/xy                                                                                                               -----------    =xy/2   (xy cancels out)
                                                                                                                          xy
Therefore x+y=x+y, f(x)= 2/x satisfies the equation

[Frozone]

y=3 cos 2 ( x + pie over 2) - 1
 

* what software are you guys using to show your mathematical notation?

[idontknow2298]

How would you do this question?

[Phenomenol]

How would you do this question?

Long division.

[Einstein]

i tried giving it a shot but got upto the second line with -x^2+5x...