VCE Methods Question Thread!

[Spiritual]

Solve each of the following equations for R:

1. sin(θ - pi/3) = -1/2, θ ∈ [0, 2pi]

2. sin(pi/3 - θ) = -1/2, θ ∈ [0, 2pi]

Can anyone help this is easy but I'm so stuck.

[lzxnl]

I'll show you how to do the first one. You do the second one.

sin(theta - pi/3) = -1/2, theta E [0, 2pi]
Let x = theta - pi/3. Then, x E [-pi/3, 5pi/3]
sin x = -1/2
Just solve this normally subject to the above domain constraint. Then use your x value to solve for theta

[Spiritual]

I'll show you how to do the first one. You do the second one.

sin(theta - pi/3) = -1/2, theta E [0, 2pi]
Let x = theta - pi/3. Then, x E [-pi/3, 5pi/3]
sin x = -1/2
Just solve this normally subject to the above domain constraint. Then use your x value to solve for theta

OH its actually really simple. Thanks!

[Yacoubb]

Hey guys My calculus SAC is tomorrow and I have a couple of questions!

1. A 2% error is made in measuring the radius of a sphere. Find the percentage error in the surface area. (The surface area of a sphere is given by A = 4*pi*r²).

2. One side of a rectangle is three times the other. If the perimeter increases by 2%, what is the percentage increase in area?

3. The radius of a sphere is measured as 4cm with a possible error of 0.05. What is the approximate error for:
(a) the surface area? (S= 4*pi*r²)
(b) the volume? (V= 4/3 * pi * r³)

Thanks

[JHardwickVCE]

Hey guys My calculus SAC is tomorrow and I have a couple of questions!

1. A 2% error is made in measuring the radius of a sphere. Find the percentage error in the surface area. (The surface area of a sphere is given by A = 4*pi*r²).

2. One side of a rectangle is three times the other. If the perimeter increases by 2%, what is the percentage increase in area?

3. The radius of a sphere is measured as 4cm with a possible error of 0.05. What is the approximate error for:
(a) the surface area? (S= 4*pi*r²)
(b) the volume? (V= 4/3 * pi * r³)

Thanks

These three questions are all to do with linear approximation.

1) We can find percentage error by dividing the error by the actual surface area.
To find the error, we use




As there is a 2% error made in measurement



% error=  = 4% error


The other two questions should be using the same method. PM me if you're still unsure

[soNasty]

Last question on the 2011 VCAA Exam 2, why was "Dt/dx<=0" used to find the "range of values of k"? Could someone explain the processes associated with solving that question?

[Frozone]

Sorry for this noob question but can someone show me how to intergrate 24/x^3.
I've just hit a brain fart!

[soNasty]

24/x^3 = 24*x^-3
Becomes 24/-2 * x^-2
= -12/x^2 + c

[Yacoubb]

Hi guys I need some assistance with this question!

Show that a small increase of q% in the radius will cause an approximate increase of 2.3%q in the volume.
Given that h=6, V = 6pir² + 2/3*pi*r³, for r=4.

Thanks!

[Frozone]

Can someone please explain in detail the difference between |f(x)| and f|x|?
My book explains it extremely poorly.

[JHardwickVCE]

Can someone please explain in detail the difference between |f(x)| and f|x|?
My book explains it extremely poorly.

When the mod is around the function, this implies that the y-values are taken as absolute and are always positive. When the mod is only around the x, the x-value  is taken as always positive, so negative values of x would in fact spit out a y-value that correspond to the positive x-value, which suggests that this graph is symmetrical about the y-axis. If you're still confused try graphing the function f(x)=ln(x) and then put the absolute sign in the two places.

[LiquidPaperz]

hey guys ive got no idea how you do velocity time graphs and position time graphs in methods. Is their a certain trick, can someone give me a quick spill on them both. i have no idea how the graphs turn into the graphs under them, not taking into account the table of values (cause who will actually make these?)

[IndefatigableLover]

hey guys ive got no idea how you do velocity time graphs and position time graphs in methods. Is their a certain trick, can someone give me a quick spill on them both. i have no idea how the graphs turn into the graphs under them, not taking into account the table of values (cause who will actually make these?)

Well you know that the derivative of displacement (position) will give you velocity so if you can somehow work out the equation for the position-time graph then you can work out the derivative of it and plot the graph which would be your velocity-time graph
^It can be a bit time consuming to work out the equation but it works.

[LiquidPaperz]

didnt quite understand that, sorry. Could you show me how 'D' is done possibly? thanks

[AngelWings]

If you're still confused try graphing the function f(x)=ln(x) and then put the absolute sign in the two places.

Good advice.

My questions are attached and circled. My calculator gave weird answers that got me nowhere.
For question 1c., my calculator gave: .
Please help by answering the questions and briefly tell me how to do it on the calculator correctly, if I was doing it wrong.
(Solving gave the same answer.)
Thanks in advance.