VCE Methods Question Thread!

[Hutchoo]

OH, I get what I did wrong now! I didn't add the + c so my workings got pretty confusing :/

Thanks bro!

[breadkay]

Hi,

I am struggling to understand this question:

Find the acute angle of intersection between x=2, y=x^2

[brightsky]

At x=2, dy/dx = 2(2) = 4.
so tan(theta) = 1/4
theta = arctan(1/4) = 14.03 degrees

Tip: Draw the graph and don't rely on formulas.

[soccerboi]

Can someone help me with this?

The graph of afunction f lies above the x axis for [0,2] and integral from 0 to 2 f(x)dx=6. The graph of f is dilated by a factor of 0.5 from the x axis, then translated 4 units up. Find the area enclosed by the graph, coordinate axes and the line x=2.

Thanks

[brightsky]

Area = int^(2)_(0) (0.5 f(x) + 4) dx
= 0.5 int^(2)_(0) f(x) dx + int^(2)_(0) 4 dx
= 0.5*6 + [4x]^(2)_(0)
= 3 + 8
= 11 units^2
hopefully that corresponds with the answer you have.

[breadkay]

At x=2, dy/dx = 2(2) = 4.
so tan(theta) = 1/4
theta = arctan(1/4) = 14.03 degrees

Tip: Draw the graph and don't rely on formulas.

Why is it 1/4 and not 4?

[Phy124]

At x=2, dy/dx = 2(2) = 4.
so tan(theta) = 1/4
theta = arctan(1/4) = 14.03 degrees

Tip: Draw the graph and don't rely on formulas.

Why is it 1/4 and not 4?

arctan(4) would give the obtuse angle as the θ in m=tan(θ) is the angle between the line and the horizontal.

If you wanted to use arctan(4) you will have to subtract the given angle from 90°

[breadkay]

Another question 

How does this work?

[b^3]

I probably wouldn't show all the steps below but this should help you get your head around it

[breadkay]

Thank you!!!! 

[ldee]

This is another question like the one a few above, but I cant understand it!

Find the acute angle of intersection of the curves y=sin(2x) and y=cox(x) at the point (pi/2, 0)..

So I found the derivatives of each of the equations to be -2 and -1 at the particular point, but where to go from here?

The worked solutions uses a formula tan(a) = ((-1)-(-2)) / (1+(-1)(-2))... But I've never seen this before, can somebody please explain to me how it works?

[brightsky]

draw the diagram/graph. let a and b be the angle the tangents to y=sin(2x) and y = cos(x) at x = pi/2 make with the negative direction of the x-axis respectively. it is clear that the required acute angle is given by a-b.
now tan a = 2 and tan b = 1. so a - b = arctan(2) - arctan(1) = arctan(2) - pi/4.

[Phy124]

They used the formula for the angle between two lines with gradients and



Alternatively you can work out the angles to the horizontal individually and add/subtract them to give the angle between the lines.

[soccerboi]

Could someone explain how to do this question:
A spinner has three equally likely sectors numbered from 1 to 3.
Find Pr(X=2 | X≠1)

[TrueTears]

Could someone explain how to do this question:
A spinner has three equally likely sectors numbered from 1 to 3.
Find Pr(X=2 | X≠1)

What did the question define the random variable X as?