VCE Methods Question Thread!

[ZanyCat]

Okay so we have v(t) = -w*A*cos(kx-wt), and we're looking for a(t).

Taking the derivative... w^2*A*-sin(kx-wt), but apparently there's no minus sign in there. Where am I going wrong?

[Alwin]

Hi!
I'm having a derp moment.

Given v(t) = cos(kx-wt), what is a(t)?

I'm thinking that you take the derivative, -sin(kx-wt) and then multiple by the constant in front of t, -w.
This gives a(t) = w*sin(kx-wt).

But using symmetry properties, cos(kx-wt) = cos(wt-kx), and the derivative of this is -w*sin(kx-wt).

Which is right?!

OR




from the identity sin(-x)=-sin(x)



can you see what you did wrong now?

[Markkiieee]

hey guys, was wondering if you could help me out with these 3 questions. thanks


questions attached below

[b^3]

1) We want to find out what rate the radius is increasing. So that is we want . Now we know that the area of the surface of the liquid is increasing at . That is . Now the third piece of information we will need is a relationship between area and radius, so for a circle that is . So then we can use the chain rule, So to get you differentiate the expression for the area in terms of the radius, and we have the second term (flipped). Once you have that substitute in the value of and you should have the rate you're looking for.

Spoiler

2) Hint: The length is increasing at 0.2 cm/s so that means that what? We want to find the rate at which the area is increasing, so that is which rate? And finally how do we relate side lengths of a square and area?

3) Hint: Similar to 1, except that you are looking for the rate that the radius is increasing given the rate that the area is increasing, so the chain rule becomes .

The main ideas here is to
1. Work out what rates you already know
2. Work out what rate you are trying to find
3. Apply the chain rule, normally from the rates you know and the rate you need to find you will be able to fill in another variable in the chain rule that will relate the two.
4. Substitute in the value given to find the final rate.

Anyways, hope that helps.

EDIT: Fixed notation error.

[Markkiieee]

Anyways, hope that helps.

EDIT: Fixed notation error.

Thanks, it did.

But could you please elaborate more on q2?

[b^3]

Well if "the edges of a square are increasing in length at a rate of 0.2 cm/s" then what is the rate (where is the side length). Now since we want the rate at which the area is increasing, we want . Now see if you can try and fill out the chain rule.
After that we still need a relationship between and to get the required derivative for the chain rule. So what is the are of a square?

[Markkiieee]

Now since we want the rate at which the area is increasing, we want dA/dt

why is this? soz :/

[b^3]

If we have , then we have the rate at which increases as we increase . Same as before with, the rate that the radius increases (with respect to time) will be . So the rate that the area of the square increases, that is by how much does the area increase for a unit increase in the time , will be .

[Markkiieee]

If we have , then we have the rate at which increases as we increase . Same as before with, the rate that the radius increases (with respect to time) will be . So the rate that the area of the square increases, that is by how much does the area increase for a unit increase in the time , will be .

thanks alot for your help mate!

[Will Sparks]

The curves with equation y=cosx and y=-2sinx intersect at the point where x= -7π/6.
Find the acute angle between the curves at this point.

Also, find the local maximum and minimum values of f(x) = 2sinx + 1 - 2(sinx)^2 (I.e. 2 sin squared x) where x is an element of [0, 2π]

[darklight]

An aeroplane is flying horizontally at a constant height of 1000 m. At a certain instant the angle of elevation is 30 degrees and decreasing and the speed of the aeroplane is 480km/h.

- How fast is angle of elevation decreasing at this instant (degrees/second)?
- How fast is the distance between the aeroplane and the observation point changing at this instant?

[e^1]

An aeroplane is flying horizontally at a constant height of 1000 m. At a certain instant the angle of elevation is 30 degrees and decreasing and the speed of the aeroplane is 480km/h.

- How fast is angle of elevation decreasing at this instant (degrees/second)?
- How fast is the distance between the aeroplane and the observation point changing at this instant?

Hint: Use diagram (if that helps).
Also note that the airplane is only going forward, since the height is constant.

How fast is angle of elevation decreasing at this instant (degrees/second)?

Note: To get from km/h to m/s, divide it by 3.6. To get from m/s to km/h, divide instead.

How fast is the distance between the aeroplane and the observation point changing at this instant?

EDIT: Huge mistake fixed.

[Alwin]

An aeroplane is flying horizontally at a constant height of 1000 m. At a certain instant the angle of elevation is 30 degrees and decreasing and the speed of the aeroplane is 480km/h.

- How fast is angle of elevation decreasing at this instant (degrees/second)?
- How fast is the distance between the aeroplane and the observation point changing at this instant?

From some notes I made recently for fellow year 12s:

(see attachment)

[e^1]

The curves with equation y=cosx and y=-2sinx intersect at the point where x= -7π/6.

Are you sure that's correct?

[shadows]

Y= e^(4x^2-8x)


Graphs similar to this, are we required to graph them cas free?

With rate of decay/ average rate of change.... Do we need to write units?