VCE Methods Question Thread!

[Lasercookie]

Rate of change of volume with respect to time

The puddle isn't just a 2D circle, it's got a height, so we can model it as a cylinder. Volume of a cylinder is

We know that the height is equal to one sixth of the radius too, so



We'll need dr/dV, so we can take the reciprocal

(pay attention to the units and how they 'cancel' out)

[sin0001]

I got the wrong answer, can someone please tell me where i went wrong :S

dr/dt = dr/dV x dV/dt = 12 x dr/dV
V= (pi)(r^2)(h) <----- sub. in h= r/6:
V = (pi)(r^3)/6
so change in volume in respect to radius, dV/dr = (pi)(r^2)/2, so the change in radius with respect to volume, dr/dV = 2/(pi)(r^2)
Then plug that into starting equation (dr/dt= 12 x dr/dV):
dr/dt = 24/(pi)(r^2) <--- sub. in r=20:
dr/dt = 3/50pi  mm/minute

[Lasercookie]

I think you might be correct in subbing in h first, and then differentiating.

Volume of a cylinder is

What I end up doing is treating h as a constant (which it isn't) and then differentiating like that.

(something along the lines of that, anyone have a better explanation?)

Edit: yeah, if I wanted to sub in the h later, product rule would be needed


(product rule)

(same result you got for dV/dr)

[Hutchoo]

I'm pretty sure he's right by subbing in h first and then differentiating.

[bonappler]

Oops sorry guys that wasn't the question I needed to ask it's this one and the answer was 3/50pi

[Lasercookie]

Oops sorry guys that wasn't the question I needed to ask it's this one and the answer was 3/50pi

, find f'(x) edit: left out the reasoning for this, if it wasn't clear, area of a square is , so side length is given by

sub those into the relationship it's asking us to use.

so we can let x = 9 and h = 0.01

sub that into the equation



Now it's just playing around with fractions to get the answer in a form we want
(three and one-six hundredth).

If it wanted the answer as a decimal, you could do division to approximate that

[bonappler]

I was just wondering why you used sqrt(x) as the function.

[TrueTears]

think about how you can obtain a side length from the area of a square, square root seems to be the best choice

[bonappler]

Oh, I understand, I was trying to let the function be x^2 then I substituted the relevant numbers and took the square root of the answer that I got so I could get the side length. (I now realise how wrong I was).

[Special At Specialist]

Someone please help me with this MC matrix transformations question:



Basically, x has been transformed into (x + 2) and y has been transformed into (5y + 2). But how do I express this in matrix form?

[Jenny_2108]

Ans is E
x -> x+2 means translation 2 units in neg x direction -> (-2)
y-> 5y+2 means dilation by 5 parallel y axis and translation 2 units in positive y direction -> x5 then +2

[Special At Specialist]

Ans is E
x -> x+2 means translation 2 units in neg x direction -> (-2)
y-> 5y+2 means dilation by 5 parallel y axis and translation 2 units in positive y direction -> x5 then +2

I'm confused... why is the x translated in the negative direction but y in the positive direction?
Does this have anything to do with the formula:
f(x) -> a*f(1/n (x - b)) + c

[Bhootnike]

is the same as


so, remember how when you have... say a quadractic: (x+1)^2 -3,   we say that the graph has been translated in the negative x-direction,, by 1 unit? and -3 in the y-direction
We 'reverse' the sign of the bracket in otherwords. and We don't change the sign for the number outside the bracket

Same thing applies above.
We have (0.5x+2) in bracket, so that means, we translate by  -2 in the x-direction, and +2 in the y-direction.

[BubbleWrapMan]

Firstly I don't really like their notation (looks like they're adding matrices of different order, wut?) but anyway

We have and

The transformed expression can be rearranged to give

In this form we can see that and , i.e. and

So we need a transformation that will take to . We can see this is E since .

[Jenny_2108]

Ans is E
x -> x+2 means translation 2 units in neg x direction -> (-2)
y-> 5y+2 means dilation by 5 parallel y axis and translation 2 units in positive y direction -> x5 then +2

I'm confused... why is the x translated in the negative direction but y in the positive direction?
Does this have anything to do with the formula:
f(x) -> a*f(1/n (x - b)) + c

Its just the shortcut I do to save time and don't have to write down anything
But if you like more details, ClimbTooHigh already explained