VCE Methods Question Thread!

[kinslayer]

For the picture (attached) is my integral for the area of the glass right?

Area
       
       

     

Looks good to me!

[Apink!]

Hi could someone please help me with this question?

I think the answer should be: h*2*(x+1)
but as you can see, it's not one of the answer choices *facepalm*

Thank you so much!

btw, the correct answer is meant to be C

[kinslayer]

Hi could someone please help me with this question?

I think the answer should be: h*2*(x+1)
but as you can see, it's not one of the answer choices *facepalm*

Thank you so much!

btw, the correct answer is meant to be C

You just need to use the chain rule for this one. The form the question is in is different to what's in your textbook but the idea is the same:

u = x(x+2)
y = f(x) = h(x(x+2)) = h(u)

dy/dx = du/dx * dy/du

dy/du = f'(x) = h'(u)
du/dx = 2x + 1

So f'(x) = dy/dx = (2x+1)h'(u) = (2x+1)h'(x(x+1))

This is option C as required.

[Apink!]

wouldn't h' =0? Because it's not asking you to find derivative with respect for h, but for x and so I thought that h could just be assumed as a constant.

Could you please clarify this for me?
Thank you!

[kinslayer]

wouldn't h' =0? Because it's not asking you to find derivative with respect for h, but for x and so I thought that h could just be assumed as a constant.

Could you please clarify this for me?
Thank you!

In the question it is implied that h is a function of x. A priori, there is no reason why h cannot be constant. The problem is that we can't assume that it is and so we need to be more general.

You can check that even if h is constant,  C is still correct.

[StressedAlready]

So... have this question, given a funnel (cone) of radius 40 and height of 100cm; the depth of the water inside being x. Water is drained at a constant rate of 1L/minute (1000cm^3/min or 0.001m^3/min) and we're asked to find the equation so that we can sketch a graph of the height of water (h) against time (t).

Question 2: How do I do this? I tried finding dt/dh by using related rates dV/dt and dV/dh, and once finding these, antideriving the answer for t= in terms of h and using t=0, h=100 to find the value of the constant but I don't know if I'm doing the right thing...

[garytheasian]

need help with q 29 c ii) as well as question 30

[cosine]

f(x) = (x+2)(x-1)(x-3) the answer says the gradient is negative for x an element of (-0.79, 2.12) but there is another option with (1, 3) which i think is correct. Who is right?

This is a multiple choice question from 2001 VCAA exam

[keltingmeith]

f(x) = (x+2)(x-1)(x-3) the answer says the gradient is negative for x an element of (-0.79, 2.12) but there is another option with (1, 3) which i think is correct. Who is right?

This is a multiple choice question from 2001 VCAA exam

The graph is negative between 1 and 3, but not the gradient. They're asking about the gradient. Between 1 and 3, the gradient is both positive and negative.

[garytheasian]

f(x) = (x+2)(x-1)(x-3) the answer says the gradient is negative for x an element of (-0.79, 2.12) but there is another option with (1, 3) which i think is correct. Who is right?

This is a multiple choice question from 2001 VCAA exam

(-0.79, 2.12) is right because for that domain the gradient is negative throughout where as between (1,3) it starts off negative but then turns positive about halfway.

[StressedAlready]

So... have this question I'm stuck on - given a funnel (cone) of radius 40 and height of 100cm; the depth of the water inside being x. Water is drained at a constant rate of 1L/minute (1000cm^3/min or 0.001m^3/min) and we're asked to find the equation so that we can sketch a graph of the height of water (h) against time (t).

How do I do this?

[garytheasian]

So... have this question I'm stuck on - given a funnel (cone) of radius 40 and height of 100cm; the depth of the water inside being x. Water is drained at a constant rate of 1L/minute (1000cm^3/min or 0.001m^3/min) and we're asked to find the equation so that we can sketch a graph of the height of water (h) against time (t).

How do I do this?

do you have a picture of the question?

[cosine]

(-0.79, 2.12) is right because for that domain the gradient is negative throughout where as between (1,3) it starts off negative but then turns positive about halfway.

Yah my bad, forgot to even derive the funciton, just expanded it and forgot to derive. Thanks anyways!

[StressedAlready]

do you have a picture of the question?

I seriously tried. But my artistic ability is questionable, at best. x is the depth of the water remaining in the funnel and we're told that at the beginning of the process, the funnel is filled to the top with liquid.

[garytheasian]

I seriously tried. But my artistic ability is questionable, at best. x is the depth of the water remaining in the funnel and we're told that at the beginning of the process, the funnel is filled to the top with liquid.

You need to use the two values provided to find the relationship between the  height and the radius. The radius at x height will be 2x/5, so now you have r=2x/5. With H = x and r= 2x/5 you can now sub them into the volume equation and then differentiate, which will give you the required graph.

The relationship can be drawn through the use of similar triangle if you are confused. Anyways that is how I would approach the question but I might not be entirely correct so don' take my word for it