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March 29, 2024, 11:23:32 pm

Author Topic: VCE Specialist 3/4 Question Thread!  (Read 2164669 times)  Share 

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darkz

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9570 on: December 31, 2019, 09:25:44 am »
+2
Hello
Could someone please explain how to graph f(x) = x+1 / x^2-4 tech free?
I was trying to divide it using long division but I am unsure what to do.
Thank you :)

Well this probably isn't the best method, but you can always do the following:
1. Find the asymptotes
2. Find the x & y intercepts
3. Differentiate to consider turning points
4. Sub in points to generate the shape
Generally, these are 4 marks I think? So you can afford to spend time to carefully sketch them.
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Re: VCE Specialist 3/4 Question Thread!
« Reply #9571 on: January 04, 2020, 01:51:20 pm »
0
Can someone help me with part b pls:

 An island has a population of rabbits of size P at time t years after 1 January 2010. Due to a virus, the population is decreasing at a rate proportional to the square root of the population at that time. 
 a)
i)Set up a differential equation to describe this situation.
ii) Solve to obtain a general solution

b) If the population was initially 15 000 and decreased to 13 500 after five years:
i) find the population after 10 years
ii)Sketch a graph of P against t.

I'm quite confused  ???

jnlfs2010

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9572 on: January 12, 2020, 08:52:29 pm »
+2
Can someone help me with part b pls:

 An island has a population of rabbits of size P at time t years after 1 January 2010. Due to a virus, the population is decreasing at a rate proportional to the square root of the population at that time. 
 a)
i)Set up a differential equation to describe this situation.
ii) Solve to obtain a general solution

b) If the population was initially 15 000 and decreased to 13 500 after five years:
i) find the population after 10 years
ii)Sketch a graph of P against t.

I'm quite confused  ???

I'd assume you already have a general solution for the differential equation already.

If the population is initially 15000, thus when t=0, P=15000
If the population is 13500 after ten years, thus when t=10, P=13500

You have now 2 equations to work with and you can solve to find k (constant of proportionality) and c (constant numerical value)

i) can then be solved by substituting t=10 and since you have the equation, you can sketch the graph to do ii)
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Re: VCE Specialist 3/4 Question Thread!
« Reply #9573 on: January 12, 2020, 09:17:22 pm »
0
I'd assume you already have a general solution for the differential equation already.

If the population is initially 15000, thus when t=0, P=15000
If the population is 13500 after ten years, thus when t=10, P=13500

You have now 2 equations to work with and you can solve to find k (constant of proportionality) and c (constant numerical value)

i) can then be solved by substituting t=10 and since you have the equation, you can sketch the graph to do ii)
I see my mistake. Thank you.

Evolio

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9574 on: January 14, 2020, 12:04:31 pm »
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Hey guys! I hope you're doing well.

In this question attached below, I was wondering why the acceleration isn't 0? Because since velocity is constant (10), doesn't that mean that the acceleration is 0?


Sine

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9575 on: January 14, 2020, 12:15:39 pm »
+3
Hey guys! I hope you're doing well.

In this question attached below, I was wondering why the acceleration isn't 0? Because since velocity is constant (10), doesn't that mean that the acceleration is 0?


From the wording of the question it seems like the initial velocity is 10 but once projected it is acted on by other forces such as gravity and friction which allows the object to slip down the slope and you need to calculate the final velocity when it comes back to the initial position (also you need to find the distance it travels up the slope).

Evolio

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9576 on: January 14, 2020, 04:57:04 pm »
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Oh ok, thank you!

I was also wondering for the second part, when they ask you to find the velocity, in the worked solutions they subtracted the downward force from the resistance force but since it's sliding down, there is a greater force downwards so wouldn't it mean subtracting the resistance force from the downward force?

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9577 on: January 14, 2020, 05:19:46 pm »
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Oh ok, thank you!

I was also wondering for the second part, when they ask you to find the velocity, in the worked solutions they subtracted the downward force from the resistance force but since it's sliding down, there is a greater force downwards so wouldn't it mean subtracting the resistance force from the downward force?
I may be wrong, but I think this is because the downward force is negative in this case, since force is a vector quantity.When the body is projected up an incline , the force is positive, hence when the body goes down the slope it is negative. (Basically what I mean is  that they are trying to resolve the forces  in the i-direction of the inclined plane.)
« Last Edit: January 14, 2020, 05:31:12 pm by ^^^111^^^ »

Evolio

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9578 on: January 15, 2020, 05:18:02 pm »
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Are you able to explain this to me a bit further?
Sorry, it's just that I'm confused and not sure if what I have been doing so far is correct.

Sine

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9579 on: January 15, 2020, 05:50:24 pm »
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Are you able to explain this to me a bit further?
Sorry, it's just that I'm confused and not sure if what I have been doing so far is correct.

As for your question a little earlier, the way in which you subtract vector quantities is that you need to be consistent in terms of which direction you arbitrarily deem positive and which way is negative.

Could you show your working/the solutions? since I am 100% sure what you mean by resistance/downward force since I can think of more than one interpretation?

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9580 on: January 15, 2020, 06:06:02 pm »
+2
As for your question a little earlier, the way in which you subtract vector quantities is that you need to be consistent in terms of which direction you arbitrarily deem positive and which way is negative.
This is what I meant. Sorry for being so vague.
Could you show your working/the solutions? since I am 100% sure what you mean by resistance/downward force since I can think of more than one interpretation?
Yes, if possible please show solutions/working as this will be really helpful.

Evolio

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9581 on: January 15, 2020, 06:11:27 pm »
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Here is the worked solution for the second part.

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9582 on: January 15, 2020, 06:21:37 pm »
+3
Here is the worked solution for the second part.
I think you meant acceleration, because to find final velocity they simply took the initial velocity as 0, and added it to 2as.
As for acceleration it is 0.25R - mg sin 20o because in the direction of i the resistance force(friction here) is positive, while the acceleration (mg sin 20 degrees) is negative.

Evolio

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9583 on: January 15, 2020, 06:25:08 pm »
0
But I was wondering why the acceleration is negative?

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Re: VCE Specialist 3/4 Question Thread!
« Reply #9584 on: January 15, 2020, 06:28:11 pm »
+4
But why is the acceleration negative?
This is because as Sine mentioned, we have to be consistent with vector quantities and as force is a vector, it has magnitude as well as direction. In the solutions they arbitrarily take the resistance force as positive. If the resistance force is positive, then the acceleration (which is in the opposing direction of the resistance force) is negative.

Hope that clears your doubt.
« Last Edit: January 15, 2020, 06:32:22 pm by ^^^111^^^ »