VCE Methods Question Thread!

[Zealous]

Yeah, I have trouble identifying related rates of change -- I just have no idea which is which. Anyone have any tips on how to approach these?

Hey Cort,
I'll show you a step by step approach for an example question - this should give you a pretty good idea on what to do for most related rates questions.

Question:
The radius of a circular puddle of water is increasing at a rate of 2.5 cm/s. Find the exact rate at which the area is increasing at the instant the radius is 12 cm.

Step 1:
Write out all the information given.



Step 2:
Set up your chain rule equation, put the rate you are trying to find on the left, and the rate you are given in the question on the right.



Step 3:
Using reasoning, figure out what you have to multiply the given rate by (dr/dt in this Q), to result in the rate you want (dA/dt in this Q).



If we multiply by "dA/dr", we can cancel out the "dr" to result in our desired rate (which is dA/dt).

Step 4:
Find the rate you have just introduced into the equation. There should be enough information in the question in order to do so.

We introduced "dA/dr" into our chain rule equation. So we need to find what "dA/dr" is. We are told the puddle is a circle shape so:



Step 5:
Substitute this rate into the chain rule equation with all the information you've acquired.



Step 6:
Substitute your given "condition". We want to find "dA/dr" when r=12, so substitute r=12.




Step 7:
Write your answer:

When the radius of the circle is 12cm, the rate of change of the area of the puddle is 60pi cm/s.

__________________________________

..and you're done!

Hopefully this helps!

[Cort]

Hot damn, thank you zealous!

[Einstein]

can someone please tell me how these answers are obtained. Thanks

[alchemy]

can someone please tell me how these answers are obtained. Thanks

For your first question (q9 on the attached document), why don't you factorise it first to find the x-intercepts? The y-intercept is clearly 12 by subbing in x=0. Since x=2 is a factor, divide the equation by (x-2) and factorise further to get the cubic in intercept form.
For your second question (q8 on the attached document), sub in x=3 into x^2+ax+b to get 9+3a+b=0, via the remainder theorem. Hence, 3a+b=-9. This means 3a+b+10=-9+10=1.

[paper-back]

Hey guys (and girls)
How would you go about finding the inverse of a modulus function?

[Zealous]

Hey guys (and girls)
How would you go about finding the inverse of a modulus function?

If you want the rule of an inverse, I would break up the modulus function into a hybrid function, then find the inverse of each component of the hybrid function. Just remember that there's a good chance you'll get an inverse relation and not an inverse function!

[paper-back]

Thanks zealous

[IndefatigableLover]

Having a serious mental blank now but what does it mean if it tells me to sketch something (say a normal hyperbola) where the function is labelled as f(x) but it asks me to sketch both:

and ?

[Champ101]

Having a serious mental blank now but what does it mean if it tells me to sketch something (say a normal hyperbola) where the function is labelled as f(x) but it asks me to sketch both:

and ?

Basically if it is modulus of x (the absolute of only around the x) it means that the graph is going to be symmetrical about the y-axis (all the y-values of the positive x values will be reflected in the y-axis to give negative x-values for the same y-values . If it is |f(|x|)|(absolute around the whole equation and a separate absolute around the x)  it means that you are going to reflect all y-values of the positive x-values in the y-axis to give negative x-values of the the same y value. The outer modulus (|f(x)|) means that once you have applied the step previously mentioned you will then reflect all the negative y-values in the x-axis.
Hope it helps!

[Reus]

Can anyone workout part c for me?
Thanks in advance.

[IndefatigableLover]

Basically if it is modulus of x (the absolute of only around the x) it means that the graph is going to be symmetrical about the y-axis (all the y-values of the positive x values will be reflected in the y-axis to give negative x-values for the same y-values . If it is |f(|x|)|(absolute around the whole equation and a separate modulus around the x)  it means that you are going to reflect all y-values of the positive x-values in the y-axis to give negative x-values of the the same y value. The outer modulus (|f(x)|) means that once you have applied the step previously mentioned you will then reflect all the negative y-values in the x-axis.
Hope it helps!

Oh wow such a brain fade T_T.. I was supposed to sketch a hyperbola as f(|x|) but the solution only showed one part of the hyperbola being reflected along the 'y-axis' whereas the other part wasn't shown in the end LOL

Thanks for that Champ101!

[IndefatigableLover]

Can anyone workout part c for me?
Thanks in advance.

Okay so it says that the population of tigers and elephants are the same.



(divide by 50)

(Changing into the same powers and then simplifying by applying index laws)

(Same base)

(Simplify)



(0.6 = 6/10)



Since t is in months after January, therefore the population will be the same on 1 June 2006

[alchemy]

Solution attached. Beaten by IndefatigableLover though

[Champ101]

Solution attached. Beaten by IndefatigableLover though

Alchemy is correct, there is just one small error in the workings on the 3rd line. When dividing by 2^-0.2t you do not drop the negative sign in front of the 0.2 otherwise when you divide it would become 2^0.2t instead of 2^0.6t 

[Reus]

Could anyone please do this for me? I ended up with
 y=√x-9 + 6
 D: x≥9
 R:R

Not too sure with it though, so if anyone could tell me if it's correct? As my teacher didn't provide answers with the sheet haha
Thanks in advance.