VCE Methods Question Thread!

[justsoundslikeaworn-outcliche]

Need help with these questions
sketch f(x) and the inverse of f(x) f(x)=4loge(x-1)-3
And can you show how you found the intercepts etc cos that is really helpful.

and how do I find x in logbase2(x)+logbase2(x-2)=3

And these attached. Thanks heaps!!!!!

[Phy124]

Need help with these questions
sketch f(x) and the inverse of f(x) f(x)=4loge(x-1)-3
And can you show how you found the intercepts etc cos that is really helpful.

and how do I find x in logbase2(x)+logbase2(x-2)=3

And these attached. Thanks heaps!!!!!

is defined for i.e.

To find the x-intercept equate









It will look similar to that of a normal log graph but translated and dilated, give it a shot now that you have the asymptote and intercept

For your second one;

















However

[justsoundslikeaworn-outcliche]

However

Thanks heaps!! I just didnt realise you chad to change the 3 into a log haha

is defined for i.e.

To find the x-intercept equate









It will look similar to that of a normal log graph but translated and dilated, give it a shot now that you have the asymptote and intercept

Yeah, I know how to figure out the inverse, it's just the actual graphing that gets me :S

[Sanguinne]

a cylinder of cheese is to be removed  from a spherical piece of cheese of radium 8 cm. what is the maximum volume of the cylinder of cheese.

[Conic]

The volume of a cylinder is given by:

 

Now you need to find the relation between the radius and the height to make it a polynomial:

From the diagram (using pythagoras):

or

Sub into original:



Then you can use the derivative to find the maximum.

[darklight]

This should be a pretty simple question but I'm not getting the correct answer :/

At a particular university, the probability that an Arts students studies a language is 0.3, literature is 0.6 and both is 0.25. What is the probability that:
a) a student studies either a language or literature?

MY WORKING:
Studies only lang = 0.3 - 0.25 = 0.05
Studies only lit = 0.6 - 0.25 =0.35

hence, student studies EITHER a lang OR lit= 0.40

Their solutions: 0.6+0.3 - 0.25 = 0.65

part b) student studies neither a language or lit?

Solns agree with me - 0.35. However, if they are saying 0.35 for this qn, and 0.65 for above doesn't that mean they haven't accounted for the probability a student studies both? :/

[b^3]

"a) a student studies either a language or literature?"
What they've done is interpret this as the union of studying a language and studying literature. That is they've counted students that study both, as if you study a language, then you fit into the above, if you study lit, then you fit into the above, and if you study a language or lit then again you fit into the above. So
Let be the event that the student studies a language.
Let be the event that the student studies literature.
Then


"part b) student studies neither a language or lit?"
To not study either, then we can find the probability that they study any (which we found previously), then take it away from .

[darklight]

"a) a student studies either a language or literature?"
What they've done is interpret this as the union of studying a language and studying literature. That is they've counted students that study both, as if you study a language, then you fit into the above, if you study lit, then you fit into the above, and if you study a language or lit then again you fit into the above.

But why have they interpreted it that way? By saying EITHER Lang OR Lit, isn't that saying do not including the union bit? I'm confused with the wording..

[Conic]

But why have they interpreted it that way? By saying EITHER Lang OR Lit, isn't that saying do not including the union bit? I'm confused with the wording..

If you mean the intersection, it does include it. You only take it away to prevent it from being included twice.
The set of people doing literature includes people doing literature alone and people doing both literature and language.
The set of people doing language includes people doing language alone and people doing both language and literature.
So if you added these together you would end up with People doing literature alone, people doing language alone, and 2 times the amount of people doing both.
The intersection is taken away from the sum for this reason.
Now the final set of people doing literature or language includes the people doing either or both of those.

[silverpixeli]

When the question is 'either language or lit', that means the union (either or both)
I'm pretty sure if it wanted the chance of either but not both, it would say so eg 'language or lit but not both'

If you study language, you fit into the category 'either language or lit'
If you study lit, you fit into the category 'either language or lit'
If you study both, you also fit into the category 'either language or lit'
If you study both, however, you would NOT fall into the category 'either language or lit but not both'

I understand the confusion that arises, why doesn't 'EITHER language OR lit' imply that the person does not study both? I'm pretty sure that the way myself and the others have explained the terminology is correct, though.

[Sanguinne]

the amount of chlorine in a jug of water t hours after it was filled from a tap is c= 20(t + 1) ^ -1
Find the rate of decrease of chlorine 9 hours after being poured

My final answer is -0.2ml/h which is correct, however I thought the negative would not be there as it is rate of decreases.

Should the negative be there or not??

[Sach1_K]

the amount of chlorine in a jug of water t hours after it was filled from a tap is c= 20(t + 1) ^ -1
Find the rate of decrease of chlorine 9 hours after being poured

My final answer is -0.2ml/h which is correct, however I thought the negative would not be there as it is rate of decreases.

Should the negative be there or not??

isn't just 20/(9+1) = c which is positive 2?
 Don't hate on me If Im completly wrong I don't do 3/4

[silverpixeli]

isn't just 20/(9+1) = c which is positive 2?

It's asking for the rate of change of chlorine when t=9, not the amount of chlorine when t=9
when t=9, there is 2ml of chlorine in the water, but for the rate of change you need to differentiate to find an expression for the rate of change of chlorine in the water.

My final answer is -0.2ml/h which is correct, however I thought the negative would not be there as it is rate of decreases.

Should the negative be there or not??

I'm not sure, it could just be the textbook/wherever the question is from's logic being wrong? If something is decreasing at a negative rate, that means it is increasing, so I would say the answer should technically be positive, unless a question asks specifically for a 'rate of change' rather than a 'rate of decrease' but again, I'm not sure

[Sanguinne]

thanks for the response

[Sanguinne]

a spherical ballon is being deflated and its radium, rcm is decreasing at a constant rate of 5cm/min. at what rate is its volume, Vcm^3, decreasing when the radius of the balloon is 4cm?

for this related rate question i used the chain rule and made this formula
dr/dt = dv/dt x dr/dv
then subbed in
5 = 4 x pi x r² x dr/dv
therefore, dr/dv = 5/4r²pi
then i did the reciproval subbed in x = 4, and then my final answer is dv/dr= 64pi/5.

what did i do wrong as the answer in the book says 320
help is appreciated