VCE Methods Question Thread!

[knightrider]

For this question attached i got my answers as follows.



and i got the domain of

Are these right?

[AndyCau]

A hint for part a - think about the largest value of that is possible (think about why this value should be maxmised as well). You could use a Karnaugh Map for this.
A hint for part b - if A and B are mutually exclusive, what can you say about ? The definition of is on the formula sheet.

If you're still stuck I've provided more explanation below.

Answers

A) As the highest value of is 0.7 because you cannot have negative probabilities. In other words, for this sample space if B occurs A also occurs. Then you use the formula . Maximising will maximise
B) Mutually exclusive means that hence . In other words, mutually exclusive events cannot occur at the same time, so if A has occured B will not occur.

thank you 

[keltingmeith]

How would you solve this equation for x?

Try raising both sides to a power that will remove both the 3 and 5. Factorising might help, too.

How would you differentiate ?

Try the chain rule.

For this question attached i got my answers as follows.



and i got the domain of

Are these right?

Not quite. The maximal domain might be what you wrote, but remember that for something to be in the domain of f(g(x)), it must also be in the domain of g(x).

[silverpixeli]

beaten

How would you solve this equation for x?

first instinct is to divide both sides by either one, but you lose the solution x=2 doing that.
to fix this, you can do it with the fractions there, follow the same factorisation steps but it's messy. instead, easiest way is to try raising both sides to the power of 3 and then to the power of 5 (this doesn't change the solutions as ^3 and ^5 are one-to-one)

answer

null factor law,
    or   
       or     

How would you differentiate ?

I'd try breaking it into a hybrid function (when is it actually ln(2x+5)? when is it actually ln(-2x-5)?) and differentiate each chunk like a regular function
after you do this you'll probably realise that both branches give you the same result, because they're just a scalar multiple (-1) apart inside the log, so you could have done it in one step. but you should probably do it the long way to convince yourself of that, and then ask if you're not sure what that means for any future ln|something| you try to differentiate

[knightrider]

beaten

first instinct is to divide both sides by either one, but you lose the solution x=2 doing that.
to fix this, you can do it with the fractions there, follow the same factorisation steps but it's messy. instead, easiest way is to try raising both sides to the power of 3 and then to the power of 5 (this doesn't change the solutions as ^3 and ^5 are one-to-one)

answer

null factor law,
    or   
       or     

I'd try breaking it into a hybrid function (when is it actually ln(2x+5)? when is it actually ln(-2x-5)?) and differentiate each chunk like a regular function
after you do this you'll probably realise that both branches give you the same result, because they're just a scalar multiple (-1) apart inside the log, so you could have done it in one step. but you should probably do it the long way to convince yourself of that, and then ask if you're not sure what that means for any future ln|something| you try to differentiate

Thanks so much  silverpixeli  really helped 

[knightrider]

For this question attached i got my answers as follows.



and i got the domain of

Are these right?

for this question

is my new answer correct?

 i got the domain of ?

[keltingmeith]

for this question

is my new answer correct?

 i got the domain of ?

Yep, that's it!

[knightrider]

Yep, that's it!

The answer says (as attached)?

How did they get that?

[AndyCau]

hey got another methods question 
if a student buys lunch one day from the canteen, the probability of buying it the next day is 72%. If they bring lunch one day, the probability of buying lunch from the canteen is 34%.


a)If Jack made lunch at home on Monday, what is the probability that Jack buys his lunch from the canteen on Friday?

b) what is the long-term probability of this occurring?
i tried using a tree diagram, but it took wayy too long for part a. im pretty  sure im supposed to use a transition matrx..?

thanks in advance 

[qwerty101]

need some help please!

[Splash-Tackle-Flail]

need some help please!

Is the answer E? (will attach working if it is, otherwise idk haha)

[Adiamond]

I would say A but i'm really not sure.
Bump for this question

[knightrider]

The answer says (as attached)?

How did they get that?

Could anyone explain this ?

thanks 

[keltingmeith]

Could anyone explain this ?

thanks 

I have no clue - it's pretty wrong, though.

[knightrider]

I have no clue - it's pretty wrong, though.

ok thanks eulerfan101 

so my answer of  the domain of is right right ?