Mathematics Question Thread

[RuiAce]

Hi guys,
i was doing this series and applications hsc question:
2007 Q3
Can you please let me know if i have the correct answers pls.
thank you
i) Tn = 750 + 100 (n-1)
ii) 1650 m
iii) 12 000 m
iv) 20 days

Quick check on WolframAlpha shows that you're correct

[vic321]

Hi, how do you differentiate tan(x^0.5)? Thanks

[RuiAce]

Hi, how do you differentiate tan(x^0.5)? Thanks

[Asereta]

I have a few maths questions I don't get. Can you help? 

Why is 0.65 * 3 different to 0.65*0.65*0.65?

Q12) Alan buys 4 tickets in a raffle in which 100 tickets are sold altogether. There are two prizes in the raffle. Find the probability that Alan will win
(c) 1 prize
For this question, I used replacement since that's have raffle usually work, where they take out the winning raffle. So my equation was (4/100*97/99) +(96/100*4/99) =193/2475 but the answer is 64/825.
(d) no prizes
I used replacement as usual and I got the equation 96/100*96/99 but the answer's 152/165
(e) at least 1 prize.
Since, I couldn't do d), I can't exactly do e)

13) Mary buys 20 tickets in a lottery that has 5000 tickets altogether. Find the probability that Mary will win
(c) neither first nor second prize.
With replacement since it's a lottery, I did (4980/5000 * 4980/4999) but the answer's 1239771/1249750.

Thank you!

[RuiAce]

I have a few maths questions I don't get. Can you help? 

Why is 0.65 * 3 different to 0.65*0.65*0.65?

Q12) Alan buys 4 tickets in a raffle in which 100 tickets are sold altogether. There are two prizes in the raffle. Find the probability that Alan will win
(c) 1 prize
For this question, I used replacement since that's have raffle usually work, where they take out the winning raffle. So my equation was (4/100*97/99) +(96/100*4/99) =193/2475 but the answer is 64/825.
(d) no prizes
I used replacement as usual and I got the equation 96/100*96/99 but the answer's 152/165
(e) at least 1 prize.
Since, I couldn't do d), I can't exactly do e)

13) Mary buys 20 tickets in a lottery that has 5000 tickets altogether. Find the probability that Mary will win
(c) neither first nor second prize.
With replacement since it's a lottery, I did (4980/5000 * 4980/4999) but the answer's 1239771/1249750.

Thank you!

\(0.65 \times 3\) is \( 0.65+0.65+0.65\)

\(0.65\times0.65\times0.65\) is \(0.65^3\)
_________________________________________________________

Be careful to make sure you know what replacement means. Replacement is when you draw something, and then put it back in there. If you do things with replacement, you denominator should not change.

Since your denominator changed, what you've done is that after you've drawn something, you don't put it back in there. This is without replacement. Which is correct, because it is a raffle, but even then you need to make sure you do not mix up your terminology.




You will find that this same issue is what caused your incorrect answers in 12c and 12d. For 12c, it would be \( \frac{4}{100}\times \frac{96}{99} + \frac{96}{100}\times \frac{4}{99} \)

[owidjaja]

Hey guys,
I need help with question 15c i). Just a bit unsure with what limits to use and which pronumeral to integrate.

Thanks in advance.

[RuiAce]

Hey guys,
I need help with question 15c i). Just a bit unsure with what limits to use and which pronumeral to integrate.

Thanks in advance.

After you sketch the semi-circle, you'll see that the limits should be \( -r \) and \(r\). But try to figure out why that's the case.

Here, \(r\) is a constant. Therefore you integrate w.r.t. \(x\)

[owidjaja]

Hey,
I'm not entirely sure how to do question 16 a).

Thanks in advance.

[Sine]

Hey,
I'm not entirely sure how to do question 16 a).

Thanks in advance.

It's the same methods as you would do otherwise for a volume of revolution. First sketch the graph in terms of "a" and "b". Then you can find the terminals required in terms of "a" and "b". Then use the relation in terms of "a" and "b" in the "volume of revolution formula" nothing changes from a question where you would have numbers in place of "a" and "b" you will just get an answer in terms of "a" and "b".

[RuiAce]

It's the same methods as you would do otherwise for a volume of revolution. First sketch the graph in terms of "a" and "b". Then you can find the terminals required. Then use the relation in terms of "a" and "b" in the "volume of revolution formula" nothing changes from a question where you would have numbers in place of "a" and "b" you will just get an answer in terms of "a" and "b".

I think a part of the problem is that in 2U, they aren't taught the graph of an ellipse. (Nor 3U for that matter)

[kauac]

Hi...
I have spent wayyyyy too long on question 24 and haven't really got anywhere... Any help greatly appreciated. 

Edit: I think the image is attached now 

[RuiAce]

Hi...
I have spent wayyyyy too long on this question and haven't really got anywhere... (There was a diagram to go with it, but I haven't yet worked out how to attach an image to my posts). Any help greatly appreciated. 

Q: Grant is at a point A on one side of a 20m wide river and needs to get to point B on the other side 80m along the bank as shown. Grant swims to any point on the other bank and then runs along the side of the river to point B. If he can swim at 7km/h an run at 11km/h, find the distance he swims (x) to minimise the time taken to reach point B. (Answer to nearest metre).

The image would actually be very helpful here. I have a feeling I know what's going on in this question but I'm not fully sure, so I don't want to dive straight into it.

If you have trouble with the direct method, then make an account on imgur, then upload a screenshot, click on it, and then copy and paste the BBC code that looks something like this

Code: [Select]

[img]some random url[/img]

[gilliesb18]

Hello! Just wondering if someone could help me with this question... its probably the most simple integration question but i cant find anyone to explain it to me!!!
Using the trapezoidal rule, find an approximation for;
\int_1^2 x^(2)dx using 1 subinterval
Is it possible to make sense of that integral??
Thanks!!

[RuiAce]

Hello! Just wondering if someone could help me with this question... its probably the most simple integration question but i cant find anyone to explain it to me!!!
Using the trapezoidal rule, find an approximation for;
\int_1^2 x^(2)dx using 1 subinterval
Is it possible to make sense of that integral??
Thanks!!

[gilliesb18]

Ok great! Thanks heaps...