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March 28, 2024, 07:46:51 pm

Author Topic: Mathematics Question Thread  (Read 1296579 times)  Share 

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emilyyyyyyy

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Re: Mathematics Question Thread
« Reply #4155 on: April 10, 2019, 10:32:11 pm »
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Hi!

I have two questions.
In the integration question, my answer is x^4/4 -2lnx + C. The answer says it should be x^2/3 + 2lnx + C, but I'm unsure how they got that.

And can someone help me with iii and iv of the probability question? Thanks!

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4156 on: April 10, 2019, 11:20:44 pm »
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Hi!

I have two questions.
In the integration question, my answer is x^4/4 -2lnx + C. The answer says it should be x^2/3 + 2lnx + C, but I'm unsure how they got that.

And can someone help me with iii and iv of the probability question? Thanks!

Are you sure you're looking at the right question and the right solution? You're right, but possibly the solutions/questions are jumbled up.

For the second one, A wins if he draws green, B wins if he draws red. For nothing to happen in a round (thus proceeding to the next round), A must draw red, then B must draw green. ie, 3/5 x 2/5, or 6/25. For iii), do it casewise; what's the probability that A wins in one turn? Two? Three? Add these up and you should have the answer. For iv) consider what you had in iii). Notice, that for the win in each increasing number of turns, you need an extra term of nothing happening ie 6/25. This forms a geometric series, see if you can work it out from there!

Hope this helps :)
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emilyyyyyyy

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Re: Mathematics Question Thread
« Reply #4157 on: April 11, 2019, 05:07:25 pm »
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Hi Im back again!

How do I do question ii? I'm unsure how to do it seeing as the question wants me to integrate with x-values, even though the curve is enclosed by the y-axis?
Thanks!

RuiAce

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Re: Mathematics Question Thread
« Reply #4158 on: April 11, 2019, 05:10:17 pm »
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Hi Im back again!

How do I do question ii? I'm unsure how to do it seeing as the question wants me to integrate with x-values, even though the curve is enclosed by the y-axis?
Thanks!
By just treating it as an area between two curves. Note that the upper curve is \(y = 5e^{-x}\), and the lower curve is \( y=e^{\frac{x}{2}}\). That is where they get the integrand (expression to be integrated) from.

Note that for the upper limit in integration, you will need to calculate the point of intersection of the two curves.
« Last Edit: April 11, 2019, 05:11:49 pm by RuiAce »

emilyyyyyyy

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Re: Mathematics Question Thread
« Reply #4159 on: April 11, 2019, 05:14:28 pm »
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By just treating it as an area between two curves. Note that the upper curve is \(y = 5e^{-x}\), and the lower curve is \( y=e^{\frac{x}{2}}\). That is where they get the integrand (expression to be integrated) from.

Note that for the upper limit in integration, you will need to calculate the point of intersection of the two curves.

thanks!
If the question didn't specify how to solve it, if I used y values, would I still get the same answer in finding the area? Or is it just easier to use the x values?

RuiAce

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Re: Mathematics Question Thread
« Reply #4160 on: April 11, 2019, 05:31:58 pm »
+1
thanks!
If the question didn't specify how to solve it, if I used y values, would I still get the same answer in finding the area? Or is it just easier to use the x values?
In theory you would, but you wouldn't want to. You'd have to deal with \( \int \ln x\,dx\), which is an MX2 integral.

emilyyyyyyy

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Re: Mathematics Question Thread
« Reply #4161 on: April 11, 2019, 08:22:14 pm »
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How do I do this question?

I get that I'm integrating it, but I'm unsure which numbers to sub in each time?

thanks!!

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Re: Mathematics Question Thread
« Reply #4162 on: April 11, 2019, 09:54:27 pm »
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How do I do this question?

I get that I'm integrating it, but I'm unsure which numbers to sub in each time?

thanks!!

Howdy! Yep, sounds like you are close, hopefully these hints are just the right amount of help ;D

- Integrate once to get \(f'(x)\). You know there is a stationary point at \(x=0\). So, when \(x=0\), \(f'(x)=0\) for the stationary point! That's how you evaluate the first constant.
- Integrate again to get \(f(x)\), and substitute the given coordinate to evaluate the second constant.

Let us know how you go :)

emilyyyyyyy

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Re: Mathematics Question Thread
« Reply #4163 on: April 11, 2019, 10:00:14 pm »
+1
Howdy! Yep, sounds like you are close, hopefully these hints are just the right amount of help ;D

- Integrate once to get \(f'(x)\). You know there is a stationary point at \(x=0\). So, when \(x=0\), \(f'(x)=0\) for the stationary point! That's how you evaluate the first constant.
- Integrate again to get \(f(x)\), and substitute the given coordinate to evaluate the second constant.

Let us know how you go :)

thank you! I got the right answer now :)

emilyyyyyyy

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Re: Mathematics Question Thread
« Reply #4164 on: April 11, 2019, 10:29:49 pm »
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Sorry to be annoying but is someone able to explain how to do this question?

I eventually got the answers by a bit of trial and error, but I don't understand why for a) I have to multiply by 5 and for b) I only have to multiply by 4 not 5 (bc the person is dealt 5 cards). Hopefully that makes sense?

thanks :)

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4165 on: April 11, 2019, 11:12:48 pm »
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For a), not sure why you'd have to multiply by 5. There's only one way of getting the four aces, but in poker you've got the 'kicker' (the 'other card') which forms the rest of the hand. Since the other four cards are aces, and it doesn't matter what the kicker is, there are 48 different kickers. The probability is going to be that over the total number of ways, which is going to be 52x51x50x49x48 (picking 5 cards) divided by 5! since it doesn't matter what order the cards appear in (effectively removing the ordering), meaning the answer will be

For b), you can first pick the suit, (of which there are 4), then pick any 5 cards from that suit. Similar to above, to pick 5 from 13 we have 13x12x11x10x9 over 5! which eliminates order. We then have all that over the total number of ways, ie the answer will be

Here, we multiply by four for the four suits :)

Hopefully this makes sense, and hope this helps :)
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RuiAce

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Re: Mathematics Question Thread
« Reply #4166 on: April 12, 2019, 09:13:47 am »
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Hello!
I just want to ask for the graph, y=xInx, why is there a point at x=0? Because when I put in 0In0 in the calculator it says MATHS ERROR.
Thank you!
\[ \text{There isn't, however the following }\textbf{limit}\text{ holds:}\\ \boxed{\lim_{x\to 0^+ }x\ln x = 0} \]
Note that if you just naively sub 0 into \(x \ln x\), you get \(0 \times \ln 0\), which can be thought of as \(0\times -\infty\) (due to the asymptote of \(y=\ln x\), which is a math error.

Graphing software like Desmos and GeoGebra would not be able to show you this, but the idea is that in a hand-drawn sketch, a discontinuity (i.e. a hole in the graph) should be located at the point (0,0).

Note that, of course, this limit is not meant to be doable with HSC methods. And that this graph should not be asked for a 2U student.
« Last Edit: April 12, 2019, 09:15:33 am by RuiAce »

Thankunext

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Re: Mathematics Question Thread
« Reply #4167 on: April 15, 2019, 02:27:46 pm »
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Can someone help with part (C) plz.
(A) Use Simpson's rule with 3 function values to find the area bounded by the curve y=Inx, the x-axis and the lines x=2 and x=4.
(B) Change the subject of y=Inx to x.
(C) Hence find the exact area in part (A).
 :'( :'( :'( Please answer me
« Last Edit: April 15, 2019, 07:51:23 pm by Thankunext »

RuiAce

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Re: Mathematics Question Thread
« Reply #4168 on: April 17, 2019, 09:30:48 pm »
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Can someone help with part (C) plz.
(A) Use Simpson's rule with 3 function values to find the area bounded by the curve y=Inx, the x-axis and the lines x=2 and x=4.
(B) Change the subject of y=Inx to x.
(C) Hence find the exact area in part (A).
 :'( :'( :'( Please answer me
This particular question was discussed here.

spnmox

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Re: Mathematics Question Thread
« Reply #4169 on: April 19, 2019, 02:25:56 pm »
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Use the trapezoidal rules with 4 sub intervals to find an approximation to the volume of the solid formed when rotating y=sqrcosx about the x-axis from x=0 to x=pi/2.

So I found the A with x=0,pi/8,pi/4,3pi/8,pi/2 and it was equal to approx 1.4 (maybe someone could confirm this?). I just don't know how to find the volume from this area. Do I square it and then multiply by pi??