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May 22, 2019, 11:20:28 pm

Author Topic: 4U Maths Question Thread  (Read 238604 times)  Share 

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RuiAce

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Re: 4U Maths Question Thread
« Reply #2280 on: May 14, 2019, 11:04:31 am »
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Hello,
I am confused with this question in the attachment below. I know how to find the area of the triangle (stated in my working out), but I don't know why Area (OLM) is independent of the point P. Can anyone please explain this thoroughly? Thanks :)
The point \(P\) depends entirely on its parameter \(t\). Since your expression for the area does not have this parameter appearing, i.e. it is independent of whatever \(t\) is, equivalently speaking it is independent of the point \(P\).

(Note that \(c\) is assumed to be a constant, not some parameter that is allowed to vary.)

david.wang28

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Re: 4U Maths Question Thread
« Reply #2281 on: May 14, 2019, 11:10:28 am »
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The point \(P\) depends entirely on its parameter \(t\). Since your expression for the area does not have this parameter appearing, i.e. it is independent of whatever \(t\) is, equivalently speaking it is independent of the point \(P\).

(Note that \(c\) is assumed to be a constant, not some parameter that is allowed to vary.)
Ahhh, I get it now. I didn't quite get this concept since the book does not clearly mention the parameter stuff with that question. Thanks Rui!
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david.wang28

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Re: 4U Maths Question Thread
« Reply #2282 on: May 21, 2019, 05:28:32 pm »
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Hello,
I am stuck on Q22 in the link below. I have done some of the question, but I don't get why PRQS is a rhombus unless t^2 = 1 (see attachment). Can anyone please help me out with the remaining part of the question? Thanks :)
HSC 2019: English Advanced(77) (Forgot everything), Chemistry, Physics, Maths Extension 1(35) (repeating), Maths Extension 2, Business Studies(80) (screw this)

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esteban

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Re: 4U Maths Question Thread
« Reply #2283 on: 16 hours ago »
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The midpoint of RS and  the midpoint of PQ are both (ct,c/t). If the diagonals of a quadrilateral are perpendicular bisectors of each other, then that quadrilateral is a rhombus.

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Re: 4U Maths Question Thread
« Reply #2284 on: 4 hours ago »
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Currently stuck on these recurrence relation questions.
Any ideas?

Cheers! :)

RuiAce

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Re: 4U Maths Question Thread
« Reply #2285 on: 4 hours ago »
+1
Currently stuck on these recurrence relation questions.
Any ideas?

Cheers! :)
Remember to also use the add/subtract or multiply/divide same thing trick for recurrence relations, not just integration by parts. The first question is relatively similar to what I did in the April lecture.
\begin{align*}I_n &= \int_0^1 (1-x^r)^n \,dx\\ &= \left[x (1-x^r)^n \right]_0^1 - \int_0^1 x\cdot -rx^{r-1} n (1-x^r)^{n-1}\,dx\\ &= - nr \int_0^1 -x^r(1-x^r)^{n-1} \\ &= -nr \int_0^1 \left[ (1-x^r) - 1 \right] (1-x^r)^{n-1}\\ &= -nr \int_0^1 (1-x^r)^n - (1-x^r)^{n-1}\,dx\\ &= -nr \left( I_n - I_{n-1} \right)\\ \therefore (nr+1) I_n &= nr I_{n-1}\end{align*}

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Re: 4U Maths Question Thread
« Reply #2286 on: 3 hours ago »
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Remember to also use the add/subtract or multiply/divide same thing trick for recurrence relations, not just integration by parts. The first question is relatively similar to what I did in the April lecture.
\begin{align*}\therefore (nr+1) I_n &= nr I_{n-1}\end{align*}

Oh my god, you're an absolute weapon. This logic makes sense. I knew I shouldn't have missed the April lectures.

Just a few questions, where did the [x(1-x^r)^n] bit go? and, How do you know when to use the add/subtract trick?

Thank you so much!!

fun_jirachi

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Re: 4U Maths Question Thread
« Reply #2287 on: 3 hours ago »
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The [x(1-x^r)^n] bit equates to zero when subbing in the boundaries, so it basically just disappears :)

Add/subtract trick comes down mostly to intuition. In this case, seeing that you have an nr out the front of the integral and xr just hanging around, with part of In-1 should tell you that you should manipulate this in some shape or form to the original, especially since you have an nr+1 coefficient for In. Basically, you're looking for an nr x (In-1 - In) to manipulate the integral to find the result. A good way of thinking about it is that if you have a result, think about what you're working towards and think about how you might get to that result. It really just comes down to practice and intuition :)
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Re: 4U Maths Question Thread
« Reply #2288 on: 3 hours ago »
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The [x(1-x^r)^n] bit equates to zero when subbing in the boundaries, so it basically just disappears :)

Ahh cheers, man! Can't wait for you to state rank this course haha. Also an absolute weapon.