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March 29, 2024, 06:56:09 am

Author Topic: 3U Maths Question Thread  (Read 1230368 times)  Share 

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IkeaandOfficeworks

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Re: 3U Maths Question Thread
« Reply #120 on: May 02, 2016, 05:15:58 pm »
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Hi!, how do you find the inverse of y=x^{3}+3x. Thank you! :D

jakesilove

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Re: 3U Maths Question Thread
« Reply #121 on: May 02, 2016, 05:56:37 pm »
+1
Hi!, how do you find the inverse of y=x^{3}+3x. Thank you! :D

Hey! This would require factorisation of cubic equations, which is immensely complicated and way beyond any curriculum dotpoint (you can check it out here http://www.math.vanderbilt.edu/~schectex/courses/cubic/). Is it possible that you have recorded the question wrong? Perhaps I have missed something, but I can't think of a way to solve this.

Sorry!

Jake
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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #122 on: May 02, 2016, 10:59:36 pm »
+2
Hey! This would require factorisation of cubic equations, which is immensely complicated and way beyond any curriculum dotpoint (you can check it out here http://www.math.vanderbilt.edu/~schectex/courses/cubic/). Is it possible that you have recorded the question wrong? Perhaps I have missed something, but I can't think of a way to solve this.

Sorry!

Jake

IkeaandOfficeworks, in case you were still curious, this is courtesy of Wolfram Alpha  ;)



amandali

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Re: 3U Maths Question Thread
« Reply #123 on: May 03, 2016, 01:20:53 pm »
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not sure how to do this 




for eg. (1+x)^3(1+x)^5
why is the coefficient
(3C3)(5C0) + (3C2)(5C1) + (3C1)(5C2) + (3C0)(5C3)

not (3C0)(5C0) + (3C1(5C1).....

RuiAce

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Re: 3U Maths Question Thread
« Reply #124 on: May 03, 2016, 02:30:06 pm »
+2
not sure how to do this 




for eg. (1+x)^3(1+x)^5
why is the coefficient
(3C3)(5C0) + (3C2)(5C1) + (3C1)(5C2) + (3C0)(5C3)

not (3C0)(5C0) + (3C1(5C1).....




RuiAce

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Re: 3U Maths Question Thread
« Reply #125 on: May 03, 2016, 02:36:09 pm »
+2









katherine123

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Re: 3U Maths Question Thread
« Reply #126 on: May 05, 2016, 03:18:56 pm »
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how do i find the coefficient of x^(-8)
in the expansion of (x-1/x)^6 times (x+1/x)^8


when im asked to find the greatest coefficient eg. (1-2x)^9  am i supposed to exclude the negative when im trying to find k   from T(k+1)/T(k)  >1
since the greatest coefficient is the number largest in magnitude how do i know if there r no 2 greatest coefficient with different sign eg. -80 and 80 

jakesilove

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Re: 3U Maths Question Thread
« Reply #127 on: May 05, 2016, 03:49:17 pm »
+1
how do i find the coefficient of x^(-8)
in the expansion of (x-1/x)^6 times (x+1/x)^8


when im asked to find the greatest coefficient eg. (1-2x)^9  am i supposed to exclude the negative when im trying to find k   from T(k+1)/T(k)  >1
since the greatest coefficient is the number largest in magnitude how do i know if there r no 2 greatest coefficient with different sign eg. -80 and 80

Hey!

I've put the answer to your first question below. You can definitely do it more algebraically, but I think it would take approximately the same amount of time. I also think that this method leaves you less likely to make a mistake!



Jake
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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #128 on: May 05, 2016, 07:43:02 pm »
+1
how do i find the coefficient of x^(-8)
in the expansion of (x-1/x)^6 times (x+1/x)^8


when im asked to find the greatest coefficient eg. (1-2x)^9  am i supposed to exclude the negative when im trying to find k   from T(k+1)/T(k)  >1
since the greatest coefficient is the number largest in magnitude how do i know if there r no 2 greatest coefficient with different sign eg. -80 and 80

Hey Katherine! For your second question, I would look at it like this. If I had the question:



That is extremely ambiguous, and I think it is unlikely to be asked in that form. Much more likely is:



As you say, without specifying the magnitude, you really aren't sure whether the question wants the number furthest from zero on the number line (greatest magnitude), or the number furthest to the right (greatest in the algebraic sense).

The answer to the question above would, by the way, be 5376! I hope this helps a little, sorry if I misinterpreted the question  ;D

amandali

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Re: 3U Maths Question Thread
« Reply #129 on: May 05, 2016, 09:57:30 pm »
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is there a faster way to do this instead of sin both sides , let α=cos^-1(4/5) and β=cos^-1(3/5) and prove sin(β+α)=1
  inverse cos^-1 (4/5) + inverse cos^-1(3/5) = pie/2

jakesilove

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Re: 3U Maths Question Thread
« Reply #130 on: May 05, 2016, 11:13:17 pm »
+2
is there a faster way to do this instead of sin both sides , let α=cos^-1(4/5) and β=cos^-1(3/5) and prove sin(β+α)=1
  inverse cos^-1 (4/5) + inverse cos^-1(3/5) = pie/2

Hey hey!

I've attached my answer below: For questions like this, you generally want to set up some right angled triangles and figure it out from there. It usually isn't this conveniently set up. Generally, you'll create the triangles, find sine of alpha and sine of beta, cosine of alpha and cosine of beta, expand whatever you're trying to solve (using double angle formulas) and just plug in the values you've found.



Jake
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RuiAce

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Re: 3U Maths Question Thread
« Reply #131 on: May 06, 2016, 09:44:36 am »
+1
Hey hey!

I've attached my answer below: For questions like this, you generally want to set up some right angled triangles and figure it out from there. It usually isn't this conveniently set up. Generally, you'll create the triangles, find sine of alpha and sine of beta, cosine of alpha and cosine of beta, expand whatever you're trying to solve (using double angle formulas) and just plug in the values you've found.

(Image removed from quote.)

Jake
Food for thought

RuiAce

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Re: 3U Maths Question Thread
« Reply #132 on: May 06, 2016, 09:47:29 am »
+2
how do i find the coefficient of x^(-8)
in the expansion of (x-1/x)^6 times (x+1/x)^8


when im asked to find the greatest coefficient eg. (1-2x)^9  am i supposed to exclude the negative when im trying to find k   from T(k+1)/T(k)  >1
since the greatest coefficient is the number largest in magnitude how do i know if there r no 2 greatest coefficient with different sign eg. -80 and 80







Note: Greatest coefficient has not been examined in the HSC since the 1980s or something. You must still study it, but it can be the least of your worries.
« Last Edit: May 06, 2016, 11:42:44 am by jamonwindeyer »

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #133 on: May 06, 2016, 11:42:22 am »
+1






Note: Greatest coefficient has not been examined in the HSC since the 1980s or something. You must still study it, but it can be the least of your worries.

That's true, it was first asked in 1988  ;D But be careful, it still appears in Extension 1 Trial Papers relatively frequently, and from memory it popped up in one of my school assessments. Certain schools LOVE it, so I wouldn't dismiss it (and indeed, never dismiss anything!), it's a good thing to know.  ;D

My lecturer for Vector Calculus actually wrote something on this style of question, with some discussion and extension problems. For the curious, you can have a read here, but it is beyond the scope of the course  ;D


amandali

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Re: 3U Maths Question Thread
« Reply #134 on: May 09, 2016, 10:48:41 pm »
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help with this ques thanks
let n be a positive even integer
expand and simplify
(a+b)^n + (a-b)^n


what i got was
2(nC0)a^n + 2(nC2)(a^(n-2))b^2 + 2(nC2)(a^(n-4))(b^4) ....+ 2(nCn)(b^n)