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March 28, 2024, 08:06:07 pm

Author Topic: Mathematics Question Thread  (Read 1296608 times)  Share 

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Aussie1Italia2

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Re: Mathematics Question Thread
« Reply #855 on: November 04, 2016, 08:52:26 pm »
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Hey!!! I have two new questions that I need help with.  :-\ I think I know how to do them but I just need some reassurance; please and thank you!!!

1. Express x2 - 4x + 5 in the form Ax (x+2) + B (x +1) + C + 4

2. Show that x2 + 2x + 9 can be written in the form a (x-2)(x+3) + b (x-2) + c where a=1, b=1, and c=17
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jakesilove

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Re: Mathematics Question Thread
« Reply #856 on: November 04, 2016, 08:55:23 pm »
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Hey!!! I have two new questions that I need help with.  :-\ I think I know how to do them but I just need some reassurance; please and thank you!!!

1. Express x2 - 4x + 5 in the form Ax (x+2) + B (x +1) + C + 4

2. Show that x2 + 2x + 9 can be written in the form a (x-2)(x+3) + b (x-2) + c where a=1, b=1, and c=17

Hey! In both methods, you just need to expand the 'form' equation (ie. Ax (x+2) + B (x +1) + C + 4). Then, equate the x^2 terms, the x terms and the constant terms with the original question. For instance, if you expand, the only x^2 term is Ax^2. Therefore, for the first one, A=1! Let me know if there's something specific you're struggling with, or if you need the whole answer; sounds like you're on the right track!
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Aussie1Italia2

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Re: Mathematics Question Thread
« Reply #857 on: November 04, 2016, 09:04:40 pm »
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Can you please try explaining that another way? It didn't make sense at all to me. Thank you!!! :D
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jakesilove

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Re: Mathematics Question Thread
« Reply #858 on: November 04, 2016, 09:11:25 pm »
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Can you please try explaining that another way? It didn't make sense at all to me. Thank you!!! :D



We equate x squared terms in each equation












Therefore, the expression can be written as

ATAR: 99.80

Mathematics Extension 2: 93
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RuiAce

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Re: Mathematics Question Thread
« Reply #859 on: November 04, 2016, 09:24:48 pm »
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Can you please try explaining that another way? It didn't make sense at all to me. Thank you!!! :D

« Last Edit: November 04, 2016, 09:29:26 pm by RuiAce »

Aussie1Italia2

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Re: Mathematics Question Thread
« Reply #860 on: November 05, 2016, 02:52:16 pm »
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Hey again!

Can we tell I suck at maths yet?
Thanks for the help!

Find values of A, B, and C if x2 + x - 2 = A (x-2)2 + Bx + C
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RuiAce

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Re: Mathematics Question Thread
« Reply #861 on: November 05, 2016, 02:55:57 pm »
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Hey again!

Can we tell I suck at maths yet?
Thanks for the help!

Find values of A, B, and C if x2 + x - 2 = A (x-2)2 + Bx + C



katnisschung

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Re: Mathematics Question Thread
« Reply #862 on: November 05, 2016, 09:37:20 pm »
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need help solving this trig identity
« Last Edit: November 05, 2016, 09:46:33 pm by katnisschung »
get me out of here

jakesilove

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Re: Mathematics Question Thread
« Reply #863 on: November 05, 2016, 09:52:46 pm »
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need help solving this trig identity

Hey! The trick to a question like this is to let sin(x) be equal to a variable; I like using u.




Now, we can just solve this like any old quadratic! You can either use the quadratic equation, or any other method you can implement. It ends up simplifying to



Great! We can now let each brackets be equal to zero







Now, let's change our u's back into sin(x)s




Can you see any issues? You definitely will as you study this area more :) sin(x) oscilates between -1 and 1, so will never equal 3! If you don't believe me, try typing shift sin of 3 into your calculator :)

That leaves us with the equation sin(x)=1/2. We can solve this in the normal way, which gives us



So those will be our answers!
ATAR: 99.80

Mathematics Extension 2: 93
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Chemistry: 93
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RuiAce

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Re: Mathematics Question Thread
« Reply #864 on: November 06, 2016, 08:58:23 am »
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need help solving this trig identity
Regarding the website you used, that was a trigonometric equation; not proving an identity. So if you chose the next option on that list on the left you would've gotten the computerised solution

katnisschung

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Re: Mathematics Question Thread
« Reply #865 on: November 06, 2016, 12:31:40 pm »
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i cant find it in exact value form  :(
get me out of here

RuiAce

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Re: Mathematics Question Thread
« Reply #866 on: November 06, 2016, 12:59:53 pm »
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katnisschung

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Re: Mathematics Question Thread
« Reply #867 on: November 07, 2016, 05:57:54 pm »
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thanks in advance  :)

question on series

The sum of the first 5 terms of an arithmetic series is 35 and the sum of the next 5 terms is 160
find the first term and the common difference
get me out of here

RuiAce

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Re: Mathematics Question Thread
« Reply #868 on: November 07, 2016, 06:08:03 pm »
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thanks in advance  :)

question on series

The sum of the first 5 terms of an arithmetic series is 35 and the sum of the next 5 terms is 160
find the first term and the common difference





RuiAce

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Re: Mathematics Question Thread
« Reply #869 on: November 08, 2016, 02:13:30 pm »
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I know that nobody really cares, but I just felt the need to share this exponential growth question which could've gotten 4-6 marks in the HSC... as opposed to in ACTL ;D



Any thoughts Jamon? :P