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March 29, 2024, 03:59:18 am

Author Topic: Mathematics Question Thread  (Read 1296797 times)  Share 

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RuiAce

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Re: Mathematics Question Thread
« Reply #675 on: October 20, 2016, 12:48:12 pm »
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Hey I'm stuck on this question:

For what values of k will the equation 2x^2 + 8kx - (1-k) = 0
have roots that differ by 2?

My first thought was to use the formula
α+β=-b/a
and αβ=c/a

I tried to replace 'β' with (α-2) but I'm not sure if I'm doing the right thing, I can't seem to get the answer



That should give the answer. Please show us your working if something happened from here onwards

jakesilove

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Re: Mathematics Question Thread
« Reply #676 on: October 20, 2016, 12:49:54 pm »
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That should give the answer. Please show us your working if something happened from here onwards

Would you also need to do a case where beta = alpha + 2? As the question only asks for 'differs'? Like I dunno if you'd get different answers, but I suppose you would. Conceptually, it shouldn't make a difference, but since I think it would change the answer...
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RuiAce

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Re: Mathematics Question Thread
« Reply #677 on: October 20, 2016, 12:52:06 pm »
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Would you also need to do a case where beta = alpha + 2? As the question only asks for 'differs'? Like I dunno if you'd get different answers, but I suppose you would. Conceptually, it shouldn't make a difference, but since I think it would change the answer...
Those cases should all be addressed at once though... If we do beta = alpha + 2 we just get beta = -2k+1 and alpha = -2k-1

jakesilove

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Re: Mathematics Question Thread
« Reply #678 on: October 20, 2016, 12:54:40 pm »
+1
Those cases should all be addressed at once though... If we do beta = alpha + 2 we just get beta = -2k+1 and alpha = -2k-1

Yeah cool cool, just couldn't be bothered actually checking for consistency aha cheers
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onepunchboy

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Re: Mathematics Question Thread
« Reply #679 on: October 20, 2016, 03:16:54 pm »
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Hey guys can someone help me with part iii) and iv)..

Thanks in adv !!

imtrying

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Re: Mathematics Question Thread
« Reply #680 on: October 20, 2016, 03:18:01 pm »
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Hey:) I'm sure this is fairly simple but i cant remember how to do it:

A rectangle is cut from a circular disc of radius 6cm. Find the area of the largest rectangle that can be produced

Thanks in advance:)
Year 12 2016 (94.20)
English (Adv), Maths Ext.1, Modern History, Biology and Physics

MysteryMarker

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Re: Mathematics Question Thread
« Reply #681 on: October 20, 2016, 03:23:30 pm »
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Hey guys, just a question from the 2005 HSC mathematics exam. I don't really understand this question, so i'd appreciate it if someone could explain how to do each part. Cheers :P

jakesilove

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Re: Mathematics Question Thread
« Reply #682 on: October 20, 2016, 03:33:34 pm »
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(Image removed from quote.)

Hey guys can someone help me with part iii) and iv)..

Thanks in adv !!

Hey! For this question, you need to think about the area under the curve. The area under the curve, when positive, is movement (displacement) in the positive direction. The area under the curve, when negative, is movement (displacement) in the negative direction. You need to find the point at which the area in the NEGATIVE portion is equal to the area in the POSITIVE portion.

For the last part, just consider how integration works. When the gradient equals zero, (ie. dy/dx =0), what does that mean? Have a go, and if you still need help let me know!
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jakesilove

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Re: Mathematics Question Thread
« Reply #683 on: October 20, 2016, 03:41:00 pm »
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Hey:) I'm sure this is fairly simple but i cant remember how to do it:

A rectangle is cut from a circular disc of radius 6cm. Find the area of the largest rectangle that can be produced

Thanks in advance:)

Hey! We basically need to set up some sort of equation, and then differentiate to find a maximum value! Not a simple question at all.

There are actually heaps of ways to do this. I would probably draw a circle, and throw in the angles to your rectangle. You can break the problem into four triangles, and four minor segments. You can easily find the area of the four segments, and then find the MINIMUM area of the four minor segments using calculus. Then, when you find this MINIMUM external area, you can subtract that from the area of the circle to find the MAXIMUM area of the rectangle! Give it a go, and let me know if you can't get a solution out.
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RuiAce

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Re: Mathematics Question Thread
« Reply #684 on: October 20, 2016, 03:42:06 pm »
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Hey:) I'm sure this is fairly simple but i cant remember how to do it:

A rectangle is cut from a circular disc of radius 6cm. Find the area of the largest rectangle that can be produced

Thanks in advance:)
Done in post #538
Hey guys, just a question from the 2005 HSC mathematics exam. I don't really understand this question, so i'd appreciate it if someone could explain how to do each part. Cheers :P
Done in post #466
« Last Edit: October 20, 2016, 04:31:19 pm by RuiAce »

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #685 on: October 20, 2016, 04:34:34 pm »
+1

RuiAce

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Re: Mathematics Question Thread
« Reply #686 on: October 20, 2016, 04:39:39 pm »
+1
How the hell do you remember these? ;D

I just have to remember a few words I typed and the fact I answered it before :P

nibblez16

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Re: Mathematics Question Thread
« Reply #687 on: October 20, 2016, 05:53:00 pm »
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Hello, can you please help me with the last question. I cannot understand properly... Thanks

jakesilove

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Re: Mathematics Question Thread
« Reply #688 on: October 20, 2016, 05:55:20 pm »
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Hello, can you please help me with the last question. I cannot understand properly... Thanks

Check out my answer HERE.
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nibblez16

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Re: Mathematics Question Thread
« Reply #689 on: October 20, 2016, 06:04:08 pm »
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Hey! Cool question, check out my solution below and let me know if I can clarify anything!

(Image removed from quote.)

Jake

Annotation by Rui: In case his first line wasn't clear, Jake rationalised the denominator
       Annotation by Jake of Annotation by Rui: Cheers buddy

Thank You so muchh! Much more easier to understand :D
Quick question... Why does root 2 go infront and root 1 becomes negative?
« Last Edit: October 20, 2016, 06:06:31 pm by nibblez16 »