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HSC 2015 Maths Marathon (archive) (1 Viewer)

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Flop21

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Re: HSC 2015 2U Marathon

How does sin^(3)x = 1/8


then turn into



sinx = 1/2
 

davidgoes4wce

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Re: HSC 2015 2U Marathon



The solution:




Must we show the 2nd derivative that it is a minimum point, since there is only one solution for the first derivative? (0=25800t-18000)

I'm not sure how examiners marking are in terms of penalising missing content.
 

psyc1011

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Re: HSC 2015 2U Marathon

Yes, David. Or otherwise, how would you show it's the minimum point continuiing with calculus? (you can't say parabola argument since that disrupts the efficiency of solution)
 

Drsoccerball

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Re: HSC 2015 2U Marathon

Yes, David. Or otherwise, how would you show it's the minimum point continuiing with calculus? (you can't say parabola argument since that disrupts the efficiency of solution)
Or you can just fudge it and say that you tested positive and negative of the stationary point.
 

InteGrand

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Re: HSC 2015 2U Marathon



The solution:




Must we show the 2nd derivative that it is a minimum point, since there is only one solution for the first derivative? (0=25800t-18000)

I'm not sure how examiners marking are in terms of penalising missing content.
Don't need to bother with second derivative or any other calculation, you can just say that the objective function (the function to be optimised) is a concave up parabola, so its stationary point is indeed the minimum. But you do need to provide some justification.
 

Trebla

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Re: HSC 2015 2U Marathon

By the way did anyone actually try answering the question in the original post?
 

leehuan

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Re: HSC 2015 2U Marathon

Is this how to do it?12003290_1483309298638971_4291698591643672812_n.jpg
 

leehuan

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Re: HSC 2015 2U Marathon

That explains why I didn't arrive at a progression. But I think my progression is wrong.









EDIT 2: Wait, how do we know if |common ratio|<1?
 
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Trebla

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Re: HSC 2015 2U Marathon

That explains why I didn't arrive at a progression. But I think my progression is wrong.









EDIT 2: Wait, how do we know if |common ratio|<1?
Think about what the question is asking. You want your savings to actually grow without bound over time, so there is a certain condition you need to impose.
 

leehuan

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Re: HSC 2015 2U Marathon

Should've trusted my instincts and forced the (absolute value of) the common ratio to be greater than 1. But yep, makes sense.
 
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