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March 29, 2024, 02:19:56 am

Author Topic: Mathematics Question Thread  (Read 1296757 times)  Share 

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onepunchboy

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Re: Mathematics Question Thread
« Reply #360 on: September 03, 2016, 08:15:36 pm »
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Hey guys im not very good at doing probability qs can someone help me out with this one?

Thanks !
« Last Edit: September 03, 2016, 10:15:57 pm by jakesilove »

jakesilove

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Re: Mathematics Question Thread
« Reply #361 on: September 03, 2016, 10:21:35 pm »
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(Image removed from quote.)

Hey guys im not very good at doing probability qs can someone help me out with this one?

Thanks !

Hey! So the smartest way to consider this question is to think about what happens if NONE of the runners finish the race in under 10 seconds. Then, we can take 1-P(none) to find the probability that AT LEAST one finishes within 10 seconds! Let me know if you need me to explain why in any more detail.

Now, the probability of NONE of the runners finishing within 10 seconds will be each of their respective probability (of not completing) multiplied together. If we want events A AND B AND C to happen simultaneously, then their probability will be P(A)*P(B)*P(C). The probability of not finishing will be 1-P(finishing)



Therefore, the probability of AT LEAST ONE of the runners finishing within 10 seconds will be

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Ali_Abbas

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Re: Mathematics Question Thread
« Reply #362 on: September 03, 2016, 10:29:53 pm »
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[IMG]http://uploads.tapatalk-cdn.com/20160903/9c8e20f1a0050a56205d57886442b93f.jpg[/IMG

Hey guys im not very good at doing probability qs can someone help me out with this one?

Thanks !

I just noticed that this question has already been answered by Jake but since mine has already been typed up I will still post it as an additional reference to potentially consolidate your understanding.

The probabilities of each competitor finishing the race in under 10 seconds are given as: respectively. So these are the probabilities of "success".

To solve this question, we make note of the sample space i.e. the list of all possible outcomes (keeping in mind the probabilities of all instances sum to 1). These are:

No successes and three failures, one success and two failures, two successes and one failure, three successes and no failures. Notice however, that the latter three cases can be captured collectively by the single statement that at least one success occurs. We thus obtain the relationship: To calculate the probability that each competitor fails, we simply take the complements of p, q, and r and multiply them together. This is using two applications of the rule that P(A and B) = P(A)P(B). Thus, and the answer is D.
« Last Edit: September 03, 2016, 10:31:32 pm by Ali_Abbas »

jakesilove

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Re: Mathematics Question Thread
« Reply #363 on: September 04, 2016, 12:01:27 pm »
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For anyone looking to absolutely smash their HSC exam, understanding what the question actually expects of you is vital. Check our Rui's beast guide of Maths verbs HERE, and get an edge in your final exam! As always, thanks must go out to the legend himself, RuiAce; Improving Atars Since 2015.
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onepunchboy

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Re: Mathematics Question Thread
« Reply #364 on: September 08, 2016, 06:50:13 pm »
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Hey guys im not really sure how to do question i)  , i got out cos(pi on 6) = -1/2 but not really sure where to go from there..

Thanks !
« Last Edit: September 08, 2016, 06:52:08 pm by onepunchboy »

RuiAce

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Re: Mathematics Question Thread
« Reply #365 on: September 08, 2016, 07:01:22 pm »
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Hey guys im not really sure how to do question i)  , i got out cos(pi on 6) = -1/2 but not really sure where to go from there..

Thanks !




onepunchboy

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Re: Mathematics Question Thread
« Reply #366 on: September 11, 2016, 11:09:17 am »
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Hello again :),  i was wondering how to get the equation for example 10.. dont really know what the question is asking. Thanks !!
Im not sure if this is past hsc

RuiAce

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Re: Mathematics Question Thread
« Reply #367 on: September 11, 2016, 11:16:00 am »
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Hello again :),  i was wondering how to get the equation for example 10.. dont really know what the question is asking. Thanks !!
Im not sure if this is past hsc



conic curve

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Re: Mathematics Question Thread
« Reply #368 on: September 13, 2016, 11:42:43 am »
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How do you do this question


jakesilove

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Re: Mathematics Question Thread
« Reply #369 on: September 13, 2016, 12:03:11 pm »
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How do you do this question

(Image removed from quote.)

You just need to think about the physical interpretation of the derivative. If the derivative is positive (ie. above the x axis), the gradient will be positive. If the derivative is negative (ie. below the x-axis), the gradient will be negative. If the derivative is zero (ie. on the x axis), the gradient will be zero, and so there will be a turning point. Have a go at sketching the function, and I'll let you know if you're correct!
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conic curve

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Re: Mathematics Question Thread
« Reply #370 on: September 13, 2016, 12:26:25 pm »
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This is what I got

I think it may be wrong


RuiAce

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Re: Mathematics Question Thread
« Reply #371 on: September 13, 2016, 12:36:39 pm »
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This is what I got

I think it may be wrong

(Image removed from quote.)
You didn't understand what Jake said.

Think about what the derivative is. If the derivative f'(x) is negative (below the x-axis), then the original function f(x) is DECREASING.
If the derivative is positive (above the x-axis), then the original function f(x) is INCREASING.
If the derivative is 0 (x-intercept), then the original function has a STATIONARY POINT.

(Also it doesn't matter where your graphs start. They can start however low and however high you like. All we care about is that your curve's stationary points are placed at a correct x-coordinate and it increases/decreases where it should be.)

As an exercise, you may wish to sketch y=4x2(x-3) and an antiderivative y=x3(x-4). Use GeoGebra or just Desmos to ensure your graph is correct.
Compare where the DERIVATIVE is ABOVE the x-axis, to where the ORIGINAL CURVE is INCREASING.
« Last Edit: September 13, 2016, 12:45:32 pm by RuiAce »

jakesilove

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Re: Mathematics Question Thread
« Reply #372 on: September 13, 2016, 02:19:41 pm »
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This is what I got

I think it may be wrong

(Image removed from quote.)

As an example, I've plotted the first two derivatives of the basic cubic graph. Can you see what's going on?



Jake
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conic curve

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Re: Mathematics Question Thread
« Reply #373 on: September 13, 2016, 05:08:17 pm »
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As an example, I've plotted the first two derivatives of the basic cubic graph. Can you see what's going on?

(Image removed from quote.)

Jake

Nah not really. Which one would be f'(x)?

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Re: Mathematics Question Thread
« Reply #374 on: September 13, 2016, 05:26:27 pm »
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Nah not really. Which one would be f'(x)?