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March 29, 2024, 01:03:51 am

Author Topic: 3U Maths Question Thread  (Read 1230264 times)  Share 

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jakesilove

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Re: 3U Maths Question Thread
« Reply #210 on: June 13, 2016, 06:29:58 pm »
+1
Oh wait, slight correction after looking at this again

You forgot the (annoying) +C when integrating

(The final answer is unaffected though because when you subtract the two resultant equations, the C cancels out)

Yeah I thought about including that, but thought it trivial (if one integral equals another, obviously any constant is going to cancel, so generally I just exclude it from the start).
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RuiAce

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Re: 3U Maths Question Thread
« Reply #211 on: June 13, 2016, 06:40:03 pm »
+1
Yeah I thought about including that, but thought it trivial (if one integral equals another, obviously any constant is going to cancel, so generally I just exclude it from the start).
Well in the second line it's kinda important because otherwise, that statement at that step is false

jakesilove

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Re: 3U Maths Question Thread
« Reply #212 on: June 13, 2016, 06:52:39 pm »
+2
Well in the second line it's kinda important because otherwise, that statement at that step is false

True, true; call it laziness!
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amandali

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Re: 3U Maths Question Thread
« Reply #213 on: June 13, 2016, 11:06:23 pm »
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how to do last part thanks

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #214 on: June 14, 2016, 12:05:54 am »
+1
Well in the second line it's kinda important because otherwise, that statement at that step is false

It's funny, at HSC level they stress this sort of thing, my Complex Analysis lecturer is happy for us to omit it in very particular circumstances where it is apparent that the constant is irrelevant. Interesting how the frame of thought changes (though I doubt a marker would take away anything in a HSC exam)  ::)

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #215 on: June 14, 2016, 12:25:19 am »
+1
how to do last part thanks

Hey hey! For a change in direction you are looking for the velocity being zero. To turn back, an object must first stop completely (if we restrict to one-dimensional travel). So, looking at the previous parts of the question, simply solve for the x-values that cause your expression for velocity squared to be equal to zero!! You probably got the expression in this way.



Using initial conditions, we can find the constant and yield:



Now we can solve for this equal to zero (usual methods for solving a quadratic), and we obtain two solutions:



The answer we are looking for is x=1. Think of it this way, the particle starts moving towards the origin from the right. When it reaches x=1, it will turn around and go back the other way. From this point, it will never come back; we can gleam this from equations we have obtained. Acceleration is always positive, it is never going to be accelerated in the negative direction, it is going, going gone  ;)

Let me know if this doesn't make sense! It is kind of intuitive, which is a little easier than the rigorous mathematical approach (unnecessary for this question)  ;D

RuiAce

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Re: 3U Maths Question Thread
« Reply #216 on: June 14, 2016, 08:35:09 am »
+1
It's funny, at HSC level they stress this sort of thing, my Complex Analysis lecturer is happy for us to omit it in very particular circumstances where it is apparent that the constant is irrelevant. Interesting how the frame of thought changes (though I doubt a marker would take away anything in a HSC exam)  ::)
HSC students only know so much so what can you emphasise :P

That's sorta why I chose a definite integral approach though. Ever since 4U mechanics, I've tended to using definite integrals wherever possible, if it makes my calculations a bit easier without loss of accuracy.


amandali

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Re: 3U Maths Question Thread
« Reply #217 on: June 14, 2016, 01:20:28 pm »
0
ques: How many different arrangements of the word MAMMOTH can be made if only five
letters are used?

i dont get the answer
is there an alternative way of doing this


RuiAce

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Re: 3U Maths Question Thread
« Reply #218 on: June 14, 2016, 05:19:17 pm »
+1
ques: How many different arrangements of the word MAMMOTH can be made if only five
letters are used?

i dont get the answer
is there an alternative way of doing this
I'm pretty sure I explained this question recently in the 4U question thread

jakesilove

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Re: 3U Maths Question Thread
« Reply #219 on: June 14, 2016, 05:28:45 pm »
+1
ques: How many different arrangements of the word MAMMOTH can be made if only five
letters are used?

i dont get the answer
is there an alternative way of doing this







Disclaimer: I thoroughly dislike combinatorics. My explanations for them are usually suboptimal to those for other topics. If the explanation is insufficient, please allow someone else to supplement my answer.
My explanations for combinatorics will improve after I do discrete maths, which may be a while.

I wasn't able to justify the method you used either.

The above is Rui's method! Hope it helps :)
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IkeaandOfficeworks

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Re: 3U Maths Question Thread
« Reply #220 on: June 14, 2016, 07:16:11 pm »
0
Can you help me with this motion question? Thanks guys!  :D

A ball is projected so that its horizontal range is 45 metres and it passes through a point 22 1/2 metres horizontally from and 11 1/4 metres vertically above the point of projection. Find the angle of projection and the speed of projection.


RuiAce

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Re: 3U Maths Question Thread
« Reply #221 on: June 14, 2016, 08:59:52 pm »
+2
Can you help me with this motion question? Thanks guys!  :D

A ball is projected so that its horizontal range is 45 metres and it passes through a point 22 1/2 metres horizontally from and 11 1/4 metres vertically above the point of projection. Find the angle of projection and the speed of projection.





RuiAce

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Re: 3U Maths Question Thread
« Reply #222 on: June 14, 2016, 09:10:15 pm »
+2

Note: In the exam, please make sure to evaluate each four of the constants of integration PROPERLY, i.e. when t=0, x'=Vcosθ etc.




imnotdani

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Re: 3U Maths Question Thread
« Reply #223 on: June 20, 2016, 06:58:16 pm »
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Can i please have help with this question? :(

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #224 on: June 20, 2016, 07:10:01 pm »
+1
Can i please have help with this question? :(

Hey there! You sure can, the first bit is to handle the integrand:



Now we complete the integration. We'll use our double angle result to handle the cos squared, which is something you may have seen before, let me know if not!



Let me know if anything here doesn't quite make sense!!  ;D
« Last Edit: June 20, 2016, 07:11:41 pm by jamonwindeyer »