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March 29, 2024, 04:52:21 am

Author Topic: Methods Assignment Help  (Read 4712 times)

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Rakuu

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Methods Assignment Help
« on: November 12, 2019, 11:39:26 pm »
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 Hello guys ,  :)
Need a bit of help on my IA1, the task is to make a structure (ex. such as waterslide/roller coaster) with different functions. I'm having an issue with connecting my functions (except for linear functions).
For example: Function 1 is trig and next is exponential. I approach this by graphing and just locating where they intersect, and they would connect. HOWEVER, whenever it's zoomed in really closely, they are a bit off (I'm not too sure if this makes sense but I inserted photos). I assumed that this may be because I'm not inputting the whole decimals values. Is this meant to happen? If not, how can I fix this?


Anyways I would greatly appreciate it for any other helpful small/major tips that may help improve my work!! Thank you very much ;D ;D
---Overview of What I know so far ---
1.Introducing diff types of functions and explaining them in details (such as dilations/transfomations..)
2. Parameters ; (height, time, close/open system) Assumptions; (frictionless,average body weight)
3.Solving (finding velocity)


Thank youuu  ;D ;D ;D ;D ;D ;D ;D



RuiAce

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Re: Methods Assignment Help
« Reply #1 on: November 13, 2019, 07:48:50 pm »
+3
Hey :)

Before I jump into this, I just want to make sure I know what's going on. Right now it looks to me as though you basically have two 'disconnected' linear functions.

Are you telling me that you know how to connect these linear functions if you had to, but would struggle with adapting this to exponential and trigonometric functions instead?

(Feel free to add more context :) )

Rakuu

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Re: Methods Assignment Help
« Reply #2 on: November 15, 2019, 04:39:12 pm »
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Hey :)

Before I jump into this, I just want to make sure I know what's going on. Right now it looks to me as though you basically have two 'disconnected' linear functions.

Are you telling me that you know how to connect these linear functions if you had to, but would struggle with adapting this to exponential and trigonometric functions instead?
(Feel free to add more context :) )

Hi, sorry just realised how all over the place my question was. Yes, that's what I meant, is there a way I could smoothly join functions such as trig and exponential together? We are free to choose any variables we want/make our own equation   :)
« Last Edit: November 15, 2019, 04:44:24 pm by Rakuu »

RuiAce

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Re: Methods Assignment Help
« Reply #3 on: November 15, 2019, 07:43:35 pm »
+2
You should be able to adapt the same method. The only thing is that in general for exponentials and sinusoids, you'd be considering functions of the form \( y=e^{bx+c}+k \) or \(y=a\sin (bx+c)+k\).

If you want a sinusoid to pass through a particular point, you can simply sub that point in. For example, if (for some reason) I want it to pass through \( (1,2)\), I would obtain
\[ 2 = a\sin (b+c)+k. \]
Usually by doing this however, I will obtain a constraint on one of these coefficients. (That coefficient could be either one of them.) For example, if I want the constraint to be on \(k\), I can simply solve for \(k\) to obtain
\[ k . = 2 - a\sin (b+c). \]
Without giving too much away, this may be something you wish to consider. A similar thing can be done with exponentials. You should think about what happens to the other unconstrained coefficients!

Specialist_maths

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Re: Methods Assignment Help
« Reply #4 on: November 16, 2019, 07:24:36 am »
+1
Hello guys ,  :)
Need a bit of help on my IA1, the task is to make a structure (ex. such as waterslide/roller coaster) with different functions. I'm having an issue with connecting my functions (except for linear functions).

For IA1, can I assume you've started Unit 3?

If so, you may also want consider the derivatives of each function so that the waterslide is not just continuous, but avoids any points of non-differentiability that may cause injury to the rider.
Teacher of 2020 Seniors: Specialist Mathematics + Mathematical Methods
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Rakuu

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Re: Methods Assignment Help
« Reply #5 on: November 17, 2019, 09:44:01 pm »
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You should be able to adapt the same method. The only thing is that in general for exponentials and sinusoids, you'd be considering functions of the form \( y=e^{bx+c}+k \) or \(y=a\sin (bx+c)+k\).

If you want a sinusoid to pass through a particular point, you can simply sub that point in. For example, if (for some reason) I want it to pass through \( (1,2)\), I would obtain
\[ 2 = a\sin (b+c)+k. \]
Usually by doing this however, I will obtain a constraint on one of these coefficients. (That coefficient could be either one of them.) For example, if I want the constraint to be on \(k\), I can simply solve for \(k\) to obtain
\[ k . = 2 - a\sin (b+c). \]
Without giving too much away, this may be something you wish to consider. A similar thing can be done with exponentials. You should think about what happens to the other unconstrained coefficients!

Thank you, I will try that  :) :)

Rakuu

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Re: Methods Assignment Help
« Reply #6 on: November 17, 2019, 09:55:09 pm »
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For IA1, can I assume you've started Unit 3?

If so, you may also want consider the derivatives of each function so that the waterslide is not just continuous, but avoids any points of non-differentiability that may cause injury to the rider.

Yep unit 3 started, thanks for reminding me on the non-differentiability bit. I asked this question,without researching/approaching it by myself first (which was a very bad idea). I have been researching for the functions having to be continuous and differentiable for it to work, since I made my initial waterslide through trial and error and therefore messing everything up (such as my velocity time graph not connecting).

I figured out how to approach linear/polynomial/quadratic stuffs (but still struggling/about to try in log/expo/trig lol   :o)

Specialist_maths

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Re: Methods Assignment Help
« Reply #7 on: November 18, 2019, 06:45:30 pm »
+1
Yep unit 3 started, thanks for reminding me on the non-differentiability bit. I asked this question,without researching/approaching it by myself first (which was a very bad idea). I have been researching for the functions having to be continuous and differentiable for it to work, since I made my initial waterslide through trial and error and therefore messing everything up (such as my velocity time graph not connecting). I figured out how to approach linear/polynomial/quadratic stuffs (but still struggling/about to try in log/expo/trig lol   :o)
I've always found 'trial and error' or 'playing around' as I call it, a very important part of mastering skills and developing creative thinking (which traditionally isn't done as much as it should be in maths classrooms). Don't worry about messing everything up to start with - that's a key opportunity for learning!
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