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Math IA guidance needed!!!!

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Hi guys. I'm in my last year of Math IB (SL) and I'm in desperate need of some guidance. I have no idea how to go about doing my IA.

I've decided that I want to find the optimal speed at which a vehicle (a tank specifically) should travel to get the best fuel efficiency. Along with this, I might also try and figure out the temperatures at which oil would freeze inside the engine by like graphing/modelling it somehow?????? 

 

As you can see, I'm really lost and I don't know how to approach this topic and I don't even know what math I should be using.

Any advice on how I should try and pursue this? 

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I think you should find the optimal speed without going into the physics (not that the oil should ever freeze).

The difficult part of the IA is finding data on fuel usage as a function of speed. Once you do, you can use regression to find a model then integrate different parts of the function to find average fuel use or efficiency. That's all you need to do for this topic. In all these stats IAs, one needs to spend quite some time searching data but the processing is mostly straightforward.

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6 hours ago, kw0573 said:

I think you should find the optimal speed without going into the physics (not that the oil should ever freeze).

The difficult part of the IA is finding data on fuel usage as a function of speed. Once you do, you can use regression to find a model then integrate different parts of the function to find average fuel use or efficiency. That's all you need to do for this topic. In all these stats IAs, one needs to spend quite some time searching data but the processing is mostly straightforward.

So do you think this is a feasible idea that I could get good marks with??? Like is there enough math in it that I can get decent marks in the maths portion?

 

And it's okay if you don't know, the fact that you responded is already super kind and helpful of you!!!! 

Edited by Lucid

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A lot of the grades depend on what you put into the IA, not the topic itself. But I say if you know what you are doing there's no reason to opt for another topic.

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Hi again! I've totally changed my IA idea, and I've hit yet another problem. I'm pretty much done everything for my IA, but the maths just aren't working out. I'm finding and comparing the volume of 2 cups, and I have found a piecewise function consisting of 3 "pieces" that works on Desmos (just from trial and error until the lines matched up). I integrated all 3 of them, and in the end the volume turned out to be around 69.7 mL which is absolutely too little. I don't know what I've done wrong and my teacher isn't willing to help at all. 

*I've learned integration by myself, so I double checked all my integrations with online calculators such as Symbolab and Wolfram Alpha. 

The integrals are: <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>&#x222B;</mo><mrow><mn>0</mn><mo>.</mo><mn>2</mn></mrow><mn>8</mn></msubsup><mi mathvariant="normal">&#x3C0;</mi><msup><mfenced><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>11</mn><mi>x</mi><mo>+</mo><mn>2</mn><mo>.</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>&#xA0;</mo><mo>d</mo><mi>x</mi></math> ,  <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>&#x222B;</mo><mn>8</mn><mrow><mn>8</mn><mo>.</mo><mn>5</mn></mrow></msubsup><mi mathvariant="normal">&#x3C0;</mi><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>5</mn><msqrt><mo>-</mo><mn>4</mn><mo>.</mo><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>8</mn><mo>.</mo><mn>5</mn></mrow></mfenced></msqrt><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup><mo>d</mo><mi>x</mi></math> , <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>&#x222B;</mo><mrow><mn>8</mn><mo>.</mo><mn>5</mn></mrow><mrow><mn>8</mn><mo>.</mo><mn>56</mn></mrow></msubsup><mi mathvariant="normal">&#x3C0;</mi><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>9</mn><msqrt><mo>-</mo><mn>8</mn><mo>.</mo><mn>5</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>8</mn><mo>.</mo><mn>56</mn></mrow></mfenced><mo>&#xA0;</mo></msqrt></mrow></mfenced><mn>2</mn></msup><mo>&#xA0;</mo><mo>d</mo><mi>x</mi></math> 

I'm sorry for always bugging you, I'm terrible at math :( 505848981_Desmosgraph3(goodversion).thumb.png.6e1d453f054689b41ae5804b1f8f8548.png

Edited by Lucid
Clarification

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Well right now you are finding the volume of a cup that is 4 cm in diameter at the open end, and about 8-8.5 cm tall, which is just honestly a tiny cup and 70 mL is not all that unreasonable.

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Omg ya I just realized my entire grid is off!! 

The cup in real life is much bigger than 4cm in diameter (it was about 20 cm tall) 

How can I make my calculations more like the ones in real life? 

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I think you should figure out that yourself, and I should say that if you have the actual cup, it's not difficult at all.

You can also try to find a way to do this without calculus, and compare your answers. The truth is that the most complicated method is not always the best. If you have the cup, there are at least 2 non-calculus ways to do this. 

EDIT:

Other than the scaling issue, there is an inherent problem/error in the way you tried to fit the curves to the cup which is that a cup does not (and should not) look like the curves. In fact you are making the volume harder to calculate than what it should be.

Alright that's enough critique/hints from me, wish you the best!

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