#$&*
Mth 173
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
proportionality
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Solve using proportionalities by stating the appropriate proportionality law and finding the proportionality constant:
If a concrete sphere 2.9 meters in diameter has a mass of 604847.3 kg, then what would we expect to be the mass of a concrete sphere 4.7 meters high?
If it requires 3.1117 liters of paint to cover the first sphere, how many liters will be required to cover the second?
???as far as I have been able to detect so far, proportionality seems very trial and error like, and knowing basic functions like
y=kx and y=ksqrt(x) and y=kx^2 . Am I missing something or is this just the case, and we can just check it by seeing if k will remain fairly constant, if not completely constant. And is proportionality just a generic group, because every function we have been working with seems to be a type of proportionality, a quadratic equation is still a proportionality of y tested to x. which makes me think that the information of just knowing y=kx and y=ksqrt(x) and y=kx^2 and things like that a little useless, unless I am trying to find a simple equation.
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If the quadratic equation is of the form y = a x^2, then it is a proportionality with the square. However a quadratic of the form y = a x^2 + b x + c, with a and either b or c, or both, nonzero, is not a proportionality.
Quantity Q is proportional to quantity P is there exists a constant k such that Q = k P.
If Q is area and P is the square of the length of a side, then the proportionality Q = k P becomes
area = k * (side length)^2.
If Q is volume and P is the cube of diameter, then the proportionality Q = k P becomes
volume = k * (diameter)^3.
If Q is the period of a pendulum and P the square root of the length, then the proportionality is
period = k sqrt(length).
Proportionalities arise in a variety of ways. The simplest to understand are proportionalities of area and volume between geometrically similar objects, because these proportionalities can be reasoned out from the properties of squares and cubes.
y = k x^2 is the proportionality between areas of geometrically similar objects. This is because, as explained in the modeling project, it is possible to cover as much of the area as desired with squares, given any simple geometrical object. If the squares are small enough, they will cover any given percent of the area, provided by percent is less than 100%. So, for example, we can cover 99.99999% of any given object with squares, if the squares are small enough. We can get as close to 100% as we wish.
Since the area of a square increases in proportion to the square of any chosen linear dimension (e.g., its side, or its diagonal, or its perimeter)), the same must be so of any set of geometrically similar objects.
A similar argument shows that any simple three-dimensional solid can be filled as completely as we wish with tiny cubes, so that the volumes of any set of geometrically similar solids must be proportional to the cube of some chosen linear dimension.
The proportionality between pendulum period (i.e., the time required for a cycle) and length arises from nongeometric physics properties of the pendulum.
Other proportionalities arise in different ways.
The one thing all proportionalities have in common, though, is that they are of the form
Q = k P
for some quantities Q and P.
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???how do I find the appropriate one? guessing?
604847.3 = k(2.9)
k=208568.03448
y=208568.03448x
????how would I test this, taking the derivative? that would make everything cancel out though would it not?
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I don't understand how to figure out, and prove a proportionality law.
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I tried doing a quiz, but I am unsure of how to do the proportionality law's and prove them. was hoping on some help before I tried again.
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The main proportionalities you have to know are the geometric proportionalities, based on the square and the cube. You should be able to figure these out.
You don't need to know how to figure out the nongeometric proportionalities involved with, say, a pendulum, though if you are given the proportionality you should be able to use it.
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Related to the current problem, the mass of a concrete sphere occupies its volume, so the appropriate proportionality is
mass = k * volume^3
or if you prefer to use x and y
y = k x^3 where y is mass and k is volume.
You are expected to know that mass occupies volume.
Similarly you are expected to know that paint covers the surface only, not the volume, and the amount of paint is proportional to the area of the surface. So the proportionality would be of the form
y = k x^2.
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I'll be glad to clarify further, or look at your reasoning and solution to this and/or other related problems.
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#$&*
Mth 173
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Computer Science math
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personal question not related to the course
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Instead of typing a long paragraph to sum things up quickly, I like to code, and in fact my major is Computer Science. The type of code I deal with likes to involve math (well almost all code seems to like to use math, but I hope you get what I mean). More specifically it likes to use arrays, and vectors a bit. as well as being able to understand how to get a generic 'equation' to solve something instead of using specifics.
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I was wondering if you would not mind to, if I ever need the help past the course, help me with any problems I have relating to math. You seem to explain things very well to my understand more than a surface level, and I can already see from things you have shown in the course that I could implement in a few lines of code.
If you are wondering what sort of stuff this could involve:
I want/like to code games. A lot of the VISUAL aspects itself are based on a window of point (x,y) where all values have to be 0 or positive, and you must render images/sprites/textures or what be you onto this window. each of these sprites/images/textures have their own rectangular/vector/triangular values, and then both get a local and global setting. the global being its original value, and how you modify it, you can scale it, transform it, rotate it, and it has to update every second. I have to be able to track each movement at times (and at a 60 frames per second, the only possible way would be to have an equation that would allow this that I can think off of the top of my head). the visuals itself aren't too hard, but still sometimes knowing a little bit of math helps solve some of the issues. But if you wish to keep reading, below is where it gets a little more useful.
The content of the game.
damage calculations, a rate of health going back up, based on modifiers, all the video game stuff.
and of course.
Physics...physics...and more physics...I really am not good at physics
(seeing as I have never had a course on it, I guess this is reasonable)
some things I can think off the top of my head is, many games have a vehicle, and in a 3d game (and although very limited, partly in a 2d game)
the acceleration, braking, type of terrain, collisions, and all of that in itself are daunting, not even thinking about the rest of it. Then in shooters, bullet trajectory, the amount it falls, how it affects the bullet if the person is moving (or if it doesn't, I don't know, im just spitballing here).
Most of this will be in the far future probably, these are just my dreams to be able to get into all of this coding. But I really do love it, even though right now I still have lots to bugs and pondering to do even working with 2d games. But I still really enjoy the way you explain things, and help to understand them, so was hoping if I ever needed it you could assist me on the math portions of my coding.
I really hope you can, now I've gotten myself all worked up. haha.
Since I have gotten this informal, if you also wish to know, I love math and science, which may be why I enjoy what I do so much, when everyone around me says they don't see how I could stand to sit at a computer and stare at logical structures, and templates, and equations for this and that.
Thank you very much in advance.
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Many of the things you are talking about are based on the same ideas as translating a graph by vertical and horizontal shifts. What you can do with a graph you can also do with a sprite or other object. You're just moving things around in 2- or 3-dimensional space.
The physics of the situation is fairly straightforward. An object moving under the influence of gravity has a vertical position described by a quadratic function, and a horizontal position described by a linear function.
You're asking great questions, and I'll welcome any other questions you might have.
You should also consider taking a physics course (mine or someone else's) at some point. There is nothing that builds programming ability like the problem-solving you encounter in physics.
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