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Old 03-30-2005, 05:14 PM   #1
randyriver10
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Struggling with Math, need help


My teacher isn't really nice, and rushes things. I can't seem to pay attention, yet in other classes, I listen well.

It's grade 10 math, who wants to help?
 
Old 03-30-2005, 08:08 PM   #2
twilli227
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Do you have tutors at your school?
Do you have any friends that could help you?
Have you tried to talk to your teacher?
Have you asked your teacher for some extra help?
Can you ask your teacher to please slow down?
Can your parents help you?

Hope this helps.
 
Old 03-30-2005, 08:21 PM   #3
penguinlnx
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are there no workhouses? no prisons? -scrooge

Hey! no sweat: just ask me anything!

If I didn't write a paper on it, it isn't important.
 
Old 04-01-2005, 02:07 PM   #4
randyriver10
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Thanks guys.

My teacher refused me extra help. She told me to look through my notes first.


penguinlnx, if you're serious, can I scan you my work, and have you explain it to me?

Explain it, don't do it for me, LoL.
 
Old 04-01-2005, 04:50 PM   #5
penguinlnx
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Sure: Math is my favourite subject!

By the time we're done, you'll be able to disprove the Sphere Theorem! (most University grads can't!)

Let's give it a go!
 
Old 04-02-2005, 10:37 AM   #6
randyriver10
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Y=MX+B

This equation. I'm sick of it. I can do the work like for example....

A(SQUARED) +4= A +6
-4 -4

A2= A+2

-a -a

A:2




I can do that work. But it's the graph work that confuses me. Plotting it, and what each character means, and how to remember it.
 
Old 04-02-2005, 02:15 PM   #7
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Yeah, I remember how boring and pointless this seemed in high-school.
And they go out of their way to make it not just incomprehensible, but impenetrable, like Superman's fortress of Solitude.

Here's the Bad News: They do this on purpose, so that all the poor kids and middle-class kids are left to piss about and waste 5-10 years of their lives, while the rich kids fly ahead with private tutors and cheat-sheets.

The Good News: You can beat these c*****kers at their own game and bypass this automated screening and weeding out process, by cheating yourself. FIrst, do just what you're doing: get as much help from anyone else you can, find out why you need this crap, master it, and make yourself essential to somebody's company. Then you will make $50,000-$200,000 a year and live happily ever after, buying all the toys and having all the hot girlfriends you want, or whatever.

Background: Why do some of us need to know about Y = mx + b ? There are two basic places equations like this pop up: Physics, (as in Newtonian or Nuclear physics, which is cool: you can make your own atomic bombs), and electronics engineering (build your own computers and cool stuff like blue-boxes that give you free long-distance and internet access, or simply make cool pedals for your electric guitar!)

What is Y = mx + b? : The whole purpose of this equation is that it is a kind of swiss-army knife. It's like an adjustable springy wire, you can bend into any shape, point in any direction, and put anywhere in cyber-space. All those 3-d games, like Quake and Morrowind, use pieces of this to make wire-frame monsters to add color to, and animate.
You can do it too!

How do I use it? This is equation is just like a handgun: you have to know which end is which, or you'll make a fool of yourself. The left side (Y) is the output of the equation, which is like a little engine, that can spew out ink in order to draw a line for instance. That is the business end of your equation/machine-gun. On the right is the engine itself, what you see when you pop the hood open to see why it isn't working.

Pretend you're a mechanic like the Fonz: certain parts of an engine, like the engine block, are big and clumsy, and hard to remove or replace, so you don't usually mess with them unless the car is completely dead. The 'x', or 'x-squared' (x^2 in typing talk) part of the equation is like the engine block in your car. You put the gas in there, but you don't usually mess with it, if it's working. The 'x' itself is like the gas tank. You are going to fill it with numbers, which the engine burns up, and the exhaust comes out the 'Y' on the left.

the 'm' (for multiplier): The 'm' spot in your equation, 'Y = mx^2 + b' is like a transmission on your car. It decides how fast the wheels turn, by multiplying whatever you put in x by some factor. Changing 'm' is like changing gears. You change it more often than the engine, but usually you leave it in one position for a while on a given grade of hill.

What the hell is 'b'? This is the easiest of all. This is the starting line. This is where on the up/down scale of your screen/space you are going to start off your little equation running. If you were drawing a wire-frame flying dragon, this little constant would be the altitude, and each piece of line in your drawing would have its own equation.

Is that all there is to it? If this seems boring so far, you are right! It is pretty boring. This equation simply lets you draw a curved line in x-y space (2-dimensions). But don't you really want 3-d for cool games? Yes: but even though you have two eyes, you can only really see a 3-dimensional view from one side or position at a time. So there is whole other set of equations, they call 'transforms' that convert a 3-d space into a 2-d flat image on your computer screen. Just like making rude gestures or shadow puppets with a projector, these transforms 'project' a 3-d object (even an imaginary one in your computer's RAM,) to a 2-d image you can look at. That is a separate job.

Let's Animate! You have to have some simple boring lines, in order to draw rigid objects in space, and then animate them. That's what the equation 'Y = mx^2 + b' is for. This equation is used again and again to draw line after line in a larger object like a space-ship or a hot robo-babe. You can often represent a big 3-d object by a series of points on its surface, each with a 3-number coordinate (x, y, z) to tell us where it is in our 3-d space. Next, we take the equation we've been talking about and use it to map or describe a line between every pair of points on the surface. This gives us a wire-frame space-ship.

Coloring 3-d objects: Later we will take 3 or 4 lines at a time to describe a flat triangle or square on the surface of our object, and add a texture or color to that surface, along with lighting and special effects. But in all this monkeying around, we've been using the equation you started with again and again.

The Bag of Tricks to Follow: In the process of your grade 10 math course, they will show you this and that trick or technique to manipulate your equations and get to know how to bend and break them, and make them explode. This all falls under weird esoteric names, like 'Function Theory' and 'Transforms' or 'Matrix Algebra'.

Don't get Bamboozled: But just ignore all the mumbo jumbo and gobbledy gook and remember, all that is just a smoke-screen, to create a special 'private' lingo or code for 'mathematicians' (whoever they are!) so that they can get $100,000 a year, while you have to pump gas or serve MacDonald's burgers for $6.00 per hour. So screw them! Master your stuff and become a great games developer or animation expert, or even NASA rocket scientist.
 
Old 04-02-2005, 09:41 PM   #8
gulo
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y=mx+b

This gave me some trouble at your age too for whatever reason. Here's how it works.

You're familiar with the x-y coordinate system? Y goes up and down, X left and right, got it? 0,0 is where the two
axis intersect.

"m" is the slope of the line. "b" is the offset. Slope means the rate at which y changes with x. For instance, if m =1, y would increase at the same rate as x does. If 'b' were also zero, then you'd just have a line y=x which would graph as a 45 degree line in quadrant one intersecting the point 0,0. The line would pass thu 0.0 1,1 2,2 etc...

Now change "b" to a value of 1 which gives you y=x+1. The angle of the line stays the same but the new line is offset by a value of 1 place higher, intersecting the point 1,0.

Now change the slope m to a value of 1/2 with b=0., or y=1/2x. This line still intersects 0.0, as in the first example, but the angle it creates with the x axis is only half that of "y=x", or 22.5 degrees. The line would pass thru 0,0 1,2 2,4 etc...

Now set b=1 in the last equation, or y=1/2x+1. The line passes thru 1,0 2,2 3,4 etc...

Example would be D=Vt or distance equals velocity x time. Lets say you were trying to calculate the distance driven at various speeds over a given time. Here the velocity would be the slope of the line and D would be ploted on what was your y axis while time would be on the x axis. You could also have an offset in this one too, so let's say D-Vt +b where be would represent starting at some head-start from your starting line.

Now you should be able to answer this burning issue graphically: You have two cars both trying to get to a city on the same interstate highway (i.e. no stoplights and driving at a constant speed or velocity).
The red car is starting 500 miles from the goal traveling at a constant rate of 70 MPH
The blue car is starting 400 miles from the goal traveling at a constant rate of 50 MPH

What is your offset? I'm sure you've figured out it is 100 miles.

red car would be D=70 x t + 0
blue car would be D=50 x t + 100

Now try graphing it out and see which car makes it to the city first as well as if the red car passes the blue car and at what time would they pass if they do.

hint: to plot a line, all you need are two points...

Last edited by gulo; 04-02-2005 at 09:53 PM.
 
Old 04-03-2005, 05:17 AM   #9
penguinlnx
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coordinates and 'spaces'

Quick Background: Something they are notoriously bad at in high-school, is explaining what the heck you are learning in math class, and how it came about. But it turns out not to be that complicated, if only someone would tell what actually happened to get us here. Briefly it's like this: For thousands of years, people thought algebra (playing with numbers) and geometry (playing with shapes and space) were two entirely different subjects, like chemistry and olympic wrestling. But geometry had pretty well petered out, and algebra has always been boring to everyone, unless you were counting money.

What happened? Then along comes this guy Descartes, who decides to mix the two together! At first everyone thought he was nuts, but it turns out alot of interesting problems can be solved by borrowing tricks from one specialty to the other. Problems that seemed difficult in geometry were now solved with number tricks, and difficult problems with numbers could be easily answered with a drawing or two. So just like adding chemistry to olympic wrestling results in Bikers on steroids and monster trucks, mixing algebra and geometry changes Heckle and Jeckle into Mr Hyde and the Hulk.

Graphs and Grids: Well, by dividing your paper into a map with x and y coordinates, and dividing space into a grid with x, y, and z coordinates, Decartes was able to attach numbers to the corners of triangles and such in a useful, if not entirely sensible way. You will immediately notice that even a right-angle triangle can only be positioned so that two of the three sides are straight (up & down or sideways). One side (the longest one) will always be on some angle relative to the x and y axis if we line up the two that are at a right angle.

Cockeyed Lines: This would be a problem, because you can't just read off the length of a line on your graph if its on an angle to both axis. But from geometry without numbers we know that the long side of a right angle is always some exact proportion to the two short sides (height and width, or rise and run).

The 'Slope' = m : Now some wise ass noticed that if a line was at 45 degrees going up to the right, the 'rise' (y) was equal to the 'run' (x) , that is, the distance upward the line reached was equal to the distance the line reaches right-ward. In fact, its just the fraction, rise/run = 1. This fraction, (rise/run) was called the 'slope', and it wasn't just an arbitrary assignment of numbers to each 'angle'. Horizontal is assigned a slope of 'zero' because no matter how far you drew your line, the 'y' value doesn't change. The 'rise' is zero. 0/x is still zero, no matter how big we make x, or how long we make the line. All the lines between 0 and 45 degrees have a 'slope' between 0 and 1.

A Simple Way to get the 'Slope' : The basic idea of slope is good, but we need to give it a clear practical definition so everyone gets the same answer when they figure it out. We have been talking of 'x' and 'y' rather loosely, and it's time to tighten it up: What we really mean isn't 'x' or 'y' themselves, but rather the change in x or y. What's the difference? Well its the difference between telling you the name of my street, (which you can find yourself) versus the distance (which helps you decide if you want to bother visiting!)

An Example Slope : Suppose we have a short line (segment) and we know the (x,y) coordinates of each end of it. (1,1) and (4,2). Well, we can plot the dots and join them together, but what is the exact slope of that line? Simple: slope = (y2 - y1)/(x2 - x1). How did we get that? Well, the distance the line stretches upward is the difference (called delta-y) between the two Y-coordinates. and likewise the stretch eastward is just (x2 - x1). So the 'rise' / 'run' is just (delta-y)/(delta-x) = (y2 - y2)/(x2 - x1) = (2-1)/(4-1) = 1/3 = .333 = slope. Notice the slope is a fraction less than one, because the line is less than 45 degrees upward from horizontal.

Unforseen Problems: Oops! What happens when the line is really steep? The fraction (slope) approaches infinity! Because the numerator is gettting larger while the denominator can be smaller and smaller. That's just the trouble with fractions. As long as our lines aren't too steep, i.e. vertical, we don't have to worry too much. But sadly, the number that represents slope doesn't increase the same way as the angle in degrees. Not all degrees are created equal! Shallow lines have tiny slopes, while steep lines have near infinite slopes! A change in one degree doesn't mean much for a small slope, but one degree could be a leap in order of magnitude for the slope of a steep line.

bad lines not allowed: And that's why good lines aren't vertical, with infinite slopes. Such a line can be represented by a simple equation, (such as x = 3) but cannot be written as 'Y = mx + b' since there is no single 'Y' for every 'x'. These badly behaved lines are not 'functional' as formulas or 'functions' of 'Y' and so are NOT 'functions' at all. In fact, any 'line' or curve that has two or more different values for 'y' is disallowed as a 'function' of 'y' since its ambiguous. Well this was partly our fault for choosing a definition of 'slope' based on delta Y/ delta x.

Why not another more reasonable way to define 'slope' ? Well, actually there is nothing stopping us from making our own definition of slope, as long as we can use it for something. Mathematicians were reluctant to throw away the current definition of 'slope' because it turns out to be so useful.

The vertical line test: Let's see how: Well, it turns out that if we know the 'slope' of a line, and can build the equation by simply plugging in the 'slope' as we have defined it, we can always calculate what the 'Y' will be for any given value of 'x'. that is, we can take a vertical ruler (an x value) and hold it anywhere on the x axis, and with our equation we can figure out exactly where (at what Y value) that vertical line would cut across our line.
 
Old 04-03-2005, 12:02 PM   #10
gulo
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nice job penguinlnx! Did you major in pure or applied?

Randyriver, one think I might suggest which could be helpful is for you to visit your local community college and look
for a basic Algebra "cookbook" for a "math lab" type class. Community Colleges sometimes will offer math classes
in a couple different formats. One type is like the one you're in now, the classic way, the other is taught mainly through
examples. Hmmmm...perhaps the way I describe it isn't all that helpful, Think of it as one comes at learning math
from more of a theory standpoint first, then teaches examples, while the other starts with examples, has you work the
examples, which then lets the student pick up the theory along the way. Some people seem to learn math more easily
in one or the other format depending who they are. For me, the latter was a nice way to get into it.

In any case, a cookbook can be a nice supplement to your textbook. If you're having trouble with a problem set or a
concept in the text, you can alway reference sample worked problems in the cookbook and walk thru a couple sample
problems there then go back to the theory in your textbook.
 
Old 04-03-2005, 12:27 PM   #11
penguinlnx
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Mathematicians: the laziest people on earth! You might have thought mathematicians were brilliant hard working geniuses who toiled over equations like real men build dig ditches on road-gangs. Of course that's nonsense. Mathematicians actually hate math, and that's why they are constantly looking for shortcuts to do just about everything. And because they have pursued this goal of being lazy for thousands of years, they have gathered together an incredible number of shortcuts, just like you have for 'cleaning' your room. You know, stuffing the closet, ramming crud under the bed, hanging stuff on a rope outside your window: well mathematicians are just as clever.

Y = mx + b Well, this equation is one of those shortcuts that lets us group a whole bunch of lines together, so we can get at just what makes them tick, and manipulate them about. There are as many ways to describe a line as there are lines, but by having a standard way to write most lines (except vertical ones) we can mess with them easily.

Two Ideas: One Equation: Well, again we've been a bit sloppy about what we are doing with this equation, and now is the time to straighten it out a bit more. We talked about this equation as a kind of engine that pumps out 'Y' numbers when we pop in 'X' numbers. And that's one use for it. (Notice for now that we are only talking about an 'x' in the equation, not the fancier version with an 'x-squared'.) For instance, when we know that we are just messing with straight lines, it's real easy to plot them on the x-y graph because we only need two points, and then we can just draw a straight line through them with a ruler.
Well, with an infinite line going in both directions, we can do the same thing, but rather than talk about 'length', which would now be stupid, we can still talk about 'slope', or 'rise' versus 'run'. And that is the more subtle idea behind the 'm' in Y = mx + b. Another way of saying it with infinite lines, is 'Rise' = m times 'Run'. From this view, 'm' is seen to be a proportional multiplier, or adjuster to the 'run', or change in X.
In this case, 'm' is a little more abstract of an idea, as we said, its kind of like saying Y is always 2 times the size of X or whatever 'm' might be for a given line with a certain slope.

The Good the Bad and the Ugly: Well, on the one hand, using this standard form to describe a straight line makes things simple, and we can get to know what 'm' and 'b' turn out to mean for where and at what angle we draw a line. The down side was that we had to ignore vertical lines entirely to use this method of organizing and grouping lines. But now, with a bit of thought, we can also use the same equation to talk about the proportions between the change in X versus the change in Y, which as it turns out is one of the most powerful ideas in mathematics and physics.

The Ugly: 'STATE Spaces' ! We have now moved into the area of 'rates' and 'acceleration', and other bizzare things you can play with using 'graphs'. You see, what they have kind of left out in your high-school course, but what they will continue to do to you behind your back, is change the meaning of the graphs and charts before your very eyes, usually without telling you at all! This is the most confusing and dirty trick ever done to high-school students in the course of forcing you into that job at MacDonalds! So pay attention now, and don't let them win, the dirty bastards.
We can all easily imagine physical space. After all, we are in it all of our waking lives. But the minute you start using an 'x-y' graph to plot things like pendulums and rocketships, you are not dealing with 'space' legitimately at all. What you are looking at is usually only ONE dimension or two, combined with some OTHER object, like TIME, or SPEED, or an abstract quantity or feature of a situation, but somehow, a mathematician or a physicist has found a way to treat that quantity as though it were some kind of 'space dimension'. Now this is a very flakey gag at best, but it turns out to be quite handy for solving problems. But you should keep constantly in mind, that there is no legitimate reason to really think or believe that the quantity involved really acts 'like a space-dimension' in real life!

Magic Spaces These 'magical' spaces, where one dimension really isn't a dimension at all, but say time or some other quantity, don't really exist, except of course in the scientist's head! And the whole bag of tricks for manipulating lines and shapes and equations with graphs (called 'Analytical Geometry' and 'Calculus') is so effective and convincing for solving all kinds of problems, that even the scientist himself tends to forget he made it up! These 'imaginary' spaces, like the whole 'complex-number' system, (another imaginary space where 'imaginary' numbers are combined with 'real' numbers) are just abstract mathematical constructions that only exist in the head of the scientist and his listeners who think they know what he's talking about, because they've all played with the geometry and the number tricks before.

Bullshit baffles even big brains: But don't believe them! Always take some scientist's or mathematician's invented 'state-space' with a grain of salt. And understand, that just because it makes a pretty graph, it doesn't mean they are accurately describing reality. For instance, Einstein (and many others) were so mesmerized by 'Minkowsky Space' for a long while that they actually thought it somehow proved that our perception of the 'past, present, and future' was some kind of illusion, and that everything was/is already fixed as little dots (called 'events' ) in some kind of a four-dimensional 'Space-Time'. What rubbish. But there it was: If you plotted one or two dimensions with time itself as a 3rd 'dimension' it seemed you could plot people's time and position completely, and 'motion itself' in the drawing was actually unnecessary, so there couldn't actually be any! Time and 'the present' was an illusion. This was just about the time of course, that everyone started smoking pot, including the scientists.
 
Old 04-04-2005, 04:13 PM   #12
randyriver10
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I printed EVERYTHING out you guys gave me.

I cant thank you enough, this may be the difference maker between me getting a shit career and an awesome career.
 
Old 04-04-2005, 08:01 PM   #13
gulo
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NP Randy. I hope it helps.

The community college book suggestion reminded me of something. If you find you just don't like your math teachers at your
high school (and a lot of times math teachers are AWFUL in high school) then you may have the option of taking math classes at your local community college instead, as well as other classes. There could be many benefits to trying this.

If you are having trouble, there's really no problem getting help. If they have a math lab, you just walk in and get to talk to a teacher, your own or another, who will help you or hook you up with a tutor.

You'd get double credit for your classes, both high school and college. It looks pretty good to have college classes under
your belt when you go to apply to a 4 year school.

Cute women. Possibly horny and French, possibly just horny.

A good way to check it out would be a spring or summer computer science class, perhaps Pascal, C or Java.

Otherwise, you could split your days, taking math and computer science at a community college in the morning, then head over to your high school for afternoon classes and any extracurricular activities like music or sports.
 
Old 04-04-2005, 08:10 PM   #14
gulo
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red car would be D=70 x t + 0
blue car would be D=50 x t + 100

70t =50t+100
20t=100
t=100/20=10/2=5 hours for the red car to overtake the blue car.

70x5=350 miles
50x5 + 100 = 350 miles so it checks

So, they would cross 150 miles before reaching the city, so the do indeed cross.

See if that checks with your graphical solution!
 
Old 04-05-2005, 03:14 AM   #15
penguinlnx
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Keep in mind Randy here has *two* problems.
One is mastering his grade 10 material (and beyond),
and Two is pleasing his *female* math teacher who isn't giving him adequate attention.

Randy: If you can list any of your hobbies and interests, those helping you can construct problems which are interesting and appeal to you, while illustrating the material you need to learn, as well as showing you surprising applications for your math skills. So tell us what you think you'd like to do. Do you like computer games? electronics? music? building robots? Anyone here could probably make up some fun examples that will help you get a grip on your math.

P.S. Tell us more about this teacher. I am disappointed but not surprised that she doesn't have time to give you extra help. There may be a way to soften her up, or she may simply be overloaded, looking for an excuse. But again, the problem with her may be more systemic: She may not understand the needs of boys your age, that is, many young men go through phases where they find it difficult to sit still and do this boring shit for more than a few minutes at a time, while a girl your age may find no difficulty sitting for hours reading a math textbook. If you are having problems in this area, then we can adjust the teaching method here to give you a fighting chance in an environment where they just don't understand your needs, or don't care.

On the other hand, perhaps you can hang around her desk after school, and see where *that* goes....just read up on the 'stalking' laws in your area first.
 
  


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