August 20, 2013
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Homework help!!
Any physic majors or even just someone good at math?
I finally figured out how to make a graph on my graphing calculator, but I’m still little stuck. In case it’s too small, “Consider the following data which represent position vs time for a moving object. Use the graphing calculator to plot this data, then do linear regression using the graphing calculator to determine the analytical expression which best represents this data. Make a rough draft sketch of the plot to the right of the data, then fill in the information at the bottom.
Time(s) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Position (m) 5, 7.2, 9.4, 11.5, 13.3, 15.1, 17.0, 18.9, 21.0, 23.2, 25.0
Equation which best represents this data: x(t) = ____________I don’t understand what it’s asking exactly.
When I put the information in my list and do linear regression I get y=ax+b; a= 1.98, b=5.27, r^2= 0.9992992949 r=0.999649586
Does it want y=1.98x+5.27??
HELP!!! D:I think I have to hand the sheet in tomorrow morning, so if no one is able to help me understand it, I’ll either just guess y=1.98x + 5.27 or try to ask someone else before class.
Comments (7)
i thought i had recently burnt some toast – but my son just told me smoke was coming from my ears… sorry i can’t be of assistance. but i’m pretty sure there’s a website that deals with these equations (along with youtube channel posts – i remember my daughter finding them…)
@xplorrn - LMAO!! XD Yeah, it’s making my brain feel like burnt toast too. I found a youtube video that explained how to plot the graph on my calculator, which was awesome because I was clueless!) but I’m still stuck with the question. Maybe I can ask someone before class.
Unfortunately, the MAC (Math Assistance Center) doesn’t open until next Monday, so if you need help on your first week you’re out of luck.
I know this stuff
it wants y=ax+b which is just as you said, or y = 1.98x + 5.27. For your problem, that’s the same as x = 1.98*m + 5.27.
In my days, we can’t use any graphical calculator (yes, they did exist in those days) or any calculator at all. We are forbidden to use them, only our brain, paper and pen/pencil (ok fingers too).
The equation sounds correct from a ballpark figure.
The point of the question to demonstrate the relationship between time and change in position. Time t is our independent variable because it will advance despite the position of the object and becomes our x axis. Position is our dependent variable and is function of time f(t)=x and is our y axis point. For the sake of clarity, I will rename the position p instead of x to make things less confusing.
You already did the hard part by plugging in data points into the calculator, graphing them, and getting the linear regression. The linear regression is a mathematical representation of the points which actually occurred or in layman’s terms, is a accurate model of the future.
R and R^2 or “R squared” are statistical factors which explain how accurate the model is. The closer these values are to 1 or -1, the more accurate the model.
I believe where you are getting confused is the naming of the funcation x(t). This is mathematical statement in English reads, The change in position x in respect to time. In respect to defines which term, x or t, is the independent and dependent variables. Since position, x, is in respect to time, t, it’s stating that position is dependent on time. In the future, a function with different terms which needs to be represented graphically can be easily plotted to find out that a(b) means a is our Y values and b is our X values.
I hope this explanation is sufficient to answer your mathematical query.
Not my forte, but I think you managed to have an answer, which is great. Good luck with all of them homeworks!
When I did it by hand i got y = 2.2x + 5 (with coordinates (0,1) and (5,7.2))
but of course listen to your graphing calculator since it estimated the line of best fit *much better* than quick-and-dirty manual calculation. Your R^2 is .99 which is pretty perfect and close to 1.0, so yeah, that line is a great estimate of the relationship between time and position. I could load that data on STATA and check the regression for you but I’m lazy lol, and I’m sure you’re right.
btw, x(t) = y
here x is the dependent variable–which can be a throw off since what we’re usually taught as dependent is “y” and independent is “x” but they’re just variable names . You can have f(x), h(z), n(k), l(x), it all means the same thing. The argument (the letter inside the parenthesis) is the x-axis/independent variable.
So whenever you see x(t), just think y(x), or simply “y”, like in 7th grade algebra.