$15 paypal to first person to solve before midnight (math)

[drinkmorejava]

uhhh, no offence, but that's a rather easy assignment. That could be like one problem out of the graphing section from the first chapter in my calc book.

If you're looking for a formula, just google polynomial graph or something.

 

[computerpro3]

Originally posted by: drinkmorejava
uhhh, no offence, but that's a rather easy assignment. That could be like one problem out of the graphing section from the first chapter in my calc book.

If you're looking for a formula, just google polynomial graph or something.

I'm not in calc.....

 

[StormRider]

This is how I learned about polynomials in high school (I never took calc in HS).

Here's a polynomial in factored form:

y = (x - 3)(x - 4)(x - 5)

It has three roots.

It's easy to plot the equation.

Draw the horizontal axis. Mark off the places where the zeroes occur. They occur at x = 3, x = 4, and x = 5. If you enter those numbers into the polynomial equation -- you get y = 0. That's why they call them zeroes.

Here's an easy trick to plot it quickly. Plug in a number for x that is not 3, 4, or 5 (i.e. one of the zeroes). For example, if you plug in x = 7, what do you get for y?

You get a positive number. So, now put your pencil above the horizontal axis at x = 7 (since y is positive at x = 7). From that point, draw your curve down towards x = 5. Cross the axis. Then draw up towards x = 4. Cross the axis. Then draw down towards x = 2 and cross the axis (and keep going down). The polynomial just goes up and down between the zeroes. They always alternate between the zeroes and cross over the horizontal axis at the zero points (except when you have a double root)

Edit: And of course, for complex roots, the polynomial doesn't cross the horizontal axis at the complex root if you know what I mean. Y = X^2 + 1 is an example.

 

[Oscar1613]

you dont need differentiation... it says increasing/decreasing, not concave up/concave down. if you cant tell if a line is increasing or decreasing just by looking at it, then you need to go back to grade school

 

[Pepsi90919]

42. i win.

 

[Fenixgoon]

sounds like a pretty easy project.....

 

[jonessoda]

This is so easy it's hilarious. First, graph ANY polynomial. Then, find its roots (factoring). Then, for the increasing/decreasing, graph its derivative and take it from there. Domain and range are easy.

What the hell is a roller-coaster polynomial?

Edit: I call the money. By 11pm EDT, I will have the answers for you.

Edit again: it'll take a little longer

 

[Howard]

Originally posted by: jonessoda
This is so easy it's hilarious. First, graph ANY polynomial. Then, find its roots (factoring). Then, for the increasing/decreasing, graph its derivative and take it from there. Domain and range are easy.

What the hell is a roller-coaster polynomial?

Cubic or higher order, I suppose.

 

[DainBramaged]

Originally posted by: Pepsi90919
42. i win.

Yup...now pay up.

 

[RichardE]

42

 

[jonessoda]

eqn is 54x^7 - 1566x^6 - 18938x^5 - 118314x^4 + 415368X^3 - 767880x^2 + 592200x
factored: x (x-1) (3x-6) (2x-6) (x-4) (3x-15) (x-6)

Roots at x = 0, 1, 2, 3, 4, 5, 6.

The other parts will come soon.

CHECK THE MATH! I may have made a mistake.

Domain: all real numbers (-8,8)
Range: all real numbers (-8,8)

Edit: working the roots of the derivative to find the areas of increasing and decreasing.

 

[txrandom]

This is very easy:

The answer to the last part can be a number of things.

F(x)= (x+7)(x+5)^2(x+2)(x-1)(x-1)(x-3)

The graph would go like this: Go through (-7,0), makes a "curve" somewhere on x=5 (but not go through y axis), goes through (-2,0), will touch (1,0) (but wont go through the y-axis, it's a double root), and finally it will go through (3,0). I would draw a graph out, but I don't want to upload a pic.

BTW This whole problem is easy.

 

[rambow]

y=sin(x) FTW (like that one guy said)

 

[reverend boltron]

Originally posted by: txrandom
This is very easy:

The answer to the last part can be a number of things.

F(x)= (x+7)(x+5)^2(x+2)(x-1)(x-1)(x-3)

The graph would go like this: Go through (-7,0), makes a "curve" somewhere on x=5 (but not go through y axis), goes through (-2,0), will touch (1,0) (but wont go through the y-axis, it's a double root), and finally it will go through (3,0). I would draw a graph out, but I don't want to upload a pic.

BTW This whole problem is easy.

Hey man, the problem might be easy for you now, but there was a point in your life where a problem like this wasn't easy. There's no reason to sit there and tell a person who has been working on a problem for 13 hours straight how easy it was for you, it's degrading and unnecessary.

 

[jonessoda]

Okay, so far I have: increasing (-8,0)...

decreasing (0, 33.3342)...

and increasing (33.3342, 8).

There you have it. You can keep the money.

Oh, and CHECK THE MATH. CHECK THE MATH. This is a project, right? So CHECK THE MATH.

 

[speg]

What's a roller coaster? Just do sine! Roots at every nth pi, the domain can be whatever you want, range is some constant multiple, and I think you can figure out the colouring!

 

[chuckywang]

WTF...this is middle school stuff. I thought you wanted a problem solved with an actual concrete answer.

 

[jonessoda]

Damn, odd doublepost

 

[MustangSVT]

42!

 

[DrPizza]

Yet another person providing more anecdotal evidence that reliance on calculators does not indicate learning in mathematics. I hate those stupid things more and more by the day.

 

[esun]

I believe this is all it wants:

1. So we have to pick a polynomial that satisfies those conditions. Let's do so:

(x - 2)^2(x - 1)(x^2 - x + 1)

The first term gives us a double root, the second means we have 2 real roots, the third is just a quadratic with discrimant less than zero (b^2 - 4ac = -3) to give two imaginary roots.

2. Use that TI-83 to plot the graph. Find a region that looks like a rollercoaster ride (wow, what a retarded assignment...). Write down the domain of that region here.

3. Write down the range of that region here.

4. Ummm, hope you can handle this. Red is the one that looks like hot iron, blue the one that looks like water.

5. It comes in factored form already. How nice!

You'll probably get a zero for creativity / originality, but you can live with that I think.

 

[kevinthenerd]

I know I'm late, but this is simple Calculus 1 that you're going to need later, so I'll explain it now anyway. Don't pay me.

No expensive calculator is necessary, but if you're really interested, download VTI and a ROM from TI to get the TI-89. (This is illegal if you don't actually own the calculator, but I do, but I like having the convenience of always having the calculator at my computer.)

Make a function like (x-1)(x-4)(x+3) or something like that, and you can just multiply it out to make a whole function.

y = (x-1)(x-4)(x+3) = x^3 - 2x^2 - 11x + 12

That way, you'll know your zeros (1,4,-3) right away, and then it's a matter of a first derivative to find the minimums and maximums and whether it's increasing or decreasing.


y' = 3x^2 - 4x - 11

Remember your quadric formula? x = (-b +- sqrt(b^2 - 4ac))/2a
That means your first derivative roots are
x = (2 +- sqrt(37))/3
x ~= {2.694, -1.361}

Then your first derivative zeros are 2.694 and -1.361, which are your maxima and/or minima.

Verifying...

y(x) = (x-1)(x-4)(x+3)


y(-2) = 18
y(-1.361) ~= 20.745 <-- relative maximum
y(-1) = 20
y(0) = 12
y(1) = 0
y(2) = -10
y(2.694) ~= -12.597 <-- relative minimum
y(3) = -12

Therefore, your graph is increasing between -inf and -1.361, decreasing until 2.694, and then increasing until inf.

The ride moves to the right from (-1.361,20.745) to (2.694,-12.597), which is where it achieves its maximum velocity. At this point, the kinetic energy (getting into physics I) is equal to the gravitational potential energy it had at the top, ignoring friction.

m=mass
v=velocity ~= speed
g=gravity=9.8 m/s^2
h=height

(1/2) m * v^2 = m * g * h
simplifying...
(1/2) v^2 = g * h
v = sqrt(2 * g * h)

It moves along the y axis from 20.745 to -12.597, so the difference between these two, 33.343, gives you your height. (Let's say it's in meters.) Using Google Calculator...

http://www.google.com/search?hl=en&lr=&safe=off&q=sqrt%282+*+g+*+33.3426+m%29&btnG=Search

= 25.573 m/s

You can go back up to the same height.

y(initial) = 20.745
y(final) = -12.597
y(back up) = 20.745 which occurs at x=4.722, which would make a good stopping point
in your ride. (This way, you won't need brakes to stop the ride.)

If I were doing this for my own project, I'd make up some sort of crazy ride including natural logs and trig functions just to make the ride rather unpredictable. The method is the same, but it involves more complex differentiation. I tended to be a smartass in open-ended projects like this, so I might have even taken the time to make a 3D roller coaster complete with vector acceleration analysis.