Math Is Fun Forum

mathsux

Member

Registered: 2007-08-06

Posts: 10

A Water Slide question

This slide is modeled by the equation of y =((x - e)(x - f)(x - g))/3000

When the graph is drawn, there are the following points on the graph line:

(0, 7.6)
(19,0)
(20, -1/3)

Using the points, find e, f and g.

Doing some pretty complex math, I have found that e, f, g can be found through paper solutions.

But this is a mere part-question in 3 different questions used in an exam. I have only a limited amount of time, so I use the TI-89 Titanium graphics calculator.

Is there any way on this calculator that I can simultaneously solve for e, f and g.

I have tried: solve(-e*f*g=7.6 and ((19-e)*(19-f*)(19-g))/3000=0 and ((20-e)*(20-f)*(20-g))/3000=-1/3, {e,f,g})

But it displays "Too Few Arguments" !!! WHY!!!!?????/

Help please.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: A Water Slide question

I'm pretty sure there's an inherant problem in that your equation for y is a cubic polynomial, but to define a unique cubic, you have to have atleast 4 points, the same way you need 3 points for a quadratic, and 2 points for a linear polynomial.

i.e. there should be an infinite number of possible solutions for e,f,g that give rise to those 3 coordinates. unless you have some other constraint on e,f,g i don't think there is a unique solution.

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Identity

Member

Registered: 2007-04-18

Posts: 934

Re: A Water Slide question

It shouldn't display "Too Few Arguments" if you typed it in correctly.

But your first part seems a little wierd... it should be

solve((-e*f*g)/3000=7.6 and ((19-e)*(19-f*)(19-g))/3000=0 and ((20-e)*(20-f)*(20-g))/3000=-1/3, {e,f,g})

Another way to do this is on the Home page, select F4: Define, then type after "Define"

f(x) = ((x-e)*(x-f)*(x-g))/3000

It should look like

Define f(x) = ((x-e)*(x-f)*(x-g))/3000

Then press enter, then you can type:

solve(f(0)=7.6 and f(19)=0 and f(20)=-1/3, {e,f,g})

Btw there are just 3 constants in 3 equations so there should be a single solution.

Last edited by Identity (2008-03-08 22:24:30)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: A Water Slide question

actually yeh, ignore what i said, it doesn't apply here since expanding out the equation you get a cubic where only 3 coeffecients are unknown, so 3 points is enough -> coeffecient of x cubed is 1/3000.

Last edited by luca-deltodesco (2008-03-08 23:00:09)

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The Beginning Of All Things To End.
The End Of All Things To Come.

mathsux

Member

Registered: 2007-08-06

Posts: 10

Re: A Water Slide question

Identity, I get "Error: Argument error" when I try to solve using the function of x method you wrote up there.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: A Water Slide question

Identity, I get "Error: Argument error" when I try to solve using the function of x method you wrote up there.

Sorry, I think I know why it didn't work...

Ok, firstly start by going
2ND F1: Clear a-z
2ND F1: NewProb

Then from the original equation, let a = e, b = f, c = g

Define f(x) = (x-a)(x-b)(x-c)/3000

Then

solve(f(0)=7.6 and f(19)=0 and f(20)=-1/3,{a,b,c})

I think the reason it didn't work is before the f has been used twice in two different places, first as f(x) and second in the actual equation. This should hopefully work

Last edited by Identity (2008-03-09 15:36:15)