1 Topic by m255173 (edited by m255173 2013-03-17 23:14:43)

Topic: Related Rates (parametric?) problem in GRAPH

I ** love GRAPH **
and use it frequently for parametric problems.

Yet, I'm having a hard time
representing the (parametric?) equations
of this simple "Related Rates" problem,
inside GRAPH:

--------------------------------------------------
A particle is moving along the curve:
     y= x^3.
At a certain instant,
the particle is at the point (2, 8)
and dx/dt = 5 ft/sec.

Q:
How fast is the distance "s"
  - from  the particle at (2,8)  to the origin at (0,0),
changing at that instant?
--------------------------------------------------

It's easy to solve using the TI-89 calculator,
(see PDF attachment lesson 14.4, page 5),
but I really want to do it in GRAPH, as well.

How do you represent/define
the Eqs. for this problem in GRAPH?

Help!

Re: Related Rates (parametric?) problem in GRAPH

I think you forgot to attach the pdf file.

I am a little unsure what exactly it is you want to calculate, but if it is the distance between (0,0) and (2,8) on f(x)=x^3, then you can use Calc|Length of path in Graph to find it.

3 Reply by m255173 (edited by m255173 2013-03-18 13:54:50)

Re: Related Rates (parametric?) problem in GRAPH

Hi Ivan!,

OK - I've re-attached the PDF file, now:
     "Related Rates on TI-89 by TI Ed.pdf"
(It's from the TI-89 Manual of TI Education):

The short  ==> "Particle Movement"  problem,
is described
in lesson 14.4, page 5 of the PDF.

Seems easy,
but I can not find a simple way to express in GRAPH
    x(t)=?  and   y(t)=?,
the (parametric?) equations of this particular problem,
as described in the PDF (for the TI-89).

The other "Related Rates" problems in that PDF,
I solved with GRAPH, no problem. Brilliant!

Thanks/Tak for help, Ivan....

Post's attachments

Attachment icon Related Rates on TI-89 by TI Ed.pdf 247.62 kb, 2692 downloads since 2013-03-18 

Re: Related Rates (parametric?) problem in GRAPH

Now I understand what you want.

I don't think you will get much help from Graph here. It is simple symbolic math which Graph cannot help with. But it is rather easy to do by hand:

y=x^3
x=2, dx/dt=5

s = sqrt(x^2+y^2) = sqrt(x^2 + x^6)
ds/dt = 1/(2sqrt(x^2 + x^6))*(2x*dx/dt + 6x^5*dx/dt)
ds/dt = 1/(2sqrt(2^2 + 2^6))*(2*2*5 + 6*2^5*5) = 59.4212

Re: Related Rates (parametric?) problem in GRAPH

Yes, now I understand better.

The TI-89 is more of a CAS (Computer Algebra System),
which also handles symbolic-type expressions.

I also tried to solve this problem
with GRAPH,
because I was previously successful in solving
and defining x(t)= and y(t)=,
for the other 4 Related Rate /Parametric problems,
shown in the same PDF file.

They all worked great in GRAPH,
except for this one.

So, I became over-enthusiastic,
and tried to define x(t)=  and  y(t)=
for the "Particle Movement"  problem in GRAPH, too.

Anyhow, GRAPH is Super-Duper...I love it.

Tusend Tak, Ivan!