[TI-M] Re: Math problem help

To: <ti-math@lists.ticalc.org>
Subject: [TI-M] Re: Math problem help
From: "Scott Noveck" <noveck@pluto.njcc.com>
Date: Tue, 8 May 2001 07:08:34 -0400
References: <20010507232203.1CE7C18031@mx-1.sollentuna.net>
Reply-To: ti-math@lists.ticalc.org


> Heres the question:
> If a pt is moving on a circle with a center of (2,-3), and the rate of
> change of the x is .25 inches/sec. then find the rate the y changes when
x=1
> and y=-1.  Radius is Rad 5.

Here goes:

Start with:
(x-h)^2+(y-k)^2=r^2
(x-2)^2+(y+3)^2=25

Take the derivative with respect to x to find dy/dx:
2*(x-2)+2*(y+3)*dy/dx=0
2(x-2)=-2(y+3)*dy/dx
dy/dx=(2(x-2))/-2(y+3)
dy/dx=-(x-2)/(y+3)

Plug in your given point:
dy/dx=-(1-2)/(-1+3)
dy/dx=-(-1)/(2)
dy/dx=1/2

But there's another substantial issue with this problem: (1,-1) is _not_ on
a circle with center of (2,-3) and a radius of 5.  If you neglect the given
radius and instead assume that the radius is equal to whatever value would
actually cross through that point, then this answer should be what you want.

    -Scott