parametric equations, Algebra

A motile cell is placed at the point (x0, y0) on a square shaped dish filled with a "nutrient bath". The concentration of nutrient at any point (x, y) in the dish is given by

N(x, y) = 10 - 2x2 - 4y2.

Cells are typically known to move, in a continuous fashion, in the direction of maximum increase of this nutrient. Furthermore, it is observed that each cell moves with a velocity proportional to the gradient vector at each point (where k is the constant of proportionality).

(a) Show that the parametric equations that represent the motion of the cell over time are given by

x(t) = x0e-4kt, y(t) = y0e-8kt.

[Hint: you may need to look up a method for solving first order ordinary differential equations, known as "separation of variables".]

 

Posted Date: 2/25/2013 7:54:14 AM | Location : United States







Related Discussions:- parametric equations, Assignment Help, Ask Question on parametric equations, Get Answer, Expert's Help, parametric equations Discussions

Write discussion on parametric equations
Your posts are moderated
Related Questions
1) The goal of the first questions is to implement some code that performs calibration using the method described in the book; by first computing a projection matrix, and then deco


How do you write 14x14x14x14x14x14x14= in exponential form?

Multiply 2(b + 5)

Let's begin with                                                       x 2 + bx and notice that the x 2 hold a coefficient of one. That is needed in order to do this. Now,

hello please help me on the solucion

HOW TO PROGRAM QUADRATIC EQUATIONS, INEQUALITIES AND FUNCTIONS INTO A TI 84 PLUS C SILVER EDITION

i dont get them i need help

Have a % 56% discount have the amount of 285.13 what was the amount used to get to 285.13? How did you get?