parametric equations, Algebra

Assignment Help:

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".]

 


Related Discussions:- parametric equations

Rational functions, In this last section we have to discuss graphing ration...

In this last section we have to discuss graphing rational functions.  It's is possibly best to begin along a rather simple one that we can do with no all that much knowledge on how

Math, what does x when y=2x=3

what does x when y=2x=3

Complex number, let x,y,z be the complex number such that x+y+z=2,x^2+y^2+z...

let x,y,z be the complex number such that x+y+z=2,x^2+y^2+z^=3,x*y*z=4,then 1/(x*y+z-1)+1/(x*z+y-1)+1/(y*z+x-1) is

Advantage and disadvantage of using algebraic distance, 1) The goal of the ...

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

List the multiplicities of the zeroes, List the multiplicities of the zeroe...

List the multiplicities of the zeroes of each of the following polynomials.              P ( x ) = 5x 5 - 20x 4 + 5x3 + 50x2 - 20x - 40 = 5 ( x + 1) 2 ( x - 2) 3 Solutio

Solving for a variable, what are the steps to solving a variable like this ...

what are the steps to solving a variable like this one -3f=g for f

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd