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

Equations with radicals, The title of this section is perhaps a little misl...

The title of this section is perhaps a little misleading.  The title appears to imply that we're going to look at equations which involve any radicals.  However, we are going to li

Charts, is (1,7),(2,7),(3,7),(5,7) a function

is (1,7),(2,7),(3,7),(5,7) a function

Math, (-3) EVALUATE X3 -2X2 + 6X -64

(-3) EVALUATE X3 -2X2 + 6X -64

Symmetry, In this section we will take a look at something that we utilized...

In this section we will take a look at something that we utilized back while we where graphing parabolas.  Though, we're going to take a more common view of it this section. Severa

Algebra 2, How do I take two points, the rise and run, and produce an algeb...

How do I take two points, the rise and run, and produce an algebraic equation?

Math, how do you simplify 18 over 24

how do you simplify 18 over 24

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