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

Algebra An Introduction, Some of the grouping symbols are braces,brackets,a...

Some of the grouping symbols are braces,brackets,and parentheses.

Determinants, sir is there any rule to use properties of determinants to so...

sir is there any rule to use properties of determinants to solve the sums

Ratio and propotion, 4 pipes can fill a tank in 70 minutes.how long will it...

4 pipes can fill a tank in 70 minutes.how long will it take to fill the tank by 7 pipes

Slope and y-intercept, One of my homework questions ask to find the slope a...

One of my homework questions ask to find the slope and y-intercept of a table and I''ve tried quite a few methods and just can''t figure it out. PLEASE HELP!!

Set-builder notation, to get a discount at the diner, you must either be le...

to get a discount at the diner, you must either be less than 10 years old or at least 55 years old.

Graphing and functions, Graphing and Functions        Graphing ...

Graphing and Functions        Graphing In this section we have to review some of the fundamental ideas in graphing.  It is supposed that you've seen some graphing at th

Sketch the graph on the similar axis system, Sketch the graph of f( x ) = 2...

Sketch the graph of f( x ) = 2 x   and g( x ) = ( 1 /2) x on the similar axis system. Solution Okay, as we don't have any ideas on what these graphs appear like we're goin

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