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

How can I simplify a fraction with varibales, Please!!! help me with my hom...

Please!!! help me with my homewrok I don''t know how to answer 1/x+2x/5.. please help me.....

Standard deviation, what is the standard deviation of a graph

what is the standard deviation of a graph

Find out the partial fraction decomposition, Find out the partial fraction ...

Find out the partial fraction decomposition of each of the following. 8x 2 -12/( x( x 2 + 2 x - 6) Solution In this case the x which sits in the front is a linear term

Geometric Sequences, How do you write an exponential decay function to mode...

How do you write an exponential decay function to model a situation?

Distance, If a jet can travel 600 mph, how long in second will it take the ...

If a jet can travel 600 mph, how long in second will it take the jet to travel 5 miles?

Methods of elimination - linear systems, Methods of elimination Example...

Methods of elimination Example 1 Solve out the given system of equations. x - 2 y + 3z = 7 2 x + y + z = 4 -3x + 2 y - 2 z = -10 Solution We will try and find

Algebraic vocab, the words and definitions to study please :)

the words and definitions to study please :)

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