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

Example of horizontal shifts, By using transformations sketch the graph of ...

By using transformations sketch the graph of the given functions.                                          h ( x ) = ( x + 2) 3 Solution With these we have to first ide

Example of linear equations, In a certain Algebra class there is a total 35...

In a certain Algebra class there is a total 350 possible points. These points come through 5 homework sets which are worth 10 points each and 3 hour exams that are worth 100 points

Word problem, A thermometer reading 79 degrees F is brought into a cold sto...

A thermometer reading 79 degrees F is brought into a cold storage room with a constant temperature of 38 degrees F. if the thermometer reads 70 degrees in 6minutes, how long will i

Piecewise functions, Whereas we are on the subject of function evaluation w...

Whereas we are on the subject of function evaluation we have to now talk about piecewise functions. Actually we've already seen an instance of a piecewise function even if we didn'

Inequality and interval notation, Solving the following inequalities.  Give...

Solving the following inequalities.  Give both inequality and interval notation forms of the solution. -2 ( m - 3) Solution Solving out single linear inequalities follo

Slope intercept, how do you do equations for sloe intercept?

how do you do equations for sloe intercept?

Perimeter, a farmer has a garden with 2 sides at right angles and the third...

a farmer has a garden with 2 sides at right angles and the third side is 423ft.long.find the perimeter of the garden. if the angle between the shortest and the longest side is 58''

Translating functions, f(x)=x square. graph g(x) by translating the graph ...

f(x)=x square. graph g(x) by translating the graph of f. g(x) = x square + 1

Using transformation sketch the graph, Using transformation sketch the grap...

Using transformation sketch the graph of each of the following.                                             g ( x ) = - x 2 Solution (a)  Depending on the placement of

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