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

Math, Linda has a total of 225 on 3 tests. The sum of the scores on the fir...

Linda has a total of 225 on 3 tests. The sum of the scores on the first and second tests exceeds her third score by 61. Her first test exceeds her second by 6 points. Find Linda''s

Example of earthquake intensity, Example    If 8 ×10 14  joules of energy ...

Example    If 8 ×10 14  joules of energy is released at the time of an earthquake what was the magnitude of the earthquake? Solution There actually isn't much to do here o

Y-intercept, how do i find the y-intercept when i already found the slope?

how do i find the y-intercept when i already found the slope?

Completing the square, Completing the Square The first method we'll lea...

Completing the Square The first method we'll learning at in this section is completing the square. This is called it since it uses a procedure called completing the square in t

Quantitative methods, how quantitative analysis has changed the current sc...

how quantitative analysis has changed the current scenario in the management world today

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

Exponetial growth and decay, in the year 2000, radio stations numbered 220....

in the year 2000, radio stations numbered 220. The number of stations has since increased by approximatly 14.3% per year. Let x represent the number of years since 2000,and y repre

Tests for symmetry, We've some rather simply tests for each of the distinct...

We've some rather simply tests for each of the distinct types of symmetry. 1. A graph will have symmetry around the x-axis if we get an equal equation while all the y's are repl

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