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 absolute value inequalities, Solve following.  2 x - 4 = 10 ...

Solve following.  2 x - 4 = 10 Solution There actually isn't much to do other than plug into the formula.  As with equations p merely represents whatever is within the a

Functions, I am trying to figure out this answer f(x) = -3/4x + 4. but thi...

I am trying to figure out this answer f(x) = -3/4x + 4. but think I am getting it all wrong

4th grade, which is the correct product of n x 7 if n =$0.25?

which is the correct product of n x 7 if n =$0.25?

Coordinates for the point - graphing, Coordinates for the point  The li...

Coordinates for the point  The listed first number is the x-coordinate of the point and the second number listed is the y-coordinate of the point. The ordered pair for any spec

Linear Equations in Linear Algebra, Question 1 [7 marks] The reduced row ec...

Question 1 [7 marks] The reduced row echelon form of ? ? ? ? ? ? ? ? ? ? ? ? 3 4 17 22 1 2 5 row a b A is equal to ? ? ? ? ? ? ? ? ? ? ? ? 0 0 0 0 0 0 1 2 1 2 0 3 R . (a) What can

Dayana, a group of circus tickets cost $12 for your 3 children.if your chil...

a group of circus tickets cost $12 for your 3 children.if your children invite a total of 7 friends you can get a discount and the total would be $30. what is the rate of change?

Vector algebra, #addition of vectors is associative

#addition of vectors is associative

Steve, The following equalities can be used to make conversion factors. 2....

The following equalities can be used to make conversion factors. 2.54 cm = 1 inch 12 inches = 1 foot 1 mile = 5,280 feet 100 cm = 1 m 1000 m = 1 km 36 inches = 1 y

Sigma notation expansion, How do you expand a sigma notation from x to x of...

How do you expand a sigma notation from x to x of a variable that is not defined in the index. For example, summation of i=1 to n of x?

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