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

Algebraic expression, how to convert algebraic expression word to number TH...

how to convert algebraic expression word to number THREE MORE THAN A NUMBER

Factoring.., w^2 + 30w + 81= (-9x^3 + 3x^2 - 15x)/(-3x) (14y = 8y^2 + y^3 +...

w^2 + 30w + 81= (-9x^3 + 3x^2 - 15x)/(-3x) (14y = 8y^2 + y^3 + 12)/(6 + y) ac + xc + aw^2 + xw^2 10a^2- 27ab + 5b^2 For the last problem I have to incorporate the following words

New math, What is the effectiveness of new math?

What is the effectiveness of new math?

Q1, I have a 12.2 bottle of mustard. I use 1/20 of mustard per serving per ...

I have a 12.2 bottle of mustard. I use 1/20 of mustard per serving per hot doog. How much mustard do I have left after 4 servings of hot dogs.

Matrices, I don''t know how to multiply matrices

I don''t know how to multiply matrices

Interval notation, Interval notation The next topic that we have to dis...

Interval notation The next topic that we have to discuss is the idea of interval notation.  Interval notation is some very pleasant shorthand for inequalities & will be utilize

Algebraic Equation, The sum of digits of a number is 9 If the digits of the...

The sum of digits of a number is 9 If the digits of the number are reversed the number increases by 45 What is the original number?

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