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

Quarditic, what is quarditic equation

what is quarditic equation

Domain, Graph each equation, and determine the domain and range. determine ...

Graph each equation, and determine the domain and range. determine whether the equation is a function.

Manipulation properties of the logarithm, For these properties we will supp...

For these properties we will suppose that x > 0 and y > 0 log b ( xy ) = log b x + log b   y log b (    x/y) = log b   x - log b   y log b (x r ) = r log  x If log

Remainder and Factor Theorems, I have a homework question to use the factor...

I have a homework question to use the factor theorem that I need to use Synthetic Substitution with. I did all the work and the divisor is a factor but the equation I have to use t

Substitution method, how do you change this (x+2y=10) equation into "y" for...

how do you change this (x+2y=10) equation into "y" form ?

Math104, financial Project. Five years ago , you bought a house for $171,00...

financial Project. Five years ago , you bought a house for $171,000, with a down payment of $30,000, which meant you took out a loan for $141,000.Your interest rate was 5.75% fixed

Exponents, 10 to the 50th exponent

10 to the 50th exponent

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