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

Variations, the kinetic energy of an object varies directly as the square o...

the kinetic energy of an object varies directly as the square of its velocity. A certain object traveling at 80 feet per second has a kinetic enrgy of 240 foot-pounds. what would b

Help please, Achieve $225,500 at 8.75% compounded continuously for 8 years,...

Achieve $225,500 at 8.75% compounded continuously for 8 years, 155 days

Finding zeroes of polynomials, We've been talking regarding zeroes of polyn...

We've been talking regarding zeroes of polynomial and why we require them for a couple of sections now. However, we haven't really talked regarding how to actually determine them f

Distance problems, robin runs 5 kilometers around the campus in the same le...

robin runs 5 kilometers around the campus in the same length of time as he can walk 3 kilometers from his house to school. If he runs 4 kilometers per hour faster than he walks, ho

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

Algebra 1, I don''t understand anything!

I don''t understand anything!

Hcf, how to find hcf easily

how to find hcf easily

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