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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".]
Not every linear system along with three equations and three variables utilizes the elimination method exclusively therefore let's take a look at another instance where the substit
simplify the following expressions for the given values x3 -x2/x2 -x x=3 how do i do this to get answer need step by step instruction
need help with homework
In this section we will discussed about non-linear systems of equations. A non-linear system of equations is a system wherein at least one of the variables contains an exponent ot
600tyou
how to to a equations ?
add - 3a + b - 10 -6c, c -d- a + 9 and - 4c +2a - 3b - 7
a=[25] 43
The integral arises in probability theory. (a) Consult the library or Internet to find how this integral relates to the calculationof a probability using the Normal dist
In this section we will see how knowledge of some rather simple graphs can help us graph some more complexes graphs. Collectively the methods we will learn in this section are cal
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