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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".]
a3=8,a5=2, n=6 what is the sum
-4(2y+x)-5(x-5y) simplify
1) Maximize z = 4x1 + 10x2 Subject to 2x1 + x¬2 2x1 + 5x¬2 2x1 + 3x¬2 x1 , x¬2 >=0
Example: Solve following. | 10 x - 3 |= 0 Solution Let's approach this one through a geometric standpoint. It is saying that the quantity in th
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20
How do I find the Domain and Range?
#question. What is central theme in algebra?
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