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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".]
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let x,y,z be the complex number such that x+y+z=2,x^2+y^2+z^=3,x*y*z=4,then 1/(x*y+z-1)+1/(x*z+y-1)+1/(y*z+x-1) is
Two cars start out at the similar point. One car starts out moving north at 25 mph. later on two hours the second car starts moving east at 20 mph. How long after the first car s
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i want the limits of this equation
(y+1/3x)^2
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