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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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w2+30w+81 need step by step and explanation.
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Solve following equations by factoring. a) x 2 - x = 12 b) y 2 + 12 y + 36 = 0 Solution a) x 2 - x = 12 First to solve it get everything on si
Now, we've got some terminology to get out of the way. Multiplicity k If r is a zero of a polynomial and the exponent on the term that produced the root is k then we say t
p(x)=x-a
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