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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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Can you get me more questions to practice on this.
27^(3X)-3 = (1/81)^(10X)-9
Bills Roast Beef sells 3 times as many sandwiches as Pete''s deli. The difference between their sales is 170 sandwiches. How many sandwiches did each sell?
what is a residual and how do you solve for it
classify 0.626539212
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