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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".]
2x+3
The point in graph to the right are (1998),177),(20087),(2002,195 and (2004,207)where the y coordinates are the thousands complete part(a)and (b)(a use the first and last data poin
7-four divided by5x is greater than3 divided by 5_
Ask quesThe above model describes the exponential decay of chemical element. t is the time in years, Q(0) is the initial amount of the chemical element, Q(t) is the amount of chemi
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16x-10y=10 -8x-6y=6
f(x)=-12x^2-24x+7
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#question.3000 board feet of maple lumber for making their classic and modern maple rocking chairs. A classic maple rocker requires 15 board feet of maple, and a modern maple rocke
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