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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".]
-3x+4y>-12
y = 4 - 3x /1 + 8x for x. Solution This one is very alike to the previous instance. Here is the work for this problem. y + 8xy = 4 - 3x 8xy + 3x = 4 - y X(8 y +3)
e^4x-5 -8=14403 Solution in Natural Log
i need help withese two problems: y=x+4; (-7,1) and y=-1/2x +1; (4,2)
Minimum 100 words accepted#
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List the multiplicities of the zeroes of each of the following polynomials. P ( x ) = 5x 5 - 20x 4 + 5x3 + 50x2 - 20x - 40 = 5 ( x + 1) 2 ( x - 2) 3 Solutio
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