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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".]
HOW TO ADD SUBTRACT MULTIPLY AND DIVEDE DISSIMILAR RADICALS?
Linda has a total of 225 on 3 tests. The sum of the scores on the first and second tests exceeds her third score by 61. Her first test exceeds her second by 6 points. Find Linda''s
2x+5=-8
Maximise, p =168x+161y+158z+132w 475x+450y+440z+438w 250x+230y+220z+210w 119x+115.5y+114.8z+112.25w 160x+50y+120z+50w 12x+8.8y+7.4z+5.3w x >=4
P=positive N=negative whats a negative - negative p+n= n-n=
Actually we will be seeing these sort of divisions so frequently that we'd like a quicker and more efficient way of doing them. Luckily there is something out there called syntheti
-3y=4x+24
I need help with my Discussion 1 for week 5 please. w^2 + 30w + 81 and ac + xc + aw^2 + xw^2 and last one is x^4 - x^3
Sketch the graph through the process of finding the zeroes Example Sketch the graph of P ( x ) = x 4 - x 3 - 6x 2 . Solution
Differential Equations, Mathematics 1.Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1)
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