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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".]
Differential Equations, Mathematics 1.Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1)
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A blue whale gains 2.3 tons a month for the first year of life. If a blue whale weighed 15 tons at birth, how much will it weigh on its first birthday?
A student''s tuition was $3008. A loan was obtained for 7/4 of the tuition. How much was the loan? The student''s loan was for?
find no. of n digit number in non decreasing order
4Log5n - log5m = 1 5log5m + 3log5m =14
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