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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".]
Definition of an exponential function If b is any number like that b = 0 and b ≠ 1 then an exponential function is function in the form,
convert 2543 to a decimal base 10 to binary base 2
#question ..
# how do I solve (4^16)1/2
(1/4)^1/2
I''m starting to learn about the Pythagorean Theorem. I need help with just the basics..
How many ways can five people line up if two of them cannot sit together?
Please exclude the values in the denominator 5m2+m
a3=8,a5=2, n=6 what is the sum
An object 4.8 feet tall casts a shadow that is 14.4 feet long. How long in feet would the shadow be for an object which is 16.8 feet tall?
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