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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".]
X6-81X2=0 what is the real solution
Sketch the graph through the process of finding the zeroes Example Sketch the graph of P ( x ) = x 4 - x 3 - 6x 2 . Solution
How to graph y=1/4x+6
2.3+5=2.3+2.5 is an example of distributive property
what is 387000000 in scientific notation 89.780000x10^6
6x960=k
If ( x+1/x)2=3 then find the value of (x72+x66+x54+x36+x24+x6+1)
Please exclude the values in the denominator 5m2+m
adding fractions
The topic along with functions which we ought to deal with is combining functions. For the most part this means performing fundamental arithmetic (subtraction, addition, multiplic
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