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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".]
In previous section we looked at the two functions f ( x) = 3x - 2 and g ( x )= x/3 + 2/3 and saw that ( f o g ) ( x ) =(g o f )( x ) =
Graph each data set. Which kind of model best describes the data? {(0,3), (1,9), (2,11) (3,9), (4,3)}
Solve following. |3x + 2| Solution Now we know that p ≥ 0 and thus can't ever be less than zero. Hence, in this case there is no solution as it is impos
I have 10 apples and my friend has 100 apples.How many apples do we have ?
Mary traveled 200 miles at an average rate of 50 miles per hour. How long did it take her?
y=2/3x-1
Note that the right side has to be a 1 to be in standard form. The point ( h, k ) is called the center of the ellipse. To graph the ellipse all that we required are the left mo
Michael bought three USB flash drives each capacity of 1.5 gigabytes.He also bought two USB flash drives each with a capacity of @ gigabytes.Express the total capacity of the three
Have a % 56% discount have the amount of 285.13 what was the amount used to get to 285.13? How did you get?
i dont know how to do this equation y=x+3 2x+y=6
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