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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".]
123/4=
How do you simplfly 25 and 15 if u say 5 and the teacher thinks it''s wrong?
Domain and Range The domain of any equation is the set of all x's which we can plug in the equation & get back a real number for y. The range of any equation is the set of all
9x^4-x^2-12x-36
x=y=3 , 2x-y=5
{5x-4y=-21} {-2x+4y=18}
2x+2=2 then x value?
Now we will discuss as solving logarithmic equations, or equations along with logarithms in them. We will be looking at two particular types of equations here. In specific we will
rectangular coordinate system
solve x+4y=8 2x+5y=7
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