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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".]
identify the sample and suggest a population from which it was selected. then classify the sample as sample, stratified, or systematic. explain your reasoning. 1} an insurance comp
(2 X2)3 BY BB
3/8=n/12
I need help solving the following Algebra problem. Give all solutions of the nonlinear system of equations, including those with nonreal complex components. xy=-20 3x+5y=5
Now it is time to look at solving some more hard inequalities. In this section we will be solving (single) inequalities which involve polynomials of degree at least two. Or, to p
changing of binary to hexadecimal
Nel skates at 18 mph and and Christine skates at 22 mph if they can keep up that pace for 4.5 hours how far will they be a part at the end of the time
9x-3y=24;7x-3y=20
4f=48
Shirley has 8 fewer pairs of earrings than bracelets. She has 15 bracelets. How many pairs of earrings does she have?
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