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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".]
when I have the equation of 6x-9y=18 and I have to graph the answers I am not sure how to come up with the answers, please help
If a graph shows all of the possibilities for the no. of refrigerators and the no. of TVs that will fit into an 18 wheeler, will the truck hold 71 refrigerators and 118 Tvs?
what are the solutions of [x+6]_> 5? write the solution as either the union or the intersection of two sets
52% of 0.40 of =
Now, let's solve out some double inequalities. The procedure here is alike in some ways to solving single inequalities and still very different in other ways. As there are two ineq
We can also indicate a strict mathematical/formula definition for absolute value. It is, It tells us to look at the sign of p & if it's positive we just drop the absolute
(b+a)+[-(a+0+b)]=0
7x+2(3x-1)
coffee was 2.50 yesterday and 2.85 today. what percent did it go up?
x-y=11 x+y=19
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