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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".]
5x=25
Alice bought a round-trip ticket to fly from Baltimore to Chicago on SuperAir for $250. That was $16 more than she would have on Jet Airlines, which only offered a one-way fair. Ho
14th term 60,68,76,84,92
45
In this section we're going to revisit some of the applications which we saw in the Linear Applications section & see some instance which will require us to solve a quadratic equat
1/3h-4(2/3h-3)=2/3h-6
John can drive his car 15 miles on 2 gallons. How many gallons of gas will john need to drive 195 miles?
y=2/3x-1
This section doesn't actually have many to do with the rest of this chapter, but since the subject required to be covered and it was a fairly short chapter it appeared like as good
-3y=4x+24
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