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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".]
3x+5y=10
Sketch the graph of function. f ( x ) =3x + 6 /x -1 Solution Thus, we'll start off with the intercepts. The y-intercept is, f (0) =6/-1=-6⇒ (0, -6)
16x-10y=10 -8x-6y=6
In the earlier section we looked at using factoring & the square root property to solve out quadratic equations. The problem is that both of these methods will not always work. Not
2 3/4 + 1 1/4 =
In this section we will take a look at something that we utilized back while we where graphing parabolas. Though, we're going to take a more common view of it this section. Severa
REENA HAS PENS AND PENCILS WHICH TOGETHER ARE 40 IN NUMBER.IF SHE HAS 5 MORE PENCILS AND 5 LESS PENS,THEN THE NUMBER PENCILS WOULD BECOME 4 TIMES THE NUMBER OF PENS.FIND THE ORIGIN
-4/-1-4/+6
The last topic that we have to discuss in this section is the change of base formula. Most of the calculators these days are able of evaluating common logarithms & natural logar
we are going to fence into a rectangular field & we know that for some cause we desire the field to have an enclosed area of 75 ft2. We also know that we desire the width of the fi
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