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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".]
x^2 + 7x + 12 factor fully
the table shows the number of minutes of excirccise for each person compare and contrast the measures of variation for both weeks
find the perimeter of an irregulary shapep blocks of land didvided into 4 Triangles ab=12m by 15m bc =15m by 60m cd =24m by25m da = 25m by 48m..
An object 4.8 feet tall casts a shadow that is 14.4 feet long. How long in feet would the shadow be for an object which is 16.8 feet tall?
f(x)=-12x^2-24x+7
solve x+4y=8 2x+5y=7
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
if there are 12 boys how many girls will it be
(-3) EVALUATE X3 -2X2 + 6X -64
By using transformations sketch the graph of the given functions. h ( x ) = ( x + 2) 3 Solution With these we have to first ide
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