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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".]
a stack of disks is 0.5cm thick.how many disk each at 0.125cm thick are in a stack?
Given a = 2^4 * 3^3 * 7 * 13 and b = 2^3 * 3^2 * 5^2 * 11 * 17 (Note ^ is my symbol for exponent) find the greatest common denominator of a and b. Find the least common mult
There are several quantities out there within the world which are governed (at least for a short time period) by the equation,
Two sides of an isosceles triangle are 7and 3. The perimeter of the triangle is?
the product of two equal negative numbers is 4/25. what are they
330 radians
-3/4(x=6/5)>-159/160
how do i solve this problem? 3Inx=In16+In4
how do you round
2. ABCD was a square sheet of paper, 6 cm on a side. As shown, corner D was folded to point F on the diagonal BD. The area of triangle EFG equals the area of the shaded L-shaped po
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