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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".]
If ( x+1/x)2=3 then find the value of (x72+x66+x54+x36+x24+x6+1)
y=-x-2 y=-5x+2
how do you evaluate 26=10(4-2)
a box whose volumeis 80cubic cm has length,width,height in the ratio 1:2:5 if each of the length,width,height is increased by 2cm how many cubic centimeters will the volume be incr
How do you simplify a radical?
This is my question I need help with: The ratio of adult dogs to puppies at a park on Monday was 3:2. There are 12 puppies there that day. Tuesday, 15 adult dogs were at the park.
Solve the following simultaneous equations by using Cramer's rule 3x+2y=13 2x-y=4
5x + 2y = 6 -2x + y = -6
Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. x2+y2+16x-18y+145=25
Let a = 2 cm, b = 6 cm, and angle A = 60°. How many solutions are there for angle B We must calculate b sin A . If it is less than a , there will be
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