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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".]
how to expand when asked to divide, multiply etc
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
turn into an inequality expression, y= (0,330) x= (110,0)
what is the expression. Of 1=1/2n(3n-1)
x cubed plus 27??
We will begin with inequalities that only have a single inequality in them. The thing that we've got to keep in mind here is that we're asking to find out all the values of the
x plus 6 equal -10
what is quarditic equation
a group of circus tickets cost $12 for your 3 children.if your children invite a total of 7 friends you can get a discount and the total would be $30. what is the rate of change?
3^x + 3^(x^1/2) - 90 =0
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