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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".]
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Using transformation to sketch the graph f ( x ) = (x - 2) 2 + 4 Solution In this part it looks as the base function is x 2 and it looks a
Solve the equation x 4 - 7 x 2 +12 = 0 Solution Now, let's start off here by noticing that x 4 = ( x 2 ) 2 In other terms, here we can
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