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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".]
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
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
How do you simplify a radical?
The last set of transformations which we're going to be looking at in this section isn't shifts, but in spite of they are called reflections & there are two of them. Reflection
how many does a rhombus have
x+6=2x+2
Distance/Rate Problems These are some standard problems which most people think about while they think about Algebra word problems. The standard formula which we will be using
on my math home work it says draw a numberline and put the following numbers on order -2.5 2.5 4\3 10percent -100percent -6\3 02 [-4] o -4\5
How do I simplify x^2+2 + -(4x-2)
(-9/8-8/9)- (-9/8-9)
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