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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".]
Example : Sketch the graph of hyperbolas. ( x - 3) 2 /25 - ( y + 1) 2 /49 =1 Solution Now, notice that the y term contain the minus sig
The dashed line along with each of these parabolas is called the axis of symmetry. Every parabola contains an axis of symmetry and, as the graph illustrates, the graph to either s
3x/4 = 2
i dont get them i need help
4(11-5)=
Finance is the field of science that explains the management of funds. The areas that generally come under finance are personal finance, business finance, and public finance. The f
``A car dealer has 22 vehicles on his lot. If 8 of the vehicles are vans and 6 of the vehicles are red, and 10 vehicles are neither vans nor red, how many red vans does he have on
(f(x+h)-f(x))/h
how do I solve the equation 0.6(x+60)+0.2x=52
Trees in urban areas help keep air fresh by absorbing carbon dioxide. A city has $2100 to spend on planting spruce and maple trees. The land available for planting is 45,000 ft2. H
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