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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".]
larry has a propane tank in the shape of a cylinder with a hemisphere on each end, the total length of the tank is 16 feet. the width of the tank is 6 feet. he intends to paint the
Find out the domain of each of the following functions. g( x ) = x+3 /x 2 + 3x -10 Solution The domain for this function is all of the values of x for which we don't hav
6[5b+9]=2b+9.
2 bicyclist riding on a circular track start at the same time. one can make it around the track in 8 min. the other takes 10 min. how long will it take the faster bicyclist to catc
w2+30w+81 need step by step and explanation.
As a last topic in this section we have to briefly talk about how to take a parabola in the general form & convert it into the following form
can you help and is it free?
(x+a) (x+b) (x+c) =
10x^2+19x+6
Multiply 2(b + 5)
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