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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".]
Actually here we're not going to look at a general cubic polynomial. Here we are jsut going to look at f ( x ) = x 3 . Really there isn't much to do here other than only plugging
so I''m having trouble. I honestly don''t under stand this. Y=4x+5. y=-1/4x+4 they want me to tell whether the line is parallel, perpendicular or neither I don''t know how.
if a-2b=5 then a3-8b3-30ab
need helpplease
Susan is driving to Mount Shasta.On her map,she is distance of 7 3/4 inches away.The scale of the map is 1/2 inch is 50 miles. a.) how far must susan travel to reach her destinat
Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. ??2+??2+16??-18??+145=25.
In the earlier section we looked at using factoring & the square root property to solve out quadratic equations. The problem is that both of these methods will not always work. Not
y=x^2+2x-15
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
On her walk, Ana decides to cut straight through a circular garden with a circumference of 753.6 feet. If she is walking at a pace of 5 feet per second, how long does it take her t
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