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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".]
A tank is filling with water from a natural spring. Two days ago the water was 10 feet deep, and yesterday the water was 12 feet deep. Assume that the water depth continues to rise
2x^4-11x^3+19x^2-13x+3
There are two forms of the parabola which we will be looking at. The first form will make graphing parabolas very simple. Unluckily, most parabolas are not in this form. The seco
5(-4x+70+5
the sum of three numbers is 396. what is the second number if the third is number 7 more than the first number and 2 more than the second number?
1/4 x 5/8 =
9x-3y=24;7x-3y=20
Sketch the graph of P ( x ) = 5x 5 - 20x 4 + 5x 3 + 50x2 - 20x - 40 . Solution We set up the zeroes & multiplicities of this polynomial in the previous section hence
We will begin with inequalities that only have a single inequality in them. The thing that we've got to keep in mind here is that we're asking to find out all the values of the
Kevin randomly selected 1 card from a standard deck of 52 cards. what is the probabilty that he will chose King of Hearts ... 17/13 ..... 17/52 .... 13/4 .... 52/12
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