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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".]
what is the proper way to state a negative exponent when dividing example 27exponent -2/3 divided by 27 exponent -1/3
How do you expand a sigma notation from x to x of a variable that is not defined in the index. For example, summation of i=1 to n of x?
(2x^2+16x+24)/(3x^2) /(x+6)
This is my question I need help with: The ratio of adult dogs to puppies at a park on Monday was 3:2. There are 12 puppies there that day. Tuesday, 15 adult dogs were at the park.
9x^2/-4x^3y^4 x 16x^4y^2/25xy
SUPPOSE Y IS DIRECTLY PROPORTIONAL TO X AND THAT Y = 35 WHEN X = 5 FIND THE CONSTANT OF PROPORTIONALITY K K=
A company makes and sells notebook computers. The company’s cost function in thousands of dollars is C(x) = 0.3x + 100, and the revenue function in thousands of dollars is R(x) = 0
are these like terms
-6k+7k=
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