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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 average rate of change if f(x) = 4x + 6 .
These are the only possibilities for solving quadratic equations in standard form. However Note that if we begin with rational expression in the equation we might get different so
1. Determine the intercepts, if there are any. Recall that the y-intercept is specified by (0, f (0)) and we determine the x-intercepts by setting the numerator equivalent to z
a carpenter had a 20 ft piece of lumber which he cut into 3 pieces. one piece was 7 1/3 ft long and other was 6 1/2 ft long. how long was the remaining piece?
{5x-4y=-21} {-2x+4y=18}
6x^3+3x^2-18x
if you have coupon for 450 off your camera purchase of $100 or at Zeke''s camera world. write a function relating a camera''s purchase price after coupon.y, to the retail price,x.
need help with solve a= 3p(4-2r) for p
A board 13 3/5 feet long is cut into 4 equal pieces to make a book shelf. What is the length of each shelf?
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