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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".]
#ques1). Using the function: y=y0,(.90)^t-1. In this equation y0 is the amount of initial dose and y is the amount of medication still available t hours after drug is administered.
two debts- the first of 800 is due six month ago and the second of 1400 borrowed one year ago for a term of three years at 6.5% compunded annulallu are to be replaced by a single p
Compounded semiannually P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + r/2)^2 represents the valu
75 band members need to raise a total of 8250.00 for a trip. So far they have raised 3120.00. How much money, in dollars, per band member, still needs to be raised for the trip
need help on intro into algebra college homework
w^2 + 30w + 81= (-9x^3 + 3x^2 - 15x)/(-3x) (14y = 8y^2 + y^3 + 12)/(6 + y) ac + xc + aw^2 + xw^2 10a^2- 27ab + 5b^2 For the last problem I have to incorporate the following words
find th e parent function g(x) = -(x + 8)2 + 4
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.
#How do you solve them????
.1.Write your birth date or the birth date of someone in your family as mm/dd/yy. (Example: March 13, 1981 is written 3/13/81, and November 7, 1967 is written 11/7/67). ?Now le
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