Question

The boundary of a circular growing cell is given by x^2 + y^2 = (k^2)(t^2) for...

The boundary of a circular growing cell is given by x^2 + y^2 = (k^2)(t^2) for some constant k with t measured in hours. The strength of a protein signal in the cell is given by f(x, y) = x^3+ (√ 3)y^3 . The cell can begin to divide when the maximum cell strength on its boundary is 4. Using the method of Lagrange multipliers, determine the radius of the cell when this occurs if the protein takes 2 hours to initiate cell division. Determine where on the boundary the maximum occurs at this time.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given f(x,y)= x^2+y^2+2, subject to the constraint g(x,y)=x^2+xy+y^2-4=0, write the system of equations which must be...
Given f(x,y)= x^2+y^2+2, subject to the constraint g(x,y)=x^2+xy+y^2-4=0, write the system of equations which must be solved to optimize f using Lagrange Multipliers.
(Lagrange Multipliers with Three Variables) Find the global minimum value of f(x,y,z)=(x^2/4)+y^2 +(z^2/9) subject to x...
(Lagrange Multipliers with Three Variables) Find the global minimum value of f(x,y,z)=(x^2/4)+y^2 +(z^2/9) subject to x - y + z = 8. Now sketch level surfaces f(x,y,z) = k for k = 0; 1; 4 and the plane x-y +z = 8 on the same set of axes to help you explain why the point you found corresponds to a minimum value and why there will be no maximum value.
Use Lagrange multipliers to find the extreme values of subject to the given constraint 3x+y; x^2...
Use Lagrange multipliers to find the extreme values of subject to the given constraint 3x+y; x^2 + y^2 = 1
Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y <...
Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y < 3} , u(x,y) = 5 (if y=1) and = 7 (when y=3) I have this problem to solve, and I'm not sure where to start. Any help would be appreciated. Thanks!
The temperature T of a flat sheet, at the point (?x, y) ?, is given by...
The temperature T of a flat sheet, at the point (?x, y) ?, is given by T (?x, y) ? ? x ^ 3 - 2xy + ? 2y ^ 22. a) Determine the rate of change of temperature in the direction of the vector v = (?2, −1) ?, from the point P (? − 1,2) ?. b) Calculate the highest rate of temperature growth from P (? − 1,2) ?, as well as the direction in which it...
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e^(−x^2...
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e^(−x^2 − 3y^2 − 9z^2) where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, −1, 2) in the direction towards the point (5, −2, 3). (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
The function y(x,t) = 0.3 sin( 2 π t -2 π x + π /4) represents...
The function y(x,t) = 0.3 sin( 2 π t -2 π x + π /4) represents the vertical position of an element of a taut string upon which a transverse wave travels. This function depends on the horizontal position along the string, x, and time, t. y and x are in units of meters and t is in units of seconds. Do not use symbols in any of your answers below. Only use integers or decimals. a. Determine the angular...
Find the absolute maxima and minima of the function on the given domain T(x,y)=x2+xy+y2-6x+3 on the...
Find the absolute maxima and minima of the function on the given domain T(x,y)=x2+xy+y2-6x+3 on the rectangular plate 0<_x<_5, -3<_y<_0 The absolute maximum occurs at (?,?) minima occurs at (?,?)
1. Solve the given initial value problem. dy/dt = (t^3 + t)/(y^2); y(0) = 2 ....
1. Solve the given initial value problem. dy/dt = (t^3 + t)/(y^2); y(0) = 2 . 2. We know from Newton’s Law of Cooling that the rate at which a cold soda warms up is proportional to the difference between the ambient temperature of the room and the temperature of the drink. The differential equation corresponding to this situation is given by y' = k(M − y) where k is a positive constant. The solution to this equation is given...
Find the directional derivative of the function f(x,y)=x^6+y^3/(x+y+6 ) at the point (2,-2) in the direction...
Find the directional derivative of the function f(x,y)=x^6+y^3/(x+y+6 ) at the point (2,-2) in the direction of the vector < - 2 ,2>. b) Also find the maximum rate of change of f at the given point and the unit vector of the direction in which the maximum occurs.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT