Question

The vector field ?(?, ?) = (? − 3?)?⃗ + 2??⃗ represents an ocean current. Suppose...

The vector field ?(?, ?) = (? − 3?)?⃗ + 2??⃗ represents an ocean current. Suppose that an iceberg is located in this current at the point (−1, 1) at time ? = 4.

Then, use Euler’s method with 2 steps to approximate the location of the iceberg in the ocean current at time ? = 5.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Hope this is fine.

Will appreciate feedback.

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
For the system ?? ?? = −2? ?? ?? = 1 2 ? with ?(0) =...
For the system ?? ?? = −2? ?? ?? = 1 2 ? with ?(0) = 0, and ?(0) = 1 . a) Show that (?(?), ?(?)) = (−2 sin(?) , cos(?)) is the solution to the initial value problem. b) Use Euler’s Method with a step size of Δ? = 0.1 to find an approximate solution. Find the approximate values at ? = 5, 10, and 20. That is, if ?(?) represents the approximation to ?(?), and ?(?) represents...
1. Consider the initial value problem dy/dx =3cos(x^2) with y(0)=2. (a) Use two steps of Euler’s...
1. Consider the initial value problem dy/dx =3cos(x^2) with y(0)=2. (a) Use two steps of Euler’s method with h=0.5 to approximate the value of y(0.5), y(1) to 4 decimal places. b) Use four steps of Euler’s method with h=0.25, to approximate the value of y(0.25),y(0.75),y(1), to 4 decimal places.    (c) What is the difference between the two results of Euler’s method, to two decimal places?   
Consider the vector field F = <2 x y^3 , 3 x^2 y^2+sin y>. Compute the...
Consider the vector field F = <2 x y^3 , 3 x^2 y^2+sin y>. Compute the line integral of this vector field along the quarter-circle, center at the origin, above the x axis, going from the point (1 , 0) to the point (0 , 1). HINT: Is there a potential?
A water current in the ocean flows with a velocity ? ⃗ in the presence of...
A water current in the ocean flows with a velocity ? ⃗ in the presence of a magnetic field ? :⊥?. The fluid has an electrical conductivity s and a volumetric mass density p. a. Evaluate the current density ? ⃗ that is induced in the fluid. b. Estimate the magnitude of ? ⃗ for terrestrial ocean currents for the parameters of the Earth’s magnetic field ~ 5x105 T, conductivity of sea water ~4 W-1m-1, and typical ocean current velocity...
Consider the vector field ?(?,?,?)=(3?+3?)?+(4?+3?)?+(4?+3?)?. a) Find a function ? such that ?=∇? and ?(0,0,0)=0. ?(?,?,?)=  ...
Consider the vector field ?(?,?,?)=(3?+3?)?+(4?+3?)?+(4?+3?)?. a) Find a function ? such that ?=∇? and ?(0,0,0)=0. ?(?,?,?)=   b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral ∫C ?⋅??
? is a vector field and ? is a scalar field 1. Prove in 3 dimensions:...
? is a vector field and ? is a scalar field 1. Prove in 3 dimensions: ∇ ∙ (∇ × ? ) = 0 2. Prove in 3 dimensions: ∇ × (∇φ) = 0 3. Prove in 3 dimensions: (?∙∇) ?= −? × (∇ × ?)+ ∇((?∙?)/ 2)
(1 point) In each case, if the vector field is conservative, give the potential function whose...
(1 point) In each case, if the vector field is conservative, give the potential function whose value at the origin is zero; otherwise answer NA. (1) 〈4yz(xyz)^3,4xz(xyz)^3,4xy(xyz)^3〉 (2) 〈−ysin(x)z,zcos(x),ycos(x)〉 (3) 〈y,x+z,y〉 (4) 〈−y,x〉 (5) 〈3y−3z,3z,−(3y+3x) (6) 〈exp(x)cos(y),−(exp(x))sin(y),4(z^3)〉 Please show all steps when finding potential functions.
The function f(x, y) = x^−2 y^3 is a potential for a vector field F. Use...
The function f(x, y) = x^−2 y^3 is a potential for a vector field F. Use this to evaluate ∫ C F · dr where C is a curve from (1, 1) to (2, 2).
Consider the vector field F = ( 2 x e y − 3 ) i +...
Consider the vector field F = ( 2 x e y − 3 ) i + ( x 2 e y + 2 y ) j , (a) Find all potential functions f such that F = ∇ f . (b) Use (a) to evaluate ∫ C F ⋅ d r , where C is the curve r ( t ) = 〈 t , t 2 〉 , 1 ≤ t ≤ 2 .
Differential Geometry   3. In each case, express the given vector field V in the standard form...
Differential Geometry   3. In each case, express the given vector field V in the standard form (b) V(p) = ( p1, p3 - p1, 0)p for all p. (c) V = 2(xU1 + yU2) - x(U1 - y2 U3). (d) At each point p, V(p) is the vector from the point ( p1, p2, p3) to the point (1 + p1, p2p3, p2). (e) At each point p, V(p) is the vector from p to the origin.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT