Find a formula F⃗ =〈 F1(x,y), F2(x,y) 〉 for the vector field in the plane that has the properti...
Find a formula F⃗ =〈 F1(x,y), F2(x,y) 〉 for the vector field in the plane that has the properties that F⃗ (0,0)=〈0,0〉 and that at any other point (a,b)≠(0,0) the vector field F⃗ is tangent to the circle x^2+y^2=a^2+b^2 and points in the counterclockwise direction with magnitude ∥F⃗ (a,b)∥=2sqrt(a^2+b^2)
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Find a formula F⃗ =〈 F1(x,y), F2(x,y) 〉 for the vector field in the plane that has the properti...
Vector A has a magnitude of 23 units and points in the positive y-direction.
3. Vector A has a magnitude of 23 units and points in the positive y-direction. Vector B is added to A, giving a resultant vector A + B that points in the negative y-direction with a magnitude of 13 units. What is the magnitude and direction of B?4. As you will see in a later chapter, forces are vector quantities, and the total force on an object is the vector sum of all forces acting on it. In the figure below, a force F1...
Tyā (x,y)メ(0,0) (x,y)= (0,0). if if 1 (d) Given the unit vector u-( find the directional deriv...
Please do the parts in the given order
tyā (x,y)メ(0,0) (x,y)= (0,0). if if 1 (d) Given the unit vector u-( find the directional derivative of f(x, y) at the 리지, ,- point (to,m) = (0,0), in the direction of the vector a. (e) Find the gradient of f(x, y) at the point (zo,o) (0,0) (c) Find the equation of the tangent plane to the graph of the function z -f(x, y) at the point (x,y,z) (1,0,0).
tyā (x,y)メ(0,0) (x,y)=...
Forces F1 and F2 with magnitudes indicated in the drawing act at point O. Determine the...
Forces
F1
and
F2
with magnitudes indicated in the drawing act at point O.
Determine the magnitudes in kilonewtons and directions in
degrees counterclockwise from the +x-axis of the following
resultant forces.
(a)
R1 = F1 + F2
magnitude kN direction ° counterclockwise from the
+x-axis
(b)
R2 = F1 − F2
magnitude kN direction ° counterclockwise from the
+x-axis
(c)
R3 = F2 − F1
magnitude kN direction ° counterclockwise from the
+x-axis
4. Let F(x,y) - PiQj be a smooth plane vector field defined for (x,y) f (0,0), and F - dr for int...
4. Let F(x,y) - PiQj be a smooth plane vector field defined for (x,y) f (0,0), and F - dr for integer j, and all suppose Q - Py for (z, y) (0,0). In the following L-JF dr for integer j, and all G are positively oriented circles. Suppose h = π where G is the circle x2 + y2-1. (a) Find 12 for G : (x-2)2 + y-1. Explain briefly. (b) Find Is for Cs: ( -2)y 9. Explain...
the figure shows a vector force field F(x,y) mapped in the x-y plane. (It depicts a...
the figure shows a vector
force field F(x,y) mapped in the x-y plane. (It depicts a vector
quantity whose magnitude and direction varies only with x and y,
Not z). Several points (A, B, and C) are indicated, and a (dashed)
path from A to B is shown.
F(x, y) =
For any vector field F⃗ and any scalar function f we define a new field a) Assuming that the app...
For any vector field F⃗ and any scalar function f we define a new field
a) Assuming that the appropriate partial derivatives are
continuous, show the following formula:
b) Let ⃗x = x⃗i + y ⃗j + z ⃗k and the vector field
Use the formula found in a) to answer
the following question: is there a number p such that F⃗ is incompressible (that is, its divergence is zero)?
f F)(x,y,z) = f(x,y,z)F(x,y, z) We were unable to transcribe...
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g ...
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g represents the direction in which g increases the fastest. Notice that this is the direction in the xy plane corresponding to the steepest slope up the surface, with magnitude equal to the slope in that direction. 1. At the point (2, π), find the gradient, and explain what it means. 2. Use it to construct a vector in the tangent...
A metal bar is in the xy-plane with one end of the bar at the origin. A force F⃗ =( 6.39 N )i^+( -3.16 N )j^ is applied to the bar at the point x = 2.29 m, y = 3.19 m.
A metal bar is in the xy-plane with one end of the bar at the origin. A force F =( 6.39 N )i +( -3.16 N )j is applied to the bar at the point x = 2.29 m, y = 3.19 m.A) What is the position vector r⃗ for the point where the force is applied?Enter the x and y components of the radius vector separated by a comma.*B) What is the magnitude of the torque with respect to...
Let F = (P,Q) be the vector field defined by P(x,y) ity, (1, y) = (0,0)...
Let F = (P,Q) be the vector field defined by P(x,y) ity, (1, y) = (0,0) 10, (x,y) = (0,0) Q(x, y) = -Ity. (x, y) = (0,0) 10, (x, y) = (0,0). (a) (3 points) Show that F is a gradient vector field in RP \ {y = 0}. (b) (4 points) Letting D = {2:2020 + y2020 < 1}, compute the line integral Sap P dx +Qdy in the counter-clockwise direction. (c) (1 point) Does your calculation in...
A uniform electric field exists everywhere in the x, y plane. This electric field has a...
A uniform electric field exists everywhere in the x, y plane. This electric field has a magnitude of 4600 N/C and is directed in the positive x direction. A point charge -5.5 times 10^-9 C is placed at the origin. Find the magnitude of the net electric field at (a) x = -0.18 m, (b) x = +0.18 m, and (c) y = +0.18 m.
Please do the parts in the given order
tyā (x,y)メ(0,0) (x,y)= (0,0). if if 1 (d) Given the unit vector u-( find the directional derivative of f(x, y) at the 리지, ,- point (to,m) = (0,0), in the direction of the vector a. (e) Find the gradient of f(x, y) at the point (zo,o) (0,0) (c) Find the equation of the tangent plane to the graph of the function z -f(x, y) at the point (x,y,z) (1,0,0).
tyā (x,y)メ(0,0) (x,y)=...
Forces
F1
and
F2
with magnitudes indicated in the drawing act at point O.
Determine the magnitudes in kilonewtons and directions in
degrees counterclockwise from the +x-axis of the following
resultant forces.
(a)
R1 = F1 + F2
magnitude kN direction ° counterclockwise from the
+x-axis
(b)
R2 = F1 − F2
magnitude kN direction ° counterclockwise from the
+x-axis
(c)
R3 = F2 − F1
magnitude kN direction ° counterclockwise from the
+x-axis
4. Let F(x,y) - PiQj be a smooth plane vector field defined for (x,y) f (0,0), and F - dr for integer j, and all suppose Q - Py for (z, y) (0,0). In the following L-JF dr for integer j, and all G are positively oriented circles. Suppose h = π where G is the circle x2 + y2-1. (a) Find 12 for G : (x-2)2 + y-1. Explain briefly. (b) Find Is for Cs: ( -2)y 9. Explain...
the figure shows a vector
force field F(x,y) mapped in the x-y plane. (It depicts a vector
quantity whose magnitude and direction varies only with x and y,
Not z). Several points (A, B, and C) are indicated, and a (dashed)
path from A to B is shown.
F(x, y) =
For any vector field F⃗ and any scalar function f we define a new field
a) Assuming that the appropriate partial derivatives are
continuous, show the following formula:
b) Let ⃗x = x⃗i + y ⃗j + z ⃗k and the vector field
Use the formula found in a) to answer
the following question: is there a number p such that F⃗ is incompressible (that is, its divergence is zero)?
f F)(x,y,z) = f(x,y,z)F(x,y, z) We were unable to transcribe...
Let F = (P,Q) be the vector field defined by P(x,y) ity, (1, y) = (0,0) 10, (x,y) = (0,0) Q(x, y) = -Ity. (x, y) = (0,0) 10, (x, y) = (0,0). (a) (3 points) Show that F is a gradient vector field in RP \ {y = 0}. (b) (4 points) Letting D = {2:2020 + y2020 < 1}, compute the line integral Sap P dx +Qdy in the counter-clockwise direction. (c) (1 point) Does your calculation in...
A uniform electric field exists everywhere in the x, y plane. This electric field has a magnitude of 4600 N/C and is directed in the positive x direction. A point charge -5.5 times 10^-9 C is placed at the origin. Find the magnitude of the net electric field at (a) x = -0.18 m, (b) x = +0.18 m, and (c) y = +0.18 m.
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