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Q2. A wire has a shape that can be modeled with the parameterization F (1) =...
A frictionless wire is bent into the shape of a cycloid curve, with coordinates given by...
A frictionless wire is bent into the shape of a cycloid curve,
with coordinates given by the parametric equations
? = ?(? + sin ?), ? = ?(1 − cos ?), for −? < ? < ?. The x
axis is horizontal, and y is vertically upwards. A bead of
mass m slides freely on the wire. Show that the distance s,
measured along the wire from the origin, is given by
? = 4? sin. Write out the potential...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evalu...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
Q2 У Q2 y = 1m I • The current in the long Wire located at...
Q2
У Q2 y = 1m I • The current in the long Wire located at x =-2 cm is increasing linearly at a rare of 100 Als • The Blue Eviangle is a loop wire ina Shape of a right eriangle. ↑ Ket2cm 2--2cin a what is the emf induced in the loop of Wire ? b] If the Wire forming the loop has a resistance Per Vait length of to ohms fermerer. What is the magnitude and direction...
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C...
Please solve these three questions!
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...
Sinusoid Shaped Wire A wire segment is bent into a sinusoidal shape with period of 2T,...
Sinusoid Shaped Wire A wire segment is bent into a sinusoidal shape with period of 2T, which gives y sin(x) and the wire has length of 2 π in the x-direction. The wire is carrying a current of 3.5 Amps in the direction shown in the figure. There is a magnetic field in the vicinity of the wire which points in the positive z-direction with a magnitude given by B-Bor, where Bo = 17.50 T/m, what is the y-component of...
Copper wire coated insulating materials on its surface is assumed perfectly insulated laterally. Thus heat in the w...
Copper wire coated insulating materials on its surface is assumed perfectly insulated laterally. Thus heat in the wire flows in x-direction only. In this case the temperature of the wire can be modeled by 1-D heat equation: =c ends (x-0 and x-L) of the wire are also insuiated for all time and initially temperature distribution of the wire can be modeled by /() Please derive u(x,t) of the copper wire. (15 points) b. If f(x) cos(x). piease tind temperature distribution...
Find the seasonalized forecast for Q2 of 2017.The sales trend has been modeled as: Sales =...
Find the seasonalized forecast for Q2 of 2017.The sales trend has been modeled as: Sales = 255.00+ 2 * t , where t= time in quarters, beginning in Q1 2014. Seasonality for the four quarterly periods is given in the table below. QUARTER SEASONAL FACTOR Q #1 1.2 Q #2 1.18 Q #3 0.5 Q #4 ** Round to 1 Decimal Place! **
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S...
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
1. (15 points). A wire, in a plane, has the shape shown in figure. The radii...
1. (15 points). A wire, in a plane, has the shape shown in figure. The radii of the semicircular segments are 20.0 cm and 30.0 cm. Current I = 60.0 A. Find (a) (10 points) magnitude and (a) (5 points) direction of the magnetic field at the semicircles center A. 20.0cm Current I 60.0A 30.00m
137 The arc of the circle with length 37 inches has a central angle of 41...
137 The arc of the circle with length 37 inches has a central angle of 41 a) Find the radius of the circle. (5 points) b) Find the area of the sector formed by the shaded region. (5 points) A 37 in 137 41 B 4 Verify the identity 2 sin? ((a+b)) sin(a) cos(a) csc(a) sec(a) - cos(B) csc(a) + sin(B) sec(a). Tip: the left side is easier to work with.
A frictionless wire is bent into the shape of a cycloid curve,
with coordinates given by the parametric equations
? = ?(? + sin ?), ? = ?(1 − cos ?), for −? < ? < ?. The x
axis is horizontal, and y is vertically upwards. A bead of
mass m slides freely on the wire. Show that the distance s,
measured along the wire from the origin, is given by
? = 4? sin. Write out the potential...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
Q2
У Q2 y = 1m I • The current in the long Wire located at x =-2 cm is increasing linearly at a rare of 100 Als • The Blue Eviangle is a loop wire ina Shape of a right eriangle. ↑ Ket2cm 2--2cin a what is the emf induced in the loop of Wire ? b] If the Wire forming the loop has a resistance Per Vait length of to ohms fermerer. What is the magnitude and direction...
Please solve these three questions!
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...
Sinusoid Shaped Wire A wire segment is bent into a sinusoidal shape with period of 2T, which gives y sin(x) and the wire has length of 2 π in the x-direction. The wire is carrying a current of 3.5 Amps in the direction shown in the figure. There is a magnetic field in the vicinity of the wire which points in the positive z-direction with a magnitude given by B-Bor, where Bo = 17.50 T/m, what is the y-component of...
Copper wire coated insulating materials on its surface is assumed perfectly insulated laterally. Thus heat in the wire flows in x-direction only. In this case the temperature of the wire can be modeled by 1-D heat equation: =c ends (x-0 and x-L) of the wire are also insuiated for all time and initially temperature distribution of the wire can be modeled by /() Please derive u(x,t) of the copper wire. (15 points) b. If f(x) cos(x). piease tind temperature distribution...
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
1. (15 points). A wire, in a plane, has the shape shown in figure. The radii of the semicircular segments are 20.0 cm and 30.0 cm. Current I = 60.0 A. Find (a) (10 points) magnitude and (a) (5 points) direction of the magnetic field at the semicircles center A. 20.0cm Current I 60.0A 30.00m
137 The arc of the circle with length 37 inches has a central angle of 41 a) Find the radius of the circle. (5 points) b) Find the area of the sector formed by the shaded region. (5 points) A 37 in 137 41 B 4 Verify the identity 2 sin? ((a+b)) sin(a) cos(a) csc(a) sec(a) - cos(B) csc(a) + sin(B) sec(a). Tip: the left side is easier to work with.
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