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Problem 1. A circular plate of radius 4 is heated. The temperature at point (x, y) on the plate i...
A circular plate of radius 4 is heated. The temperature at point (x, y) on the plate is given by ...
A circular plate of radius 4 is heated. The temperature at point (x, y) on the plate is given by f(x, y) = 2x 2 + 3y 2 − 4x + 5. Assume (0,0) is the center of the plate. (a) Find the hottest and coolest points on the edge of the plate. (b) Is there a point inside the disc that is hotter? Is there a point that’s cooler?
The flat circular plate shown on the right has the shape of the region x +y?...
The flat circular plate shown on the right has the shape of the region x +y? 51. The plate, including the boundary where x² + y2 = 1, is heated so that the temperature at the 5 point (x,y) is T(x,y)=x + 3y2 + 3. Find the temperatures at the hottest and coldest points on the plate. degrees The hottest temperature on the plate is (Type an integer or a simplified fraction.) The coldest temperature on the plate is degrees....
The temperature of points on an elliptical plate x² + y2 + xy s 4 is...
The temperature of points on an elliptical plate x² + y2 + xy s 4 is given by the equation T(x,y)=9(x² + y2). Find the hottest and coldest temperatures on the edge of the elliptical plate. Set up the equations that will be used by the method of Lagrange multipliers in two variables to solve this problem. The constraint equation is The vector equation is =1(O The hottest temperature is degrees. The coldest temperature is degrees.
R105 m Problem #1 (3e ruines) A rigid circular plate of 123.mm radius is attached to...
R105 m Problem #1 (3e ruines) A rigid circular plate of 123.mm radius is attached to a solid SO x 200-mm rectangular post, with the center of the plate directly above the center of the post. If a 4-kN force P is applied at E with e- determine (a) the stress at point d, () the stress at point B (e) the point whore the neutral axis intersects hine AD Problem # 2 (40 Points)
Problem 1 (25 points): Magnetic Fields. A circular loop of current I, and radius ro lies in the x...
Problem 1 (25 points): Magnetic Fields. A circular loop of current I, and radius ro lies in the x-y plane as shown. P (ro,0,zo) a) Using the Biot-Savart Law, set up the integral expression to evaluate the magnetic flux density at the point P (ro,0,zo). Do not evaluate the integral(s) in this part but specify the expressions for the x, y, and z components of the resulting flux density Problem 1 (continued): b) Given the right-hand rule for magnetic fields...
PLEASE DO LETTER d.) PLEASE DO LETTER f.) The plane from e.) is 4(x-2)+6(y-1)+(z-1)=0 or 4x+6y+z=15...
PLEASE DO LETTER d.)
PLEASE DO LETTER f.)
The plane from e.) is 4(x-2)+6(y-1)+(z-1)=0 or 4x+6y+z=15
15. The temperature on an unevenly heated metal plate positioned in the first quadrant of the xy-plane is given by 25xy + 25 C(x, y) = 7 (x - 1)2 + (y - 1)2 +1° Assume that temperature is measured in degrees Celsius and that x and y are each measured in inches. (Note: At no point in the following questions should you expand...
An ant is crawling on a hot plate and z= T(x,y) gives the temperature on the...
An ant is crawling on a hot plate and z= T(x,y) gives the temperature on the plate in °C at position (x, y) (measured in cm). The ant's current position is (1, -2). It senses that to cool down as fast as possible it should move towards the point (-1,1) and it will cool at a rate of 2 C/cm. Give the gradient vector of T at(1, -2). Give each component numerically rounded to 2 decimal places. f(3,-2) =( Note:...
a circular ring of charge of radius 1 m lies in the x-y plane and is...
a circular ring of charge of radius 1 m lies in the x-y plane and is centered at the origin. Assume also that the ring is in air and carries a density 2rho C/m. A) find the electric potential V AT (0,0,Z) b) Find the corresponding electric field E. (Assume electric field @point have x,y direction because Rho(l) is not constant)
Problem 3 (25 points): Magnetic Field from Superposition. A circular disk of radius ro is uniformly...
Problem 3 (25 points): Magnetic Field from Superposition. A circular disk of radius ro is uniformly coated with charge with a surface charge density of ps the disk lies in the x-y plane and the disk axis is the z-axis. This disk is spinning about the z-axis at a rate of one revolution every T seconds. The resulting surface current density on the disk is given by 2Tps a) What is the magnetic field intensity on the z-axis at a...
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z)...
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z) = 200e-x=y+14–2–19, where T is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (-1, 1,-1) in the direction toward the point (-4,-5, -5). In which direction...
The flat circular plate shown on the right has the shape of the region x +y? 51. The plate, including the boundary where x² + y2 = 1, is heated so that the temperature at the 5 point (x,y) is T(x,y)=x + 3y2 + 3. Find the temperatures at the hottest and coldest points on the plate. degrees The hottest temperature on the plate is (Type an integer or a simplified fraction.) The coldest temperature on the plate is degrees....
The temperature of points on an elliptical plate x² + y2 + xy s 4 is given by the equation T(x,y)=9(x² + y2). Find the hottest and coldest temperatures on the edge of the elliptical plate. Set up the equations that will be used by the method of Lagrange multipliers in two variables to solve this problem. The constraint equation is The vector equation is =1(O The hottest temperature is degrees. The coldest temperature is degrees.
R105 m Problem #1 (3e ruines) A rigid circular plate of 123.mm radius is attached to a solid SO x 200-mm rectangular post, with the center of the plate directly above the center of the post. If a 4-kN force P is applied at E with e- determine (a) the stress at point d, () the stress at point B (e) the point whore the neutral axis intersects hine AD Problem # 2 (40 Points)
Problem 1 (25 points): Magnetic Fields. A circular loop of current I, and radius ro lies in the x-y plane as shown. P (ro,0,zo) a) Using the Biot-Savart Law, set up the integral expression to evaluate the magnetic flux density at the point P (ro,0,zo). Do not evaluate the integral(s) in this part but specify the expressions for the x, y, and z components of the resulting flux density Problem 1 (continued): b) Given the right-hand rule for magnetic fields...
PLEASE DO LETTER d.)
PLEASE DO LETTER f.)
The plane from e.) is 4(x-2)+6(y-1)+(z-1)=0 or 4x+6y+z=15
15. The temperature on an unevenly heated metal plate positioned in the first quadrant of the xy-plane is given by 25xy + 25 C(x, y) = 7 (x - 1)2 + (y - 1)2 +1° Assume that temperature is measured in degrees Celsius and that x and y are each measured in inches. (Note: At no point in the following questions should you expand...
An ant is crawling on a hot plate and z= T(x,y) gives the temperature on the plate in °C at position (x, y) (measured in cm). The ant's current position is (1, -2). It senses that to cool down as fast as possible it should move towards the point (-1,1) and it will cool at a rate of 2 C/cm. Give the gradient vector of T at(1, -2). Give each component numerically rounded to 2 decimal places. f(3,-2) =( Note:...
Problem 3 (25 points): Magnetic Field from Superposition. A circular disk of radius ro is uniformly coated with charge with a surface charge density of ps the disk lies in the x-y plane and the disk axis is the z-axis. This disk is spinning about the z-axis at a rate of one revolution every T seconds. The resulting surface current density on the disk is given by 2Tps a) What is the magnetic field intensity on the z-axis at a...
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z) = 200e-x=y+14–2–19, where T is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (-1, 1,-1) in the direction toward the point (-4,-5, -5). In which direction...
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