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Question: Consider the Laplace equation ?^2u/(?x^2) + ?^2u/(?y^2) = 0 that models the steady-state heat distribution u(x, y) in a rectangular plate 0 = x = a and 0 = y = b. In physics, the Fourier's law of heat conduction states that the heat flux density (heat energy that flows through a surface per unit time) is proportional to the temperature gradient. From multivariable calculus, we know that the gradient vector is given by ?u = (?u/?x, ?u/?y ) Suppose that the plate is held at zero degrees at y = 0 and y = b, and that it is insulated at x = 0 so that the heat flux there is zero. These three boundary conditions can be expressed mathematically as: u(x, 0) = u(x, b) = ux(0, y) = 0 . Given a heat flux profile at x = a such that u_x(a, y) = f(y), solve the Laplace equation using separation of variables.
A space vehicle is traveling at 3570 km/h relative to Earth when the exhausted rocket motor is disengaged, What is the speed (in km/h) of the command module relative to Earth just after the separation
An astronaut wants to remove a bolt from a satellite in orbit. He positions himself so that he is at rest with respect to the satellite, What is wrong with his method
A baseball has a velocity of 41.5 m/s (92.8 mi/h), directed horizontally, as it is released by a pitcher. Calculate the ball's instantaneous acceleration just before it is released
Find the four possible ways of arranging the three resistors, and calculate the maximum power that can be dissipated in each of the ways.
A technician wraps wire around a tube of length 40.0 cm having a diameter of 7.90 cm. find the self-induced emf in the solenoid?
Sound enters the ear, travels through the auditory canal, and reaches the eardrum. What is the fundamental frequency of the canal
water has a mass per mole of 18.0 gmol and each water molecule h2o has 10 electrons. a how many electrons are there in
A copper rod has a length of 1.7 m and a cross-sectional area of4.1 x10-4 m2. One end of the rod is incontact with boiling water and the other with a mixture of ice andwater. What is the mass of ice per second that melts? Assume that no heat is lo..
Four solid plastic cylinders all have radius 2.75 cm and length 6.42 cm. Find the charge of each cylinder given the following additional information about each one.
1. The string's tension is doubled. 2. The string's mass is quadrupled (but its length is unchanged). 3. The string's length is quadrupled (but its mass is unchanged). 4. The string's mass and length are both quadrupled.
An electrically charged bullet of mass 0.010 kg leaves thebarrel of a gun traveling parallel to the ground and perpendicularto the Earth's magnetic field at 1.400e+3 m/s. Intheory, what charge could the bullet carry in order to remain at aconstant..
q1. planet zero has a mass of 5.0 acute 1023 kg and a radius of 2.0 acute 106 m. a space probe is launched
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