The function is a solution to the heat equation and gives the temperature at the point in 3-space and time . the constant is the thermal conductivity of the medium through which the heat is flowing. (a) show that the function is a solution to the heat equation for all in 3-space and . (b) for each fixed time , what are the level surfaces of the function in 3-space? (c) regard as fixed and compute grad . what does grad tell us about the direction and magnitude of the heat flow?

Two thin 80.0- cm rods are oriented at right angles to each other. each rod has one end at the origin of the coordinates, and one of them extends along the x- axis while the other extends along the yaxis. the rod along the x- axis carries a charge of - 15.0 μ c distributed uniformly along its length, and the other rod carries 15.0 μ c uniformly over its length. find the magnitude and direction of the net electrical force that these two rods exert on an electron located at the point (40.0 cm, 40.0 cm). (e

If steel is more dense that lake water, why can a boat float

Unpolarized light falls on two polarizer sheets whose transmission axes are at right angles. a third polarizer is placed between the first two so that its axis makes a 52-degree angle with the axis of the first polarizer. a) what fraction of the incident light intensity is transmitted through the first polaroid? b) what fraction of the incident light intensity is transmitted through the second polaroid? c) what is the angle of polarization of the light that enters the third polaroid? d) what fraction of the incident light intensity is transmitted through the third polaroid. e) what happens if the middle polaroid is removed?