A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges at an angle θ of 3.5×10−5 rad rad. Part A What diameter spot will it make on the Moon? Express your answer using two significant figures.

A jet leaves palermo, sicily, whose latitute is 38 degrees N flying due west. Eventually it returns to palermo again. Assuming that the earth has a 3960-mile radius:   a.) find the distance the jet travels b.)find the distance from palermo to the equator along the surface of the earth.  SHOW WORK AND PICTURES

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A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 5 ft from the house, the base is moving away at the rate of 36 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? y 13-ft ladder y(t) x(t) X

Elliptical cylindrical (EC) coordinates are defined by the variables u, v and z, with aconstant a, in terms of Cartesian coordinates as follows:x = a cosh u cos v ;y = a sinh u sin v ; (75)z = z .a. Find the EC metric.b. Describe surfaces of constant u, v and z for various values of the constant a.c. Find the EC basis vectors for arbitrary a.d. Make vector field plots of the EC basis vectors in the x-y plane.e. Find the incremental area and volume expressions.f. Express the gradient, divergence, curl and Laplacian operators in EC coordinates.

A toy racecar races along a circular race track that has a radius of 32 meters. The racecar starts at the 3-o'clock position of the track and travels in the CCW direction. Suppose the racecar has traveled 51 meters along the race track. How many radians has the racecar swept out?  __radians    What is the racecar's distance to the right of the center of the race track (in meters)? ____ meters

For this problem the average distance of the earth from the sun is about 1.5×10^8km. Assume that the earth's orbit around the sun is circular and that the sun is at the origin of your coordinate system.