Consider an insulating sphere of radius 6 cm surrounded by a conducting sphere of inner radius 18 cm and outer radius 26 cm. Fur- thermore, suppose that the electric field at a point 10 cm from the center is measured to be 1610 N/C radially inward while the elec- tric field at a point 35 cm from the center is 120 N/C radially outward.

R 2R 3R
6 cm 18 cm
26 cm

Find the charge on the insulating sphere. Answer in units of C.
Find the net charge on the conducting sphere. Answer in units of C.
Find the total charge on the inner surface of the hollow conducting sphere.
Find the total charge on the outer surface of the hollow conducting sphere.

The discovery that the universe appears to be expanding led to a widely accepted theory called a.) the big bang theory b.) the doppler effect c.) hubble’s law d.) solar nebular theory e.) the seyfert theory

The bubba chump shrimp company processes and packages shrimp for sale to wholesale seafood distributors. the shrimp are transported to the main plant by trucks that carry 1,000 pounds (lb) of shrimp. once the continuous flow processing of the shrimp begins, no inventory is allowed in buffers due to spoilage and all of the shrimp must be processed within 12 hours to prevent spoilage. the processing begins at the sorter, where the trucks dump the shrimp onto a conveyor belt that feeds into the sorter, which can sort up to 500 lb per hour. the shrimp then proceed to the desheller, which can process shrimp at the rate of 400 lb per hour. however, after 3 hours and 45 minutes of processing, the desheller must be stopped for 15 minutes to clean out empty shrimp shells that have accumulated. the veins of the shrimp are then removed in the deveining area at a maximum rate of 360 lb per hour. the shrimp proceed to the washing area, where they are processed at 750 lb per hour. finally, the shrimp are packaged and frozen. what is the daily process capacity of the processing plant (excluding the packaging and freezing)?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k