A solid nonconducting sphere of radius R = 5.4 cm has a nonuniform charge distribution of volume charge density rho = (14.3 pC/m3)r/R, where r is radial distance from the sphere's center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r = 0, (c) r = R/3.0, and (d) r = R?

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Which is an example of gaining a static charge by conduction? a) rubbing a balloon against your hair. b) shuffling your shoes across a carpet. c) bringing a charged rod near an electroscope. d) touching your car on a cold day and getting a shock.

Standing side by side ,you and a friend step off a bridge at different times and fall for 1.6s to the water below.your friend goes first,and you follow after he has dropped a distance of 2.0m.when your friend hits the water,is the seperation between the two of you 2.0m or more than 2.0m? verify your answer with a calculation.