A30-mf capacitor is charged to an unknown potential v0 and then connected across an initially uncharged 10-mf capacitor. if the final potential difference across the 10-mf capacitor is 20 v, determine v0.

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.

Awoman holds a book by placing it between her hands such that she presses at right angles to the front and back covers. the book has a mass of m = 1.8 kg and the coefficient of static friction between her hand and the book is μs = 0.67. no attempt 50% part (a) what is the weight of the book, fgb in newtons?

Arunner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. let a coordinate system have its origin at the center of the circle with the x-axis pointing east and the y-axis north. the runner starts at (x, y) = (50 m, 0 m) and runs 2.5 times around the track in a clockwise direction.