Suppose that a bored student wants to go to a restaurant for lunch, but she only has an hour in which to go, eat, and get back in time for class. Considering that it usually takes about 30 minutes in most restaurants to get served and to eat, what is the farthest restaurant the student can go to without being late for class? Assume in this part that the student has a car that can accelerate to its top speed in a negligible amount of time. Also, the local speed limit is 30 mph and the student would not like to get a speeding ticket. Express your answer in miles.

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.

Adielectric-filled parallel-plate capacitor has plate area a = 30.0 cm2 , plate separation d = 9.00 mm and dielectric constant k = 3.00. the capacitor is connected to a battery that creates a constant voltage v = 15.0 v . throughout the problem, use ϵ0 = 8.85x10-12 c2/n.m2 . find the energy u1 of the dielectric-filled capacitor.

Ahockey puck sliding along frictionless ice with speed v to the right collides with a horizontal spring and compresses it by 3.0 cm before coming to a momentary stop.