You place a box weighing 268.3 N on an inclined plane that makes a 42◦ angle with the horizontal. Compute the component of the gravitational force acting down the inclined plane.

Answer in units of N.

Abaseball picther can throw a ball at about 90 miles per hour, v = 40 m/s, on solid rock ground. we now put him into space. when he throws the ball, which weighs mb = 0.15 kg moves away from himat the same speed. how long does it take the ball thrown in space to travel the 30 meters to the batter? he weighs mp = 100kg

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.

Aforce of 200 n is applied to an input piston of cross-sectional area 2 sq. cm pushing it downward 2.8 cm. how far does the output piston of cross-sectional area 12 sq. cm move upward? show all work.