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1. Liverpool played 38 games and obtained 84 points in a particular season. You obtain no points for losing a game, one point for drawing a game and three points if you win a game. If Liverpool won twice as many games as they lost, how many games did they win, draw and lose?2. Consider a series of integers a1 < a2 < ··· < a43 < a44 that are all positive and all of the numbers are taken to be less than 125. There are 43 differences between adjacent numbers in this series defined as, di = ai+1 - ai. Can you prove that some value of the differences (which must also be positive integers) must occur at least 10 times? 3. Jane is walking her dog, Spot. She sees her friend, Dick, walking toward her along the same long, straight road. Both Dick and Jane are walking at 3 mph. When Dick and Jane are 600 feet apart, Spot runs from Dick to Jane, turns and runs back to Dick, and then back and forth between them at a constant speed of 8 mph. Dick and Jane both continue walking toward each other at a constant 3 mph. Neglecting the time lost each time Spot reverses direction, how far has Spot run in the time it takes Dick and Jane to meet?
Two blocks of masses m1 = 2.00 kg and m2 = 3.60 kg are each released from rest at a height of h = 4.80 m on a frictionless track, Determine the velocity of each block just before the collision
The coefficient of static friction between a rope and the table on which it rests is µs. Find the fraction of the rope that can hang over the edge of the table before it begins to slip. (Use mu_s for µs.)
the electric field on the axis of a uniformly charged ring has magnitude 380 knc at a point 6.4 cm from the ring
A circular disk of mass 10.0 kg and radius 0.500 m rotates at 30.0 revolutions per second on a vertical axle, What is the final angular velocity of the combination of disks
The potential difference between two points in a wire 10 m apart is 12 V. When the current density is 4*10^7 A/m^2. find the resistivity of the material in the wire
How do domestic political institutions affect development? Select one: a. Colonial powers did not invest in their countries so colonies had little infrastructure at independence. b. Powerful interest groups at times oppose government policies ai..
One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at a frequency 125Hz, What is the speed of a transverse wave on the rope
A concave mirror has a focal length of 69.6 centimeter. Evaluate what is its radius of curvature, Locate the image when the object distance is 100 centimeter
Mary and her younger brother Alex decide to ride the 17-foot-diameter carousel at the State Fair. What is Mary angular speed compared to that of Alex's angular speed
q1. a toyota prius driving north at 59.0 and the vw passat driving south at 37.0 are on the same road heading toward
A merry-go-round with moment of inertia of 550 kg m 2 has a boy of mass 45 kg riding in the center of the merry-go-round with an initial angular velocity of 9 revolutions per minute. The boy then travels from the center to the outside rim of the m..
A solid cylinder of mass M = 27 kg, radius R = 0.29 m and uniformdensity is pivoted on a frictionless axle coaxial with its symmetryaxis. What is its angular velocity after the collision
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