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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?
a 1340-kg car has just passed a diner. The closest the car came to the diner was R=16.5m, but the car has driven another x=22.7m in the 2.05 seconds elapsed since then. what is the current magnitude of the anguar momentum of the car
a person is riding a bicycle and its wheels have an angular velocity of 18.5 rads. then the brakes are applied and the
in a scientific test conducted in arizona a special cannon called harp shot a projectile straight up to an altitude of
An object placed 20 cm from a concave mirror forms an image that is three times as large as the object on a screen. Discover the radius of curvature of the mirror.
A playground is on the flat roof of a city school, 6.1 m above the street below (see figure). The vertical wall of the building is h = 7.60 m high, forming a 1.5-m-high railing around the playground. A ball has fallen to the street below, and a pa..
Assume the corners of a cube of side a are occupied each by a positive charge q, What is the net force on each of the eight charges
A fan is rotating at a rate of 710 rpm. When the motor is turned off, the blades slow to rest in 3.5 s. What is the angular acceleration of the blades as they slow down
A vacuum gauge connected to a tank reads 30.0 kPa. If the local atmospheric pressure is 13.5 psi, What is the absolute pressure in units of psi
A beam of unpolarized light of intensity26.0 W/m2 passes during a polarizing sheet. What is the electric field amplitude of the transmitted beam?
A microwave oven is powered by a magnetron, an electronic device that generates electromagnetic waves of frequency 2.45 GHz. calculate the speed of the microwaves
Your little sister (mass 25.0 kg) is sitting in her little red wagon (mass 8.35 kg) at rest. Calculate the impulse you imparted to the wagon and its passenger
an electric dipole consists of charges 2e and -2e separated by 0.60 nm. it is in an electric field of strength 4.6 x
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