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Erik's puzzle. In a stripped-down version of Conway's game of life, cells are arranged on a square grid. Each cell is either alive or dead. Live cells do not die. Dead cells become alive if two or more of their immediate neighbours are alive. (Neighbours to north, south, east and west.) What is the smallest number of live cells needed in order that these rules lead to an entire N × N square being alive?
In a d-dimensional version of the same game, the rule is that if d neighbours are alive then you come to life. What is the smallest number of live cells needed in order that an entire N × N × · · · × N hypercube becomes alive? (And how should those live cells be arranged?)
A 10.0-g wad of sticky clay is hurled horizontally at a 110-g wooden block initially at rest on a horizontal surface. what was the speed of the clay immediately before impact
A 48 g piece of ice at 0.0 degree C is placed in an insulated calorimeter of negligible heat capacity containing 100 g of water at 100 degree C. What is the final temperature of the water once thermal equilibrium is established? Find the entropy chan..
Two parallel plates are 4.0 cm apart. The bottom plate is charged positively and the top plate is charged negatively, producing a uniform electric field of 5.0 * 10 exp 4 N/C in the region between the plates.
A flashlight beam strikes the surface of a pane of glass (n = 1.58) at a 63 degree angle to the normal. What is the angle of refraction? Express your answer using two significant figures.
A wire coil of 35 turns has a cross-sectional area of 12 cm2. The coil is placed in a uniform field of a large magnet with B = 0.32 T. What is the magnitude of the average emf produced
A liquid mixture containing 40% cyclohexane, 20% benzene, 25% toluene, and 15% n-heptane is in equilibrium with its vapor at 1 bar. Determine the temperature and the vapor composition.
The G string of a guitar which should be 397 Hz is playing flat at 380 Hz. What percentage change in the tension of the wire is necessary so as to tune the string to 392 Hz.
The minimum distance required to stop a car moving at 34 mi/h is 42 ft. What is the minimum stopping distance for the same car moving at 64.0 mi/h, assuming the same rate of acceleration.
A charge of -5.8 micro-Coulombs is placed at x = 0, y = 0. A charge of +17.1 micro-Coulombs is placed at x = 0, y = +36 cm. Another charge of +34.8 micro-Coulombs is placed at x = +33 cm, y = 0 cm. What is the magnitude of the total electric force..
A source delivers an AC voltage of the form ?v = 98.0 sin (80?t), where ?v is in volts and t is in seconds, to a capacitor. The maximum current in the circuit is 0.500 A. Find the rms voltage of the source
Starting from rest, a 96-kg firefighter slides down a fire pole. The average frictional force everted on him by the pole has a magnitude of 790 N, How far did he slide down the pole
A Styrofoam box has a surface area of 0.74 m2 and a wall thickness of 2.0 cm. The temperature of the inner surface is 5.0°C, determine the thermal conductivity of the Styrofoam
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