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Consider the differential equation give by y′ = -10(y - sin t) (a) Derive by hand exact solution that satis?es the initial condition y(0) = 1. (b) Numerically obtain the s
Q. Find the number of ways three letter "words" can be chosen from the alphabet if none of the letters can be repeated? Solution: There are 26 ways of choosing the first lett
WON 5 GAMES
Define an ordered rooted tree. Cite any two applications of the tree structure, also illustrate using an example each the purpose of the usage. Ans: A tree is a graph like t
sum of sine series
cos^2a+sin^2a
Examples on Log rules: Example: Calculate (1/3)log 10 2. Solution: log b n√A = log b A 1/n = (1/n)log b A (1/3)log 10 2 = log 10 3 √2 = log 10 1.
The given figure consists of four small semicircles and two big semicircles. If the smaller semicircles are equal in radii and the bigger semicircles are also equal in radii, find
Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
A straight line AB on the side of a hill is inclined at 15.0° to the horizontal. The axis of a tunnel 486ft. long is inclined 28.6° below the horizontal lies in a vertical plane wi
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