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Assume that (X, d) is a metric space and let (x1, : : : , xn) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , xn) obtained by removing every xi from X is open in X. (Sketch a picture to get some intuition!)
A dealer sells a toy for Rs.24 and gains as much percent as the cost price of the toy. Find the cost price of the toy. Ans: Let the C.P be x ∴Gain = x % ⇒ Gain = x
Justin earned scores of 85, 92, and 95 on his science tests. What does he required to earn on his further science test to have an average (arithmetic mean) of 93%? To earn an a
Jon ran around a track that was one eighth of a mile long.He ran around the track twenty four times.How many miles did Jon run in all
If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans : AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2
#in a picnic the ratio of boys to girls is 3:4. when 6 boys joined the group the ratio became even. how many boys were there before? how many children were there before? how many b
Give an Equations with the variable on both sides ? Many equations that you encounter will have variables on both sides. Some of these equations will even contain grouping sy
01010011 01100101 01101101 01110000 01100101 01110010 00100000 01000110 01101001 00100001
Fermat's Theorem : If f ( x ) contain a relative extrema at x = c & f ′ (c ) exists then x = c is a critical point of f ( x ) . Actually, it will be a critical point such that f
find middle term [2a-a2/4]9
simplex methord
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