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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
Graph ( x - 2) 2 /9+4(y + 2) 2 = 1 Solution It is an ellipse. The standard form of the ellipse is ( x - h
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A circular pool is filling along with water. Supposing the water level will be 4 ft deep and the diameter is 20 ft, what is the volume of the water required to fill the pool? (π =
Two circles touch internally at a point P and from a point T on the common tangent at P, tangent segments TQ and TR are drawn to the two circles. Prove that TQ = TR. Given:
get the viscosity of particle to apply the stoke''s law
We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a
We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2
how do you simplify ratios
two sides of an equilateral triangle have lengths 3x-1 and 3x-1. Which of 27-x or 2x-4 could be the length of the third side?
Find the middle term of the AP 1, 8, 15....505. A ns: Middle terms a + (n-1)d = 505 a + (n-1)7 = 505 n - 1 = 504/7 n = 73 ∴ 37th term is middle term a 37
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