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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.
All things considered, in a sense of ethnicity (a sense of identification with and loyalty to one's group) good or bad? is it harmful or helpful? What would be lost if Americans lo
Solve the subsequent differential equation and find out the interval of validity for the solution. Let's start things off along with a fairly simple illustration so we can notic
how do you add 1,ooo and 100?
Martha has $20 to spend and would like to buy as several calculators as possible along with the money. The calculators that she needs to buy are $4.50 each. How much money will she
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ABCD is a rectangle. Δ ADE and Δ ABF are two triangles such that ∠E=∠F as shown in the figure. Prove that AD x AF=AE x AB. Ans: Consider Δ ADE and Δ ABF ∠D = ∠B
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Ionic solids, which have anionic vacancies because of metal excess defect develop colour. Illustrate with the help of a suitable example.
prove same homotopy type is an equivalent relation
Here we have considered the following points. 1. Mathematics is omnipresent, powerful and beautiful. 2. Mathematics is useful in all spheres of life. 3. Mathematics can al
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