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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.
An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss
Average Function Value The average value of a function f(x) over the interval [a,b] is specified by, f avg = (1/b-a) a ∫ b f(x) dx Proof We know that the average
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
Consider the temperature distribution in a 1D flat plate, insulated at x = L and exposed to convective heat transfer at x = 0. On the axes below, sketch what the distribution looks
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Raul's bedroom is 4 yards long. How many inches long is the bedroom? There are 36 inches within a yard; 4 × 36 = 144 inches. There are 144 inches in 4 yards.
Find out the least number of cables required to connect 100 computers to 20 printers to assurance that 20 computers can directly access 20 different printers. Justify your answer.
MINIMAX regret method Minimax method assumes that the decision maker will experience 'regret' after he has made the decision and the events have happened. The decision maker ch
If ABC is an obtuse angled triangle, obtuse angled at B and if AD⊥CB Prove that AC 2 =AB 2 + BC 2 +2BCxBD Ans: AC 2 = AD 2 + CD 2 = AD 2 + (BC + BD) 2 = A
we know that log1 to any base =0 take antilog threfore a 0 =1
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