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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.
use an expression to write an expression with five 3s that has a value of 0
The cost of a student ticket is $1 more than half of an adult ticket. Six adults and four student tickets cost $28. What is the cost of one adult ticket? Let x = the cost of a
Three mixtures were prepared with very narrow molar mass distribution polyisoprenesamples with molar masses of 8000, 25,000, and 100,000 as indicated below. (a) Equal numbers of
1. Construct a grammar G such that L(G) = L(M) where M is the PDA in the previous question. Then show that the word aaaabb is generated by G. 2. Prove, using the Pumping Lemma f
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
Evaluate the given limit. Solution: In this question none of the earlier examples can help us. There's no factoring or simplifying to accomplish. We can't rationalize &
ogive for greater than &less than curves
If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y. (Ans:5, -2 (Not unique) Ans: Using Euclid's algorithm, the HCF (30, 72) 72 = 30 × 2 + 12
principal=2000 rate=5% time=2 years find compound interest
Multiplicative Rule - Rules of Probability It is used when there is a string of independent events for that individual probability is known and it is essential to know the ove
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