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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
4 boys and 4 girls are to seated in arow i)no. of girls sit together ii)not all girls sit together iii)boys and girls are altenate to each other iv)if a particular boy and g
Differentiate the following functions. (a) f (t ) = 4 cos -1 (t ) -10 tan -1 (t ) (b) y = √z sin -1 ( z ) Solution (a) Not much to carry out with this one other
Evaluate algebraic word problems: A utility has three nuclear facilities which supply a total of 600 megawatts (Mw) of electricity to a particular area. The largest facility
in 2000,nearly 18% of cars in north America were sliver. what percent of the cars sold were not sliver?
mathematical induction theorem
long ago, people decided to divide the day into units called hours. they choose 24 as the number of hours in one day. why is 24 a more convenient choice than 23 or 25?
If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
using 5 rectangles what is the area under a curve using the function f(x)=3x+4 and boundries [0,2]
Rental car agency has 50 cars. Rental rate in winter is 60%. What is probability that in give winter month the rental rate is fewer than 35 cars rented? Use normal distribution to
how to sketch feasible set
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