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1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies.
1. C(n) = 3C(n/2) + n
2. G(n) = G(n - 1) + 1/n
3. I(n) = I(n/2) + n/ lg(n)
2. Define a (p,q)-tree as a rooted tree where every internal node has between p and q (inclusive) children. Use the Master Theorem to give asymptotic bounds for the height of the tree. You can assume both p and q are constants with 2 ≤ p ≤ q.
3. (‡) Dominos
A 2 × 10 rectangle filled with ten dominos, and a 2 × 2 × 10 box filled with ten slabs.
1. A domino is a 2×1 or 1×2 rectangle. How many different ways are there to completely fill a 2 × n rectangle with n dominos?
2. A slab is a three-dimensional box with dimensions 1 × 2 × 2, 2 × 1 × 2, or 2 × 2 × 1. How many different ways are there to fill a 2 × 2 × n box with n slabs? Set up a recurrence relation and give reasonable exponential upper and lower bounds.
Do you subtract when you add integers.
det(adj A)for 1*1 matrix
A die is rolled and a coin is tossed. What is the probability that a 3 will be rolled and a tail tossed? Find the probability of each event separately, and then multiply the an
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Are the two angles of a rectangles congruent ? why ?
calculate
Standard interpretations to derivatives Example Assume that the amount of money in a bank account is specified by P (t ) = 500 + 10
how does it work?
dividing decimals
Determine the value of a $1800 investment after six years at 9.3% per year, simple interest
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