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1- For n belongs to N (set of natural numbers) let B(n) denote the number of digits used in the binary representation of n. For exampleB(1) = 1;B(2) = 2;B(3) = 2;B(4) = 3:
Find a closed formula for B(n) for an arbitrary n belongs to N.
2: Prove that if gcd(a, b) = d then a/d and b/d are relatively prime.
3- Find the smallest prime factor of (p1)(p2)...(pk) +1, where p1, p2, ... pk are the kth smallest primes for all positive integers k not exceeding 50.
Suppose a culture of bacteria starts with 5000 bacteria. After one hour, the count is 6000. Find an exponential equation that models the number of bacteria in hours. Keep at least 4 decimal places in your formula for rounded values. Find the doubling..
Tomorrow is going to be a hot one. Right now the temperature is 87 degrees and it will fluctuate at least 11 degrees by 3pm. What is the range of possible temperatures it could be at 3 pm.
Problem based on Stone-Weierstrass Theorem. Show that any continuous function on J x J ∈ R2 to R can be uniformly approximated by functions of the form f1(x)g1(y) + ... + fn(x)gn(y) where fi, gi, ∈ A.
An over night express company must include 5 cities on its route. How many different routes are possible, assuming that it does not matter in which order the cities are included in the routing?
What are the differences among expressions, equations, and functions? Provide examples of each. If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept?
Make a cost function for the problem
Linear equation on three variables
Why is it important to follow the order of operations? What are some possible outcomes when the order of operations is ignored?
a clown weighs 60 lb more than a trapeze artist. the trapeze artist weighs two-thirds as much as the clown. how much
Who wins the race? How far is Bob past the finish line when his car stops? How far is Sam past the finish line when his car stops?
Problems on distance.
What are two symbolic techniques used to solve linear equations? Which do you feel is better?
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