Homework: Math for Developers

Problem 1.	Some Primes
Find the 24th, 101st and 251st prime number.

Solution:
24th prime number is 89
101st  prime number is 547
251st prime number is 1597
-	Source for solution: http://www.wolframalpha.com/

Problem 2.	Some Fibonacci Primes
Check if the 24th, 101st and 251st prime numbers are part of the base Fibonacci number set. What is their position?
Solution:
24th prime number ( 89 ) is part of the base Fibonacci number set. Its position is: 11th
101st  prime number is not part of the base Fibonacci number set;
251th prime number ( 1597 ) is part of the base Fibonacci number set. Its position is: 17th
-	Source for solution: http://www.wolframalpha.com/

Problem 3.	Some Factorials
Find 100!, 171! and 250! Give all digits.
Solution:
100! =   93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

171! = 1241018070217667823424840524103103992616605577501693185388951803611996075221691752992751978120487585576464959501670387052809889858690710767331242032218484364310473577889968548278290754541561964852153468318044293239598173696899657235903947616152278558180061176365108428800000000000000000000000000000000000000000

250! =
3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676527240189264733218041186261006832925365133678939089569935713530175040513178760077247933065402339006164825552248819436572586057399222641254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000
-	Source for solution: http://www.wolframalpha.com/

Problem 4.	Calculate Hypotenuse
You are given three right angled triangles. Find the length of their hypotenuses.
1.	Catheti: 3 and 4
Solution:
Hypotenuses = √(32+42)= 5
2.	Catheti:  10 and 12
Solution:
Hypotenuses = √(102+122)= 15.6204993518
3.	Catheti 100 and 250
Solution:
Hypotenuses = √(1002+2502)= 269.258240357

Problem 5.	Numeral System Conversions
Convert 1234d to binary and hexadecimal numeral systems.
Solution:
1234d = 10011010010b=4D2hex

Convert 1100101b to decimal and hexadecimal numeral systems.
Solution:
1100101b=101d=65hex

Convert ABChex to decimal and binary numeral systems.
Solution:
ABChex=2748d=101010111100b

-	Source for solution: Windows 7 - Calculator

Problem 6.	Least Common Multiple
Find LCM(1234, 3456).
Solution:
LCM(1234, 3456) = 2 132 352

-	Source for solution: http://www.wolframalpha.com/