Define a piecewise function of 𝑥 so that the value of the function is 0, if 𝑥<−(𝑟1+ 𝑟2+𝑟3) or 𝑥>𝑟1+ 𝑟2+𝑟3, and it is equal to the area of confined region if −(𝑟1+ 𝑟2+𝑟3)<𝑥<𝑟1+ 𝑟2+𝑟3. 

a) Given real values 𝑟1,𝑟2,𝑟3>0, consider the curve of the positive part of the circle with radius 𝑟1+ 𝑟2+𝑟3 and center at the origin and three semi-circles below with radii 𝑟1,𝑟2,𝑟3 so that they are arranged from left to right like the following graph. Define proper functions and plot this graph in Maple for 𝑟1=10,𝑟2=2,𝑟3=8. 

The question:

Write a Maple code to find the sum of digits of the number 12^6^5, and then it returns the message ‘This number is divisible by 3’ if the sum is a multiple of 3. Otherwise, it returns either ‘This number is a prime number’ or ‘This number is neither prime nor divisible by 3’.  

I have already found the divisors and placed them on a list, now I want the loop code stating whether there is 3 or not in the list.

For given positive integers 𝑎 and 𝑏, there exist positive integers 𝑟 and 𝑠 (the so-called Bezout’s coefficients) so that 𝑔𝑐𝑑(𝑎,𝑏)=𝑟 𝑎+𝑠 𝑏. Using Euclidean algorithm, one can find these coefficients by using a forward and a backward substitution. Surf the web, let say this one https://brilliant.org/wiki/bezouts-identity/, or use any Discreet Mathematics textbook to find out how these coefficient can be computed using Euclidean algorithm. Now, write a code in Maple to compute Bezout’s coefficients for the numbers 18344 and 65208.