Problem 3. Consider finite strings over the alphabet Σ = {a, b, c, d}. The power operation represents string repetition, for example a 3 b 4 c denotes the string aaac. Define a contextfree grammar G generating the language L(G) = {w|(∃i, j, k)w = a i b (i+j+k) c jd k}, the set of words where the number of b’s is the same as the number of all other letters together and the letters are ordered alphabetically. For example, the words ab, aaad, abbbcd belong to the language, words abba, aac, abc do not belong to the language. Justify your answers

Assume that to_the_power_of is a function that expects two int parameters and returns the value of the first parameter raised to the power of the second parameter. write a statement that calls to_the_power_of to compute the value of cube_side raised to the power of 3 and that associates this value with cube_volume.

Write a program that begins by reading in a series of positive integers on a single line of input and then computes and prints the product of those integers. integers are accepted and multiplied until the user enters an integer less than 1. this final number is not part of the product. then, the program prints the product. if the first entered number is negative or 0, the program must print “bad input.” and terminate immediately. next, the program determines and prints the prime factorization of the product, listing the factors in increasing order. if a prime number is not a factor of the product, then it

Write a function so that the main0 code below can be replaced by the simpler code that calls function mphandminutes tomiles0. original main0 int main) l double milesperhour-70.0; double minutestraveled = 100.0; double hourstraveled; double milestraveled; hourstraveled = minutestraveled / 60.0; milestraveled = hourstraveled * milesperhour; cout < "miles" 2 using namespace std; 4 /* your solution goes here/ 6 int maino 1 test passed 7 double milesperhour 70.0 all tests passed 8 double minutestraveled 100.0; 10 cout < < "miles: " < < mphandminutestomiles(milesper-hour, minutestraveled) < < endl; 12 return 0; 13