For positive constants a and b, the force between two atoms in a molecule is given f(r) = −a r2 + b r3 , where r > 0 is the distance between the atoms. note: a and b are upper case letters. (a) find f '(r) = (b) find the critical point for f(r). r = (c) find f ''(r) = (d) find the value of r so that f ''(r) = 0.

Kyle, a receptionist for a building supply company, recently won an award for saving his company money on their phone system. after being presented with kyle's research, the company changed the way in which it made long-distance phone calls and cut their expenses in this area by 75 percent. the new system the kyle's company most likely adopted was wired communications switching stations voip hdtv

Develop a function to create a document in the mongodb database “city” in the collection “inspections.” be sure it can handle error conditions gracefully. a. input -> argument to function will be set of key/value pairs in the data type acceptable to the mongodb driver insert api call b. return -> true if successful insert else false (require a screenshot)

Write a program that uses a random number generator to generate a two digit positive integer and allows the user to perform one or more of the following operations: a. double the number. b. reverse the digits of the number. c. raise the number to the power of 2, 3, or 4. d. sum the digits of the number. e. if the number is a two-digit number, then raise the first digit to the power of the second digit. f. if the number is a three-digit number and the last digit is less than or equal to 4, then raise the first two digits to the power of the last digit. after performing an operation if the number is less than 10, add 10 to the number. also, after each operation determine if the number is prime. each successive operation should be performed on the number generated by the last operation. your program should not contain any global variables and each of these operations must be implemented by a separate function. also, your program should be menu driven. 7. (fraction calculator) write a program that