Draw N = 100 random points uniformly distributed over D. For each point, run a local minimization of f using scipy. optimize. minimize with the following methods: CG, BFGS, Newton-CG, L-BFGS-B. For this task, you will have to write two other functions, one that returns the Jacobian matrix of f and one that returns the Hessian matrix of f . Store the answers in an array with shape N x 6, each row of which has the following data:

(x1, y1,x2, y2,v, c),

where (x1, y1) and (x2, y2) are respectively the starting and the final point of the optimization, while v is the final value of f . The final element of the row c is code of the used method, according to this correspondence: CG:1, BFGS:2, Newton-CG:3, L-BFGSB:4

must be submitted as a Jupyter notebook

What statement best describes operating systems? it’s possible for modern computers to function without operating systems. most operating systems are free or very inexpensive. operating systems are managed by the computer’s microprocessor (cpu). operating systems manage the computer’s random access memory (ram).

List a few alternative options and input and output over the standerd keyboard and monitor. explain their functioning in details.

Fill in the following program so that it will correctly calculate the price of the orange juice the user is buying based on the buy one get one sale.#include //main functionint main() { int cartons; float price, total; //prompt user for input information printf("what is the cost of one container of oj in dollars? \n"); scanf(" [ select ] ["%d", "%c", "%f", "%lf"] ", & price); printf("how many containers are you buying? \n"); scanf(" [ select ] ["%d", "%c", "%f", "%lf"] ", & cartons); if ( [ select ] ["cartons / 2", "cartons % 1", "cartons % 2", "cartons % price", "cartons / price", "cartons / total"] [ select ] ["=", "==", "! =", "< =", "> =", "< "] 0) total = [ select ] ["price * cartons", "cartons * price / 2 + price", "(cartons / 2) * price", "cartons / (2.0 * price)", "(cartons / 2.0) * price + price", "((cartons / 2) * price) + price"] ; else total = ((cartons / 2) * price) + price; printf("the total cost is $%.2f.\n", total); return 0; }