1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of identical atoms; (a) in the Debye approximation;

Create a C++ program for managing a grocery store's Inventory system. The Inventory information is stored in a text file named "grocery inventory.txt." Each line in the file represents a grocery item with the following format: "SKU, Name, Category, Quantity Price" The program should allow the user to add new items, update the quantity of existing Items, and display the total value of the inventory. Ensure that the program checks for the existence of "grocery inventory.txt" and handles cases where the file is empty. Utilize functions to organize your code effectively, with comments explaining each function's purpose. You can use data structures like arrays or structs to store and manipulate inventory data. The program should output the updated inventory information to a file named "updated_grocery_Inventory.txt." Ex: grocery Inventory.txt: 101, Apples, Fruits, 50, 0.75 102, Bread, Bakery, 20, 2.50 103, Milk, Dairy, 30, 3.99 (updated grocery inventory.txt after adding 100 packs of Eggs…

For answer to part B, when I apply the equation for displacement; x = a sin(wt) and therefore get x = 0.2 sin(12.56 x 0.3) ---> = 0.2 x 0.06571 ----> = 0.013 for x which is not the correct answer ( x = 0.117 m ) Where did I go wrong here? The values were all applied in the calculator and the result was what it gave me. Am I missing something? Please explain

Study Area Student Workbook Document Sharing User Settings An electron moves along the z-axis with v₂ = 2.6 × 107 m/s. As it passes the origin, what are the strength and direction of the magnetic field at the following (x, y, z) positions? Part A (1.0 cm, 0 cm, 0 cm) Express your answers in teslas separated by commas. ► View Available Hint(s) LIVE ΑΣΦ B₂, By, B₂ = Submit Part B (0 cm, 0 cm, 2.0 cm) Express your answers in teslas separated by commas. ► View Available Hint(s) B₂, By, B₂ = Submit IVE ΑΣΦ ? ? T T + 8

Let X (capital x) = (m1x1 + m2x2)/(m1 + m2).  Calculate d2X/dt2, and simplify your expression as much as possible.

I need help with number 3