For the system of earlier problem, determine the displacement x of the mass as a function of time if the mass is released at time t = 0 from a position 2 in. to the left of the equilibrium position with an initial velocity of 7 in./sec to the right. Determine the amplitude C of the motion.

Write a class Bug that models a bug moving along a horizontal line. The bug moves either to the right or left. Initially, the bug moves to the right, but it can turn to change its direction. In each move, its position changes by one unit in the current direction. Provide a constructor def _ _ init _ _(self, initialPosition) and methods - def turn(self) - def move(self) - def getPosition(self) Sample usage: bugsy = Bug(10) bugsy.move() # Now the position is 11 bugsy.turn() bugsy.move() # Now the position is 10 Your driver program should construct a bug, make it move and turn a few times, and print the actual and expected positions.

Write a program that carries out the following tasks:

Open a file with the name hello.txt.

Store the message “Hello, World!” in the file.

Close the file.

Open the same file again.

Read the message into a string variable and print it.

Write a program that reads a file containing text. Read each line and send it to the output file, preceded by line numbers. If the input file is Mary had a little lamb Whose fleece was white as snow. And everywhere that Mary went, The lamb was sure to go! then the program produces the output file /* 1 / Mary had a little lamb / 2 / Whose fleece was white as snow. / 3 / And everywhere that Mary went, / 4 */ The lamb was sure to go! Prompt the user for the input and output file names.

A tank initially contains 100 gal of pure water. Starting at t = 0, a brine containing 4 lb of salt per gallon flows into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring and the well-stirred mixture flows out at the slower rate of 3 gal/min. (a) How much salt is in the tank at the end of 20 min? (b) When is there 50 lb of salt in the tank?

For the system determine the displacement $x$ of the mass as a function of time if the mass is released at time $t=0$ from a position 2 in. to the left of the equilibrium position with an initial velocity of $7 \mathrm{in} . / \mathrm{sec}$ to the right. Determine the amplitude $C$ of the motion.

What happens when you pass an ArrayList<String> to a method with an ArrayList parameter variable, and the method stores an object of type BankAccount into the array list? Try it out and explain.

Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt has been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 2 lb/gal, determine a differential equation for the amount $A(t)$ of salt in the tank at time $t$.

For the system of previous problem, determine the displacement x of the mass as a function of time if the mass is released from rest at time t = 0 from a position 2 in. to the right of the equilibrium position.

Suppose $z = f (x, y)$ has continuous partial derivatives. Let $x=e^{r} \cos \theta, \ y=e^{r} \sin \theta$. Show that then $\left(\frac{\partial z}{\partial x}\right)^{2}+\left(\frac{\partial z}{\partial y}\right)^{2}=e^{-2 r}\left[\left(\frac{\partial z}{\partial r}\right)^{2}+\left(\frac{\partial z}{\partial \theta}\right)^{2}\right]$

To define a vector in your program, you must #include the _______ header file.

Are there fixed costs in the long-run? Explain briefly

What does a point inside the production possibility frontier represent?

Find all critical points and then use the first-derivative test to determine local maxima and minima. Check your answer by graphing. $f(x)=\frac{x}{x^{2}+1}$