A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for a round-trip fare of $20. The operator estimates that for each$1 increase in fare, 20 fewer people will take the trip. What fare will maximize the number of people taking the ferry?

Briefly describe how the && operator works.

A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) = 35x - 0.25x². Using this model, what is the maximum profit the tour operator can expect?

(a) Confirm that the kinetic energy operator, $- \left( \hbar ^ { 2 } / 2 m \right) \mathrm { d } ^ { 2 } / \mathrm { d } x ^ { 2 }$, is hermitian. (b) The operator corresponding to the angular momentum of a particle is $( \hbar / \mathrm { i } ) \mathrm { d } / \mathrm { d } \phi ,$ where $\phi$ is an angle. Is this operator hermitian?

Form the operator $\hat{A}^2$ if $\hat{A}=d^2 / d y^2+3 y(d / d y)-5$. Be sure to include an arbitrary function on which the operator acts.

The Boolean operator ⊕, called the XOR operator, is defined by 1 ⊕ 1 = 0, 1 ⊕ 0 = 1, 0 ⊕ 1 = 1, and 0 ⊕ 0 = 0. Show that x ⊕ y = y ⊕ x.

Discuss the concept of polymorphism/operator overloading.

Determine whether the statement is true or false, and justify your answer. If there is a nonzero vector in the kernel of the matrix operator

$$T_A: R^n→R^n$$

then this operator is not one-to-one.

Briefly describe how the | | operator works.

Using the fact that the radial momentum operator is given by $\hat{p}_r=-i \hbar \frac{1}{r} \frac{\partial}{\partial r} r$, calculate the commutator $\left[\hat{r}, \hat{p}_r\right]$ between the position operator, $\hat{r}$, and the radial momentum operator.

Briefly describe how the or operator works

Design the class linetype to implement a line so that the class lineType:

1. Overloads the stream insertion operator, $<<$, for easy output.
2. Overloads the stream extraction operator, $>>$, for easy intput. (The line $a x+b y=c$ is input as $(a, b, c)$.
3. Overloads the assignment operator to copy a line into another line.
4. Overloads the unary operator $+$, as a member function, so that it returns true if a line is vertical; false otherwise.
5. Overloads the unary operator -, as a member function, so that it returns true if a line is horizontal; false otherwise.
6. Overloads the operator $==$, as a member function, so that it returns true if two lines are equal; false otherwise.
7. Overloads the operator $| |$, as a member function, so that it returns true if two lines are parallel; false otherwise.
8. Overloads the operator $\& \&$, as a member function, so that it returns true if two lines are perpendicular; false otherwise. Write a program to test your class.

What is returned by the function that overloads the operator << for a class?

An operator may be _______ to work with a specific class.