Write a recursive program to generate random sentences from a given BNF grammar. A BNF grammar is a recursively defined file that defines rules for creating sentences from tokens of text. Rules can be recursively self-similar. The following grammar can generate sentences such as “Fred honored the green wonderful child”:

<s>::=<np> <vp>
<np>::=<dp> <adjp> <n>|<pn>
<dp>::=the|a
<adjp>::=<adj>|<adj> <adjp>
<adj>::=big|fat|green|wonderful|faulty|subliminal|pretent
ious
<n>::=dog|cat|man|university|father|mother|child|televisi
on
<pn>::=John|Jane|Sally|Spot|Fred|Elmo
<vp>::=<tv> <np>|<iv>
<tv>::=hit|honored|kissed|helped
<iv>::=died|collapsed|laughed|wept

Solve the initial-value problem

$$y''+5y'+4y=16x+20e^x,y(0)=0,y'(0)=3$$

Given the matrices $A$ and $\mathbf{B},$ find the product $\mathbf{A B}$. Also, find the product $\mathbf{B} \mathbf{A}$ in each case in which it is defined.

$$\mathbf{A}=\left( \begin{array}{rr}{3} & {2} \\ {-1} & {4} \\ {5} & {-2}\end{array}\right), \quad \mathbf{B}=\left( \begin{array}{rrr}{3} & {0} & {2} \\ {-1} & {2} & {-3}\end{array}\right)$$

Describe an O(n)-time algorithm that, given a set S of n distinct numbers and a positive integer k ≤ n, determines the k numbers in S that are closest to the median of S.

Given the matrices $A$ and $\mathbf{B},$ find the product $\mathbf{A B}$. Also, find the product $\mathbf{B} \mathbf{A}$ in each case in which it is defined.

$$\mathbf{A}=\left( \begin{array}{rr}{5} & {-2} \\ {4} & {3}\end{array}\right), \quad \mathbf{B}=\left( \begin{array}{rr}{-1} & {8} \\ {2} & {-5}\end{array}\right)$$

Draw a number line like the one in the given figure. Place equally spaced tick marks on your number line so that you can plot $\displaystyle \frac{1}{3}$ on a tick mark without first plotting $1$. Then plot $\displaystyle \frac{1}{3}$. Explain your reasoning.

Find 3u - 2v.

u = (-1, 2, 1), v = (0, 1, 1)

Write a program that reads in two floating-point numbers and tests whether they are the same up to two decimal places. Here are two sample runs. Enter a floating-point number: 2.0 Enter a floating-point number: 1.99998 They are the same up to two decimal places. Enter a floating-point number: 2.0 Enter a floating-point number: 1.98999 They are different.

(a)Why does the speaker compare dreams to pocket handkerchiefs? (b)Do you think this is an effective comparison? Why or why not?

This essay may include references that are unfamiliar to you. Choose at least one unfamiliar detail, and briefly research it. Then, explain how the information you learned from research sheds light on an aspect of the essay.

(a) In what state is the washwoman when she arrives at the author's home? (b) What has she endured to get there, and how is that situation more difficult when she leaves? Explain.

What is a client when discussing home networks?

Generalize methods mazeTraversal and mazeGenerator of earlier exercises to process mazes of any width and height.

Use the Distributive Property to multiply. Explain why

$$5 x + 15 = 5 ( x + 3 )$$