Find the minimum and maximum values of the function subject to the given constraint.

$$f ( x , y ) = x ^ { 2 } + y ^ { 2 } , \quad x ^ { 4 } + y ^ { 4 } = 1$$

Using z-transform methods, solve the following difference equations:

$$\begin{array}{l}{\text { (a) } y_{k+2}-2 y_{k+1}+y_{k}=0 \text { subject to } y_{0}=0, y_{1}=1} \\ {\text { (b) } y_{n+2}-8 y_{n+1}-9 y_{n}=0 \text { subject to } y_{0}=2, y_{1}=1} \\ {\text { (c) } y_{k+2}+4 y_{k}=0 \text { subject to } y_{0}=0, y_{1}=1} \\ {\text { (d) } 2 y_{k+2}-5 y_{k+1}-3 y_{k}=0 \text { subject to } y_{0}=3, y_{1}=2}\end{array}$$

Draw two lines under the verb in parentheses that agrees with the subject.

The highlight of the celebration (remains, remain) the fireworks.

Consider the problem of maximizing the function $f(x, y) = 2x + 3y$ subject to the constraint $\sqrt{x} + \sqrt{y} = 5$. What is the significance of $f(9, 4)$?

Underline the subject and the correct word or word group in parentheses in each of the following sentences.

(Who's, Who are) the student assistant today?

For the following sentence, underline the correct form of the verb in parentheses. Then, underline the subject of the sentence twice.

Here (is, are) the samples you requested.

Find the solution $y=y(x)$ of

$$x \frac{d y}{d x}+y-\frac{y^2}{x^{3 / 2}}=0,$$

subject to $y(1)=1$.

Draw two lines under the verb in parentheses that agrees with the subject.

Three games (remains, remain) a complete set.

A 75.0-kg painter climbs a ladder that is 2.75 m long and leans against a vertical wall. The ladder makes a $30.0 ^ { \circ }$ angle with the wall. (a) How much work does gravity do on the painter? (b) Does the answer to part (a) depend on whether the painter climbs at constant speed or accelerates up the ladder?

Consider the general quadratic function which is given as $f(x)=ax^2+bx+c$, with $a \neq 0$. Find the coordinates of the vertex in terms of a, b, and c.

In each of the following sentences, underline the verb or helping verb in parentheses that agrees with its subject.

They (is, are) trying to save these ballads.

Write $U$ beside each sentence that has you as its understood subject. Write $I$ beside each sentence that is in inverted order. If the sentence is in inverted order, draw one line under the subject and two lines under each simple predicate.

Over the outfield wall sailed the ball.

Underline the subject and the correct word or word group in parentheses in each of the following sentences.

Where (is, are) the other assignments for the class?

If you were the subject of the flyer given, how would you feel? How might you respond to it ?