Find the maximum and minimum values of

$$x ^ { 2 } + y ^ { 2 }$$

subject to the constraint

$$x ^ { 2 } - 2 x + y ^ { 2 } - 4 y = 0.$$

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.

There (lies, lie) Julia's prize rosebush.

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

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

Find the maximum and minimum values of the quadratic form on the unit circle in $\mathbb{R}^2$, or unit sphere in $\mathbb{R}^n$, and find all points on the unit circle or sphere where the extrema are assumed.

$$x y, n=2$$

Find the minimum value of

$$f(x, y)=x^2-2 x y+2 y^2+20$$

subject to the constraint $2 x-6 y=15$.

Use the clue to complete the crossword puzzle. The answer consists of the vocabulary word.

Across 5. sticks to the subject

In the following sentence, circle the subject of the underlined verb. Then, if the verb does not agree in number with its subject, write the correct form of the verb above the incorrect form. If the verb is already correct, write C above it.

Has Julie told everyone what time the movie $\underline{\text{begins}}$?

Underline the form of the verb that agrees with the subject.
Anyone who (excavates, excavate) a dinosaur has many stories to tell.

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.

In each of the following sentences, underline the parts of the compound subject. Alfalfa or soybeans will grow in those fields next year.

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.

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?

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

Here (begins, begin) a fascinating story.