Use Green’s theorem to evaluate $\oint_{C} \mathbf{F} \cdot d R.$ All closed curves are oriented positively. $\mathbf{F}=8 x y^{2} \mathbf{j} ,$ and C is the circle of radius 4 about the origin.

Poets often use parallel structure-repeated use of the same grammatical form or pattern to make their writing memorable and effective. These lines from "Not Palaces" contain parallel prepositional phrases.
Rewrite given underscored item to make the sentence structure parallel.
I am not interested in building palaces or $\underline{\text{the creation}}$ of rare objects.

What minimum intensity must a laser beam have if it is to levitate a tiny black ( $100 \%$ absorbing) sphere of radius $r=0.5 \mu \mathrm{m}$ and mass $=1.6 \times 10^{-15} \mathrm{~kg}$ ? Comment on the feasibility of such levitation. If the radius of the sphere is doubled but its mass remains the same, will the minimum intensity be greater than, less than, or equal to the value found above? Explain.

Will an airplane's speed relative to the ground be lower than its speed relative to the air if it is travelling through a crosswind that is blowing at a $90^{\circ}$ angle to the direction it is pointing?

In this exercise, compute the derivative using derivative rules that have been introduced so far.

$$y=\left(x^4+5\right)^3$$

Find a simple closed curve C with counterclockwise orientation that maximizes the value of

$$\oint _ { C } \frac { 1 } { 3 } y ^ { 3 } d x + \left( x - \frac { 1 } { 3 } x ^ { 3 } \right) d y$$

and explain your reasoning.

What are the symptoms of dementia with behavioral disturbances?

Interpreting Categorical Data, you learned about relative risk. In the study of kinship versus foster care presented in the earlier exercise, of the 572 children in kinship care, 173 had behavioral problems. Of the 736 children in foster care, 391 had behavioral problems.

a. Compute and interpret the relative risk for this situation.

b. Computing a 95% confidence interval for relative risk can be complicated, so a calculator may be found on the given website, for example. First, compute the relative risk. Note that you must input the number with behavioral problems and the number without for each group (not the sample size $n$). Does the relative risk agree with the one you computed in Part a?

c. Interpret the confidence interval computed by the online calculator.

d. Compare the relative risk formula used by the online calculator with the representation that you used.

One war veteran was quadriplegic, and another was paraplegic. Explain the relative locations of their injuries.

The graph shows the population of a rare species of bird, where $t$ represents years since 1994 and $n(t)$ is measured in thousands.

(a) Find a function that models the bird population at time $t$ in the form $n(t)=n_0 e^{r t}$.

(b) What is the bird population expected to be in the year 2005?

Use Green’s Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C. F(x, y) = (3x² + y)i + 4xy²j C: boundary of the region lying between the graphs of y = √x, y = 0, and x = 9

In the sentence below, underline demonstrative, interrogative, and relative pronouns. Then, above each underlined pronoun, write D for demonstrative, I for interrogative, or R for relative.

“Those are footprints,” replied the great detective.

Use the first four rules of inference to derive the conclusions of the following symbolized arguments. $1. J \supset(K \supset L) \\ 2. L \vee J \\ 3. \sim L \ / \sim K$

Use rules of divisibility to determine whether each number is divisible by a. 2 b. 3 C. 4 d. 5 e. 6 f. 8 g. 9 h. 10 i. 12.

$$7245$$