Calculate.

$$\int_0^{\pi / 2} \int_0^{3 \sin \theta} r^2 d r d \theta$$

The nurse is reviewing the medication history of a patient who is taking hydroxychloroquine. However, the patient’s chart does not reveal a history of malaria or travel out of the country. The patient is most likely taking this medication for what
a. Plasmodium.
b. thyroid disorders.
c. roundworms.
d. rheumatoid arthritis.

What is the rationale for using drugs such as B2 agonists, acetylcholine antagonists, leukotriene inhibitors, corticosteroids, and mast cell stabilizers to manage obstructive pulmonary disorders?

Predict the number of vertices and faces on each closo-borane. a. $\mathrm{B}_{4} \mathrm{H}_{4}^{2-}$ b. $\mathrm{B}_{9} \mathrm{H}_{9}^{2-}$

Given matrices $A, B$, and $C$, multiply, if possible.

$$A=\left[\begin{array}{ll} 1 & 1 \\ 2 & 3 \end{array}\right] \quad B=\left[\begin{array}{rr} 3 & 2 \\ -1 & 1 \end{array}\right] \quad C=\left[\begin{array}{lll} 0 & 2 & 0 \\ 3 & 1 & 4 \end{array}\right]$$

CA

A sample of air with a mole ratio of $\mathrm{N}_2$ to $\mathrm{O}_2$ of $79: 21$ is heated to $2500 \mathrm{~K}$. When equilibrium is established in a closed container with air initially at $1.00 \mathrm{~atm}$, the mole percent of $\mathrm{NO}$ is found to be $1.8 \%$. Calculate $K_p$ for the reaction below, assuming pressures are expressed in atmospheres.

$$\mathrm{N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})$$

Calculate whether or not a precipitate will form in the following mixed solutions:

(a) $100 \mathrm{~mL}$ of $0.010~M\mathrm{~Na}_2 \mathrm{SO}_4$ and $100 \mathrm{~mL}$ of $0.001~M\mathrm{~Pb}\left(\mathrm{NO}_3\right)_2$
(b) $50.0 \mathrm{~mL}$ of $1.0 \times 10^{-4}~M\mathrm{~AgNO}_3$ and $100 . \mathrm{mL}$ of $1.0 \times 10^{-4}~M\mathrm{~NaCl}$
(c) $1.0 \mathrm{~g} \mathrm{~Ca}\left(\mathrm{NO}_3\right)_2$ in $150 \mathrm{~mL} \mathrm{~H}_2 \mathrm{O}$ and $250 \mathrm{~mL}$ of $0.01~M\mathrm{~NaOH}$\

$$K_{\text {sp }} \mathrm{PbSO}_4=1.3 \times 10^{-8}$$

$$K_{\mathrm{sp}} \mathrm{AgCl}=1.7 \times 10^{-10}$$

$$K_{\mathrm{sp}} \mathrm{Ca}(\mathrm{OH})_2=1.3 \times 10^{-6}$$

a) What is a recurrence relation?

b) Find a recurrence relation for the amount of money that will be in an account after $n$ years if 1,000,000 dollars is deposited in an account yielding 9%.

Graph each function. Based on the graph, state the domain and the range and find any intercepts.

$$f(x)=\left\{\begin{array}{ll}{\ln (-x)} & {\text { if } x \leq-1} \\ {-\ln (-x)} & {\text { if }-1<x<0}\end{array}\right.$$

(Continuation of the previous Exercise) Suppose $\mathbf{r}(t)=f(t) \mathbf{i}+$ $g(t) \mathbf{j}+h(t) \mathbf{k}$ and $f, g$, and $h$ have derivatives through order three. Use the results of the Exercise discussed before to show that

$$\frac{d}{d t}\left(\mathrm{r} \cdot \frac{d \mathbf{r}}{d t} \times \frac{d^2 \mathbf{r}}{d t^2}\right)=\mathrm{r} \cdot\left(\frac{d \mathbf{r}}{d t} \times \frac{d^3 \mathbf{r}}{d t^3}\right) .$$

(Hint: Differentiate on the left and look for vectors whose products are zero.)

Find the reciprocal of the number.

-1/5

Evaluate the given integral by changing to polar coordinates.

$\iint_R y d A$, where $R$ is the region in the first quadrant bounded by the circle $x^2+y^2=9$ and the lines $y=x$ and $y=0$

Many people believe that $\sqrt{x^2}=x$. We will investigate this claim graphically and numerically.

(a) Graph the two functions $x$ and $\sqrt{x^2}$ in the window $-5 \leq x \leq 5,-5 \leq y \leq 5$. Based on what you sec, do you believe that $\sqrt{x^2}=x^2$? What function does the graph of $\sqrt{x^2}$ remind you of?

(b) Complete the table below. Based on this table. do you believe that $\sqrt{x^2}=x^2$ ? What function does the table for $\sqrt{x^2}$ remind you of? Is this the same function you found in part (a)?

(c) Explain how you know that $\sqrt{x^2}$ is the same as the function $|x|$.

(d) Graph the function $\sqrt{x^2}-|x|$ in the window $-5 \leq$ $x \leq 5,-5 \leq y \leq 5$. Explain what you see.

Find the $x$-coordinate(s) of the point(s) on the graph of the function at which the tangent line has the indicated slope.

$$f(x)=\cot x ; \quad m_{\tan }=-2$$