Underline each personal pronoun and its antecedent. I am interested in seeing China, where my parents were born.

Find the area of the surface generated by revolving the curve about the indicated axis. y = √2x-x², 0.5 ≤ x ≤ 1.5; x-axis

A bowl contains many red, orange, and green jelly beans, in equal numbers. You are to make a line of 3 jelly beans by randomly taking 3 beans from the bowl. Determine the probability of $(\text{b})$ all 3 beans red.

The graph of the Julia set in the previous figure appears to be symmetric with respect to both the $x$-axis and $y$-axis. Complete the below exercise to show that this is true.

Conclude that the graph of the Julia set must be symmetric with respect to the $x$-axis.

Find the sum of the convergent series \

$$\sum_{n=0}^{\infty}\left(-\dfrac{1}{2}\right)^n$$

Calcium chloride is a salt used in a number of food and medicinal applications and in brine for refrigeration systems. Its most distinctive property is its affinity for water: in its anhydrous form it efficiently absorbs water vapor from gases, and from aqueous liquid solutions it can form (at different conditions) calcium chloride hydrate $\left(\mathrm{CaCl}_{2} \cdot \mathrm{H}_{2} \mathrm{O}\right)$, dihydrate $\left(\mathrm{CaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right)$, tetrahydrate $\left(\mathrm{CaCl}_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}\right)$, and hexahydrate $\left(\mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\right)$. You have been given the task of determining the standard heat of the reaction in which calcium chloride hexahydrate is formed from anhydrous calcium chloride: $\mathrm{CaCl}_{2}(\mathrm{s})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}): \quad \Delta H_{\mathrm{r}}^{\circ}(\mathrm{kJ})=?$ By definition, the desired quantity is the heat of hydration of calcium chloride hexahydrate. You cannot carry out the hydration reaction directly, so you resort to an indirect method. You first dissolve 1.00 mol of anhydrous $\mathrm{CaCl}_{2}$ in 10.0 mol of water in a calorimeter and determine that 64.85 kJ of heat must be transferred away from the calorimeter to keep the solution temperature at $25^{\circ} \mathrm{C}$. You next dissolve 1.00 mol of the hexahydrate salt in 4.00 mol of water and find that 32.1 kJ of heat must be transferred to the calorimeter to keep the temperature at $25^{\circ} \mathrm{C}$. a) Use the results to calculate the desired heat of reaction. (Suggestion: Begin by writing out the stoichiometric equations for the two dissolution processes.) b) Calculate the standard heat of reaction in kJ for $\mathrm{Ca}(\mathrm{s}), \mathrm{Cl}_{2}(\mathrm{g}) \text { and } \mathrm{H}_{2} \mathrm{O}$ reacting to form $\mathrm{CaCl}_{2}$ (aq, r = 10). c) Speculate about why the standard heat of reaction in forming calcium chloride hexahydrate cannot be measured directly by reacting the anhydrous salt with water in a calorimeter.

True or False

All squares are rectangles.

Show that $\tan x>x$ for all $x\in (0,\pi/2)$.

The solubility of two slightly soluble salts of $M^{2+}, MA$ and $MZ_2,$ is the same, $4 \times 10 ^ { - 4 } \mathrm { mol } / \mathrm { L }$ If you added an equal volume of a solution saturated in MA to one saturated in $MZ_2,$ what would be the equili brium concentration of the cation, $M^{2+}?$

Find the eigenfunction expansion of the given function in the eigenfunctions of the Sturm-Liouville problem. In each case, determine what this expansion converges to and graph the Nth partial sum of the expansion and the function on the same set of axes. Do the graph for L = 1. $f(x)=1-x$ for $0 \leq x \leq L \\ y^{\prime \prime}+\lambda y=0 ; y(0)=y(L)=0 ; N=40$

All of the following are examples of remote sensing except

(a) Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.

(b) Find the x- and y-intercepts of the graph of the equation.

y = 9 - (x squared)

Determine whether the series is convergent or divergent.

$$\sum_{n=1}^{\infty}\frac{\sin n}{n^2+1}$$

Prove that $|\sin x-\sin y|<|x-y|$ for all numbers $x \neq y$.