When 2.00 mo! of $SO_2Cl_2$ is placed in a 2.00-L fla sk at 303 K, 56% of the $SO_2Cl_2$ decomposes to $SO_2$ and $Cl_2:$ $\mathrm { SO } _ { 2 } \mathrm { Cl } _ { 2 } ( g ) \rightleftharpoons \mathrm { SO } _ { 2 } ( g ) + \mathrm { Cl } _ { 2 } ( g )$ According to Le Chatelier's principle, would the percent of $SO_2Cl_2$ that decomposes increase, decrease or stay the same if the mixture were transferred to a 15.00-L vessel?

Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum.

$$\frac { 1 } { 3 ^ { 6 } } + \frac { 1 } { 3 ^ { 8 } } + \frac { 1 } { 3 ^ { 10 } } + \frac { 1 } { 3 ^ { 12 } } + \cdots$$

Graph the inequality.

$$y < x^2 – 6x + 10.$$

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric, find the common ratio and the sum of the first n terms. $\left\{-\frac{1}{2} \cdot 4^{n}\right\}$

Write the first five terms of each sequence. Assume that represents the common difference of an arithmetic sequence and r represents the common ratio of a geometric sequence.

$$a _ { 1 } = 5 , r = - 3$$

A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine whether the mass passes through the equilibrium position if (a) the mass is initially released from rest from a point 1 meter below the equilibrium position, and then (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s. In each case find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?

Factor the trinomial.

$$4x^2 - 81$$

La familia Quinones esta de vacaciones. Subraya la palabra apropiada para decir que necesita. (Underline the correct word.)

Solve the equation. Write all proposed solutions. Cross out those that are extraneous.

$$\sqrt { 3 x } + 5 = 2$$

Find sin 2x, cos 2x, and tan 2x from the given information.

$$\cos x = \frac { 4 } { 5 } , \quad \csc x < 0$$

The systems of equations are nonlinear. Find substitutions (changes of variables) that convert each system into a linear system and use this linear system to help solve the given system.

$$\begin{array} { l } { x ^ { 2 } + 2 y ^ { 2 } = 6 } \\ { x ^ { 2 } - y ^ { 2 } = 3 } \end{array}$$

Find the first partial derivatives of the following functions. h(w, x, y, z)=$\frac { w z } { x y }$

a. What are three harmful substances in tobacco smoke? b. How does each of the harmful substances directly affect the body? c. Why might nicotine-containing products, such as chewing gums or skin patches, help a person who is trying to quit smoking?

Given a vector v, show that its negative -v is uniquely determined by the property in axiom A5.