Identify the constant of variation. Then write the equation of variation.

w varies inversely with z; w = -8 when z = 3.

The value of the equilibrium constant for the reaction below is 40.0 at a specified temperature. What would be the value of that constant for the reverse reaction under the same conditions?

$$\mathrm { H } _ { 2 } ( g ) + \mathrm { I } _ { 2 } ( g ) \Longleftrightarrow 2 \mathrm { HI } ( g )$$

For this exercise, how does the constant difference in the new column relate to the patterns you observed?

In which one of the following situations can the equations of kinematics not be used? (a) When the velocity changes from moment to moment, (b) when the velocity remains constant, (c) when the acceleration changes from moment to moment, (d) when the acceleration remains constant.

Look at the following statement, which declares an enumerated data type:

 enum Flower { ROSE, DAISY, PETUNIA }

a) What is the name of the data type?

b) What is the ordinal value for the enum constant ROSE? For DAISY? For PETUNIA?

c) What is the fully qualifed name of the enum constant ROSE? Of DAISY? Of PETUNIA?

d) Write a statement that declares a variable of this enumerated data type. The variable should be named flora. Initialize the variable with the PETUNIA constant.

Explain why an applied force is necessary to keep the bar in Figure moving with a constant speed.

Use mathematical induction to prove statement.

For constant positive integers $m$ and $n$, show that $\left(x^m\right)^n=x^{m n}$.

For a temperature increase of $\Delta T_1$, a certain amount of an ideal gas requires $30 \mathrm{~J}$ when heated at constant volume and $50 \mathrm{~J}$ when heated at constant pressure. How much work is done by the gas in the second situation?

Match the equations with the graphs labeled I–VI and give reasons for your answers. Determine which families of grid curves have u constant and which have v constant.

$$x = cos^3u cos^3v, y = sin^3u cos^3v, z = sin^3v$$

Match the equations with the graphs labeled I–VI and give reasons for your answers. Determine which families of grid curves have u constant and which have v constant.

$$r(u, v) = sin vi + cos u sin 2v j + sin u sin 2vk$$

Prove $\frac{d}{d x} \ln |a x|=\frac{d}{d x} \ln |x|$ for any constant a.

If k is a positive constant, show that $x^2 e^{-k x}$ approaches 0 as $x \rightarrow \infty$.

In the position shown the thin rod moves at a constant speed $u=3\ \mathrm{in} . / \mathrm{s}$ out of the tube $B C$. At the same time tube $B C$ rotates at the constant rate $\omega_2=1.5\ \mathrm{rad} / \mathrm{s}$ with respect to arm $C D$. Knowing that the entire assembly rotates about the $X$ axis at the constant rate $\omega_1=1.2\ \mathrm{rad} / \mathrm{s}$, find the velocity and acceleration of end $A$ of the rod.

Using the Maclaurin series, show that if f(z) is even, its integral (with a suitable constant of integration) is odd.