Find the derivative of each function at the number indicated using a graphing utility. $f(x)=x \sec x$ at $\frac{\pi}{6}$

What does the term passive reference configuration imply? When do we have this configuration if we are using double subscript notation for an element having terminals a and b?

To compare two weight reduction diets A and B, 60 dieters were randomly selected. One group of 30 dieters was placed on diet A and the other 30 on diet B, and their weight losses were recorded over a 30-day period. The means and standard deviations of the weight-loss measurements for the two groups are shown in the table. Find a 95% confidence interval for the difference in mean weight loss for the two diets. Interpret your confidence interval.

Diet A: $\overline{x}_A$=21.3 and $s_A$=2.6 Diet B: $\overline{x}_B$=13.4 and $s_B$=1.9

A card is picked at random from a standard deck of 52 cards. Find each probability. P(king of clubs)

A local deli sells 4-inch sub sandwiches for $2.95. It has decided to sell a "family sub" that is 50 inches long. How much should it charge? What is the unit rate in dollars per foot? Show all work.

(a) What do you think the speaker might have said to Odysseus if he could have advised him during his journey? (b) Take a Position: Do you agree with this advice? Explain.

Simplify each expression.

$$\left( 3 t ^ { 2 } \right) ^ { 3 } \left( 2 t ^ { 0 } \right) ^ { - 3 }$$

Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. $\sqrt{\frac{n}{m^{3}}}$

What is chromatin?

The formulas for permutations and combinations must always evaluate to a natural number. Explain why.

The equations of motion of three equal masses connected by springs of equal stiffness are

$$\begin{array}{l}{\ddot{x}=-2 x+y} \\ {\ddot{y}=x-2 y+z} \\ {\ddot{z}=y-2 z}\end{array}$$

Show that for normal modes of oscillation x = X cosωt, y = Y cosωt, z = Z cosωt to exist then the condition on $\lambda=\omega^{2}$ is

$$\left| \begin{array}{ccc}{\lambda-2} & {1} & {0} \\ {1} & {\lambda-2} & {1} \\ {0} & {1} & {\lambda-2}\end{array}\right|=0$$

Find the three values of λ that satisfy this condition, and find the ratios X : Y : Z in each case.

Mentally convert each base ten numeral to a numeral in the given base. 9 to base five

You are sitting on a stationary train next to an open window, and the pressure of the air in your inner ear is equal to the pressure outside your ear. The train starts up, and as it accelerates to a high speed, your ears "pop." Your eardrums respond to a decrease or increase in the air pressure by "popping" outward or inward, respectively. Assume that the air pressure in your inner ear has not had time to change, so it remains the same as when the train was stationary. Do your eardrums "pop" (a) outward or (b) inward?

Let A be the matrix of a function f from X to Y (relative to some orderings of X and Y). What conditions must A satisfy for f to be onto Y?