An appositive is a noun or pronoun placed next to another noun or pronoun to identify or explain it. An appositive phrase is an appositive with modifiers. The underlined appositive phrase below gives additional information about Beowulf:
In his far-off home Beowulf, $\underline{\text{Higlac's}}$

$$\underline{\text{Follower and the strongest of the Geats}}$$

If an appositive is necessary to identify who or what is being spoken about, it is not set off with commas. If an appositive is not essential to the meaning of the sentence, it should be set off with commas.
Appositive phrases are a key element of epic style, in which naming and renaming things and people is an important poetic act.
In the given item, identify the appositive phrase and name what is being described.
"And we have come seeking / Your prince, Healfdane's son, protector / Of this people, only in friendship: instruct us, ... "

Janelle can walk $3\frac{3}{4}$ miles in $1\frac{1}{2}$ hours. At this rate, how many miles can Janelle walk in 4 hours?

A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?

Tell whether each statement is sometimes, always, or never true.

If the $y$-intercept of a linear function is positive and the slope is negative, then the $x$-intercept is positive.

Use the information. Underwater, pressure increases $4.3$ pounds per square inch (psi) for every $10$ feet you descend. This can be expressed by the equation $p=0.43 d+14.7$, where $p$ is the pressure in pounds per square inch and $d$ is the depth in feet. Divers cannot work at depths below about $400$ feet. Given this information, determine a reasonable domain and range for this situation.

Let

$$q ( \mathbf { x } ) = \mathbf { x } ^ { T } A \mathbf { x }$$

be a quadratic form,

$$A=A^T$$

. (a) Show that q(x)>0 for all

$$\mathbf { x } \neq \mathbf { 0 }$$

, if and only if A is positive definite (all eigenvalues are positive). In this case, q is called positive definite. (b) Show that new variables y can be found such that

$$q = \| \mathbf { y } \| ^ { 2 }$$

and y=Ux where U is upper triangular with positive diagonal entries.

A large uniform cylindrical steel rod of density ρ = 7.8 g/cm³ is 2.0 m long and has a diameter of 5.0 cm. The rod is fastened to a concrete floor with its long axis vertical. What is the normal stress in the rod at the cross-section located at (a) 1.0 m from its lower end? (b) 1.5 m from the lower end?

A circular rod with a diameter of $3 / 8$ in supports part of a storage shelf in a warehouse. As products are loaded and unloaded, the rod is subjected to a tensile load that varies from $1800$ to $150\ \mathrm{lb}$.

Calculating the Time of a Trip From a parking lot you want to walk to a house on the ocean. The house is located 1500 feet down a paved path that parallels the beach, which is 500 feet wide. Along the path, you can walk 300 feet per minute, but on the sand, on the beach, you can only walk 100 feet per minute.

b) Calculate the time $T$ if you walk in the sand directly toward the ocean for 500 feet and then turn left and walk along the beach for 1500 feet to the house.

Given the following data for bromine:

$$\begin{aligned} \operatorname{Br}_2(l) ; S^{\circ} & =152.2 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \operatorname{Br}_2(g) ; S^{\circ} & =245.4 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \quad \Delta H_{\mathrm{f}}^{\circ}=30.91 \mathrm{~kJ} / \mathrm{mol} \end{aligned}$$

Estimate the normal boiling point of bromine.

Find the equation of the line that is the perpendicular bisector of the line segment connecting $(-4,2)$ and $(2,10)$.

Find the equations of the lines normal to the indicated curves at the given points. Use a calculator to view the curve and normal line.

$y=8-x^3$ at $(-1,9)$

In the previous section, we defined a positive definite matrix as a square symmetric matrix $C$ such that $\mathbf{y}^T C \mathbf{y}>0$ for every nonzero vector $\mathbf{y}$ in $R^n$. Prove that any eigenvalue of a positive definite matrix is positive.

Find the surface area of rectangular prism, If l= 12 inch w = 7 inch and h = 3 inch.