Determine whether each triangle should be solved by beginning with the Law of Sines or the Law of Cosines. Then solve the triangle.

$$\operatorname { In } \Delta H J K , h = 18 , j = 10 , \text { and } k = 23$$

Subtract. - 3 - (-4).

Complete the sentence using each term once. a. social stratification b. feminization of poverty c. social class d. social mobility e. bourgeoisie f. vertical mobility g. proletariat h. intergenerational mobility i. wealth j. horizontal mobility k. income l. open-class system m. prestige n. absolute poverty o. relative poverty p. caste system. The economic resources possessed by an individual or group is called _____.

Assume $f \in R(\alpha)$ on [a, b], where $\alpha$ is of bounded variation on [a, b]. Let $V(x)$ denote the total variation of a on [a, x] for each x in (a, b], and let $V(a) = 0$. Show that $\left|\int_{a}^{b} f d \alpha\right| \leq \int_{a}^{b}|f| d V \leq M V(b)$, where M is an upper bound for $|\boldsymbol{f}|$ on [a, b]. In particular, when $\alpha(x)=x$, he inequality becomes $\left|\int_{a}^{b} f(x) d x\right| \leq M(b-a)$.

Discuss in depth the differences between concentric, isometric, and eccentric contractions and provide examples of how each one is used in daily life.

From what kinds of interactions do intermolecular forces originate?

A ball is kicked on Earth from a location $\langle 9,0,-5\rangle \mathrm{m}$ (on the ground) with initial velocity $\langle- 10,13,-5\rangle \mathrm{m} / \mathrm{s}$. Neglecting air resistance: What is the maximum height reached by the ball?

What is the first person singular presente tense form of the verb 'poder'?

Find the coordinates of the point on the curve $y=5 x-2 x^{2}-3$ at which the gradient of the curve is 9.

Write these three sentences describing people you know. Use the verb ser and the indefinite articles un una unos unas.

Consider gas flow through a converging–diverging nozzle. Of the five following statements, select the one that is incorrect: (a) The fluid velocity at the throat can never exceed the speed of sound.(b) If the fluid velocity at the throat is below the speed of sound, the diversion section will act like a diffuser.(c) If the fluid enters the diverging section with a Mach number greater than one, the flow at the nozzle exit will be supersonic.(d) There will be no flow through the nozzle if the back pressure equals the stagnation pressure.(e) The fluid velocity decreases, the entropy increases, and stagnation enthalpy remains constant during flow through a normal shock.

Let

$$T _ { 1 } : V \rightarrow W \text { and } T _ { 2 } : V \rightarrow W$$

be linear transformations, and let c be a scalar. We define the sum

$$T _ { 1 } + T _ { 2 }$$

and the scalar product

$$c T _ { 1 }$$

by

$$\left( T _ { 1 } + T _ { 2 } \right) ( \mathbf { v } ) = T _ { 1 } ( \mathbf { v } ) + T _ { 2 } ( \mathbf { v } )$$

and

$$\left( c T _ { 1 } \right) ( \mathbf { v } ) = c T _ { 1 } ( \mathbf { v } ) \text { for all } \mathbf { v } \in V.$$

This problem consider the properties of these mappings. Let

$$T _ { 1 } : \mathbb { R } ^ { 2 } \rightarrow \mathbb { R } ^ { 2 } \text { and } T _ { 2 } : \mathbb { R } ^ { 2 } \rightarrow \mathbb { R } ^ { 2 }$$

be the linear transformations with matrices

$$A = \left[ \begin{array} { r r } { 3 } & { 1 } \\ { - 1 } & { 2 } \end{array} \right] , \quad B = \left[ \begin{array} { r r } { 2 } & { 5 } \\ { 3 } & { - 4 } \end{array} \right].$$

Find

$$T _ { 1 } + T _ { 2 } \text { and } c T _ { 1 }.$$

Two friends decide to have a race. On "go," Jess takes off on her jet ski, headed upstream against a 10-mph current. 60 sec later, Deb gives chase with her dune buggy on a dirt track parallel to the river. If the top speed of the jet ski is 35 mph on still water and the dune buggy can hit 45 mph, how long will it take Deb to pass Jess?

If you were given the task of reducing entitlement programs to limit deficit spending, which ones would you select to reduce or alter? Write a short essay that includes the reasons for your choices.