Actividades: 1) Hallar dominio, imagen, vértice, intersección con cada eje, eje de simetria, concavidad, intervalos de crecimientos y decrecimientos y luego graficar las siguientes funciones: \( \begin{array}{llll}\text { a) } y=(x-1)^{2}-1 & \text { b) } y=\frac{1}{2}(x+2)^{2}-2 & \text { c) } y=-(x+3)^{2}+\frac{1}{4} & \text { d) } y=2\left(x-\frac{1}{2}\right)^{2}\end{array} \)

Which term characterizes what Andrew Carnegie believed should be the philanthropic efforts of the wealthy? social Darwinism Gospel of Wealth socialism for the poor capitalism in action

In a laboratory setup, a block of ice of mass mi at an initial temperature of \( -15^{\circ} \mathrm{C} \) is needed to transform 0.5 kg of steam contained in a sealed glass container from \( 110^{\circ} \mathrm{C} \) into water at \( 15^{\circ} \mathrm{C} \). The specific heat capacity of ice, \( \underline{\text { water and }} \) steam are respectively \( \mathrm{Ci}=2090 \mathrm{~J} / \mathrm{kg}^{\circ} \mathrm{C}, \mathrm{Cw}=4186 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C} \) and \( \mathrm{Cs}=2010 \mathrm{~J} / \mathrm{kg}^{\circ} \mathrm{C} \), the steam and the glass container are in thermal equilibrium Fusion point of water (or melting point of ice) \( 0^{\circ} \mathrm{C} \) Vaporization point of water \( 100^{\circ} \mathrm{C} \) The latent heat of condensation steam Lc= \( 2.26 \times 10^{\wedge} 6 \mathrm{~J} / \mathrm{kg} \) Latent heat of Fusion of ice \( \mathrm{Lf}=3.36 \times 10^{\wedge} 5 \mathrm{~J} / \) kg The amount of heat Qg gained during the

Consider the following equilibrium system: \[ \mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \] A 10.00 L evacuated flask is filled with 0.4150 mol \( \mathrm{PCl}_{5}(\mathrm{~g}) \) at \( \mathbf{2 9 7 . 4} \mathrm{K} \). The temperature is then raised to 501.7 K , where the decomposition of \( \mathrm{PCl}_{5} \) gas takes place to an appreciable extent. When equilibrium is established, the total pressure in the flask is 2.433 atm.

Solve the equation and check your solution. (If there is no solution, enter NO SOLUTION.) \[ \frac{2}{3 x+1}-\frac{27 x}{3 x-1}=-9 \] \( x=\square \)

136. Даны натуральное число \( n \), действительные числа \( a_{1}, \ldots, a_{n} \) Вычислить: \( \begin{array}{ll}\text { а) } a_{1}+\ldots+a_{n} ; & \text { б) } a_{1} a_{2} \ldots a_{n} ; \\ \text { в) }\left|a_{1}\right|+\ldots+\left|a_{n}\right| ; & \text { г) }\left|a_{1}\right| \cdot\left|a_{2}\right| \cdot \ldots \cdot\left|a_{n}\right| ; \\ \text { д) } a_{1}^{2}+\ldots+a_{n}^{2} ; & \text { е) } a_{1}+\ldots+a_{n} \text { и } a_{1} a_{2} \ldots a_{n} ; \\ \text { ж) } a_{1}-a_{2}+a_{3}-\ldots+(-1)^{n+1} a_{n} ; \\ \text { з) }-\frac{a_{1}}{1!}+\frac{a_{2}}{2!}-\ldots+\frac{(-1)^{n} a_{n}}{n!} ; \\ \text { и) } \frac{a_{1}}{0!}+\frac{a_{2}}{1!}+\ldots+\frac{a_{n}}{(n-1)} ; \\ \text { к) } 2\left(a_{1}+\ldots+a_{n}\right)^{2} ; \quad \text { л) } \sqrt{\left|a_{1} a_{2} \ldots a_{n}\right|} ; \\ \text { м) } \sin \left|a_{1}+\ldots+a_{n}\right| ; \\ \text { н) }\left(\sqrt{\left|a_{1}\right|}-a_{1}\right)^{2}+\ldots+\left(\sqrt{\left|a_{n}\right|}-a_{n}\right)^{2} ; \\ \text { о) } \sqrt{10+a_{1}^{2}}+\ldots+\sqrt{10+a_{n}^{2}}\end{array} \)