9.10: Examen de Aptitud
- Page ID
- 112393
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Examen de competencia
Para los siguientes problemas, simplifique cada una de las expresiones de raíz cuadrada.
\(\sqrt{8} \cdot \sqrt{5}\)
- Responder
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\(2 \sqrt{10}\)
\(\dfrac{\sqrt{80}}{\sqrt{12}}\)
- Responder
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\(\dfrac{2 \sqrt{15}}{3}\)
\(\dfrac{\sqrt{n^2 + n - 12}}{\sqrt{n-3}}\)
- Responder
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\(\sqrt{n + 4}\)
\(\sqrt{24a^3b^5c^8}\)
- Responder
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\(2ab^2c^4 \sqrt{6ab}\)
\(\sqrt{\dfrac{64x^4y^5z^6}{49a^3b^2c^9}}\)
- Responder
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\(\dfrac{8x^2y^2z^3\sqrt{acy}}{7a^2bc^5}\)
\(\sqrt{(x-2)^2(x+1)^4}\)
- Responder
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\((x-2)(x+1)^2\)
\(\sqrt{a^2-8a+16}\)
- Responder
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\(a-4\)
\(\dfrac{4}{2 + \sqrt{x}}\)
- Responder
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\(\dfrac{8 - 4\sqrt{x}}{4 - x}\)
\(\dfrac{\sqrt{3a}}{\sqrt{2a} + \sqrt{5a}}\)
- Responder
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\(\dfrac{\sqrt{15} - \sqrt{6}}{3}\)
\(2x\sqrt{27} + x\sqrt{12}\)
- Responder
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\(8x\sqrt{3}\)
\(-3a\sqrt{a^5b^3} + 2a^3b\sqrt{ab}\)
- Responder
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\(-a^3b\sqrt{ab}\)
\(\sqrt{10}(\sqrt{8} - \sqrt{2})\)
- Responder
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\(2\sqrt{5}\)
\((3 + \sqrt{6})(2 + \sqrt{5})\)
- Responder
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\(6 + 3\sqrt{5} + 2\sqrt{6} + \sqrt{30}\)
\((\sqrt{10} - \sqrt{3})(\sqrt{5} + \sqrt{2})\)
- Responder
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\(5\sqrt{2} + 2\sqrt{5} - \sqrt{15} - \sqrt{6}\)
\((4 - \sqrt{5y})^2\)
- Responder
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\(16 - 8\sqrt{5y} + 5y\)
\(\dfrac{6 - \sqrt{3}}{4 + \sqrt{2}}\)
- Responder
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\(\dfrac{24 - 6\sqrt{2} - 4\sqrt{3} + \sqrt{6}}{14}\)
\(\dfrac{\sqrt{2} + \sqrt{3}}{\sqrt{3} - \sqrt{5}}\)
- Responder
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\(-\dfrac{3 + \sqrt{6} + \sqrt{10} + \sqrt{15}}{2}\)
Para los siguientes problemas, resolver las ecuaciones.
\(\sqrt{x + 8} = 4\)
- Responder
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\(x = 8\)
\(\sqrt{3a + 1} = 4\)
- Responder
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\(a = 5\)
\(\sqrt{2x} = -3\)
- Responder
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Sin solución
\(\sqrt{3x + 18} + 7 = 0\)
- Responder
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Sin solución real
\(\sqrt{3m - 5} = \sqrt{2m + 1}\)
- Responder
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\(m = 6\)
\(2\sqrt{a + 2} - 2= 0\)
- Responder
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\(a = -1\)
\(\sqrt{b - 7} - \sqrt{5b + 1} = 0\)
- Responder
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Sin solución
En una pequeña empresa, el número de ventas mensuales\(S\) se relaciona aproximadamente con el número de empleados\(E\) por\(S = 175 + 7\sqrt{E - 3}\)
a) Determinar el número aproximado de ventas si el número de empleados es\(39\)
b) Determinar el número aproximado de empleados si el número de ventas en\(224\)
- Responder
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a)\(S = 217\)
b)\(E = 52\)