9.9: Suplemento de ejercicio
- Page ID
- 112387
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Suplemento de ejercicio
Expresiones de raíz cuadrada - Suma y resta de expresiones de raíz cuadrada
Para los siguientes problemas, simplifique las expresiones.
\(\sqrt{10}\sqrt{2}\)
- Responder
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\(2\sqrt{5}\)
\(\sqrt{6}\sqrt{8}\)
\(\sqrt{18}\sqrt{40}\)
- Responder
-
\(12\sqrt{5}\)
\(\sqrt{11}\sqrt{11}\)
\(\sqrt{y}\sqrt{y}\)
- Responder
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\(y\)
\(\sqrt{r^3}\sqrt{r^3}\)
\(\sqrt{m+3}\sqrt{m+3}\)
- Responder
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\(m+3\)
\(\sqrt{a-7}\sqrt{a-7}\)
\(\sqrt{x^2+4x+4}\)
- Responder
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\(x+2\)
\(\sqrt{y^2 - 12y + 36}\)
\(\dfrac{\sqrt{x+5}}{\sqrt{x+2}}\)
- Responder
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\(\dfrac{\sqrt{(x+5)(x+2)}}{x+2}\)
\(\dfrac{\sqrt{n-3}}{\sqrt{n-1}}\)
\(\dfrac{\sqrt{50}}{\sqrt{2}}\)
- Responder
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\(5\)
\(\dfrac{\sqrt{75}}{5\sqrt{3}}\)
\(\dfrac{\sqrt{a^2 + 6a + 9}}{\sqrt{a + 3}}\)
- Responder
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\(\sqrt{a+3}\)
\(\dfrac{\sqrt{4x^2 + 4x + 1}}{\sqrt{2x + 1}}\)
\(\dfrac{\sqrt{x^2 - 11x + 24}}{\sqrt{x-8}}\)
- Responder
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\(\sqrt{x-3}\)
\(\dfrac{\sqrt{y^2 + 11y + 28}}{\sqrt{y+4}}\)
\(\sqrt{3}(\sqrt{5} + \sqrt{3})\)
- Responder
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\(3 + \sqrt{15}\)
\(\sqrt{5}(\sqrt{6} - \sqrt{10})\)
\(\sqrt{a}(\sqrt{a} - \sqrt{bc})\)
- Responder
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\(a - \sqrt{abc}\)
\(\sqrt{x}(\sqrt{x^5} - \sqrt{3x})\)
\(\sqrt{7a^3}(\sqrt{2a} - \sqrt{4a^3})\)
- Responder
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\(a^2\sqrt{14} - 2a^3\sqrt{7}\)
\(\dfrac{3}{\sqrt{7}}\)
\(\dfrac{2}{\sqrt{5}}\)
- Responder
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\(\dfrac{2\sqrt{5}}{5}\)
\(\dfrac{6}{\sqrt{2}}\)
\(\dfrac{8y}{\sqrt{y}}\)
- Responder
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\(8\sqrt{y}\)
\(\dfrac{16a^2}{\sqrt{5a}}\)
\((2 + \sqrt{3})(2 - \sqrt{3})\)
- Responder
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\(1\)
\((x + \sqrt{8})(3x + \sqrt{8})\)
\((4y - \sqrt{3x})(4y + \sqrt{3x})\)
- Responder
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\(16y^2 - 3x\)
\((6r + \sqrt{2s})(4r + \sqrt{2s})\)
\(\dfrac{2}{2 + \sqrt{7}}\)
- Responder
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\(-\dfrac{2(2- \sqrt{7})}{3}\)
\(\dfrac{4}{1 - \sqrt{6}}\)
\(\dfrac{6}{x + \sqrt{y}}\)
- Responder
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\(\dfrac{6(x - \sqrt{y})}{x^2 - y}\)
\(\dfrac{10}{a - \sqrt{2b}}\)
\(\dfrac{\sqrt{5}}{a + \sqrt{3}}\)
- Responder
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\(\dfrac{a\sqrt{5} - \sqrt{15}}{a^2 - 3}\)
\(\dfrac{\sqrt{2}}{1 + \sqrt{10}}\)
\(\dfrac{8 + \sqrt{3}}{2 + \sqrt{6}}\)
- Responder
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\(\dfrac{8\sqrt{6} - 2\sqrt{3} + 3\sqrt{2} - 16}{2}\)
\(\dfrac{4 + \sqrt{11}}{4 - \sqrt{11}}\)
\(\sqrt{\dfrac{36a^4b^5c^{11}}{x^2y^5}}\)
- Responder
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\(\dfrac{6a^2b^2c^5\sqrt{bcy}}{xy^3}\)
\(\sqrt{x^{12}y^{10}z^8w^7}\)
\(\sqrt{32x^5y(x-2)^3}\)
- Responder
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\(4x^2(x-2)\sqrt{2xy(x-2)}\)
\(-2\sqrt{60r^4s^3}\)
\(\sqrt{\dfrac{3}{16}}\)
- Responder
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\(\dfrac{\sqrt{3}}{4}\)
\(\sqrt{\dfrac{4}{25}}\)
\(\sqrt{\dfrac{9}{16}}\)
- Responder
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\(\dfrac{3}{4}\)
\(\sqrt{\dfrac{5}{36}}\)
\(\sqrt{\dfrac{1}{6}}\)
- Responder
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\(\dfrac{\sqrt{6}}{6}\)
\(\sqrt{\dfrac{3}{10}}\)
\(\sqrt{(x+4)^4(x-1)^5}\)
- Responder
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\((x+4)^2(x-1)^2(\sqrt{x-1})\)
\(\sqrt{(3x + 5)^3(2x - 7)^3}\)
\(\sqrt{(y-3z)^{12}(y+3z)^{10}(y-5z)^3}\)
- Responder
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\((y-3z)^6(y+3z)^5(y-5z)\sqrt{y-5z}\)
\(\sqrt{(8a-5b)^{26}(2a - 9b)^{40}(a-b)^{15}}\)
\(4\sqrt{11} + 8\sqrt{11}\)
- Responder
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\(12\sqrt{11}\)
\(-\sqrt{6} + 5\sqrt{6}\)
\(5\sqrt{60} - 7\sqrt{15}\)
- Responder
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\(3\sqrt{15}\)
\(4ax^2\sqrt{75x^4} + 6a\sqrt{3x^8}\)
\(-3\sqrt{54} - 16\sqrt{96}\)
- Responder
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\(-73\sqrt{6}\)
\(\sqrt{18x^2y}\sqrt{2x^2y}\)
\(\sqrt{4x^2+32x+64} + \sqrt{10x^2+80x+160}\)
- Responder
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\((2 + \sqrt{10})(x + 4)\)
\(-2\sqrt{9x^2 - 42x + 49} + 5\sqrt{18x^2 - 84x + 98}\)
\(-10\sqrt{56a^3b^7} + 2a^2b\sqrt{126ab^5}\)
- Responder
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\((-20ab^3 + 6a^2b^3)\sqrt{14ab}\)
\(\dfrac{\sqrt{3x} - \sqrt{5x}}{\sqrt{7x} + \sqrt{2x}}\)
\(\dfrac{\sqrt{6a} + \sqrt{2a}}{\sqrt{3a} - \sqrt{5a}}\)
- Responder
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\(\dfrac{-3\sqrt{2} - \sqrt{30} - \sqrt{6} - \sqrt{10}}{2}\)
Ecuaciones de raíz cuadrada con aplicaciones
Para los siguientes problemas, resolver las ecuaciones.
\(\sqrt{3x} = 9\)
\(\sqrt{4a} = 16\)
- Responder
-
\(a = 64\)
\(\sqrt{x} + 7 = 4\)
\(\sqrt{a + 6} = -5\)
- Responder
-
Sin solución
\(\sqrt{4a + 5} = 21\)
\(\sqrt{3m + 7} = 10\)
- Responder
-
\(m = 31\)
\(\sqrt{y + 10} = 5\)
\(\sqrt{a - 7} = 6\)
- Responder
-
\(a = 43\)
\(\sqrt{4x - 8} = x - 2\)
\(\sqrt{2x + 3} + 8 =11\)
- Responder
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\(x=3\)
\(\sqrt{a^2 + 5} + 5 = a\)
\(\sqrt{5b + 4} - 5 = -2\)
- Responder
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\(b = 1\)
\(\sqrt{2a + 1} - 10 = -3\)
\(\sqrt{2x + 5} = \sqrt{x + 3}\)
- Responder
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\(x = -2\)
\(\sqrt{5a - 11}\)
En una pequeña empresa, el número mensual de ventas\(S\) está aproximadamente relacionado con el número de empleados\(E\) por\(S = 140 + 8\sqrt{E - 2}\)
a) Determinar el número aproximado de ventas si el número de empleados es\(27\).
b) Determinar el número aproximado de empleados si las ventas mensuales son 268.
- Responder
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a)\(S = 180\)
b)\(E = 258\)
La frecuencia de resonancia\(f\) en un circuito electrónico que contiene inductancia\(L\) y capacitancia\(C\) en serie viene dada por:
\(f = \dfrac{1}{2\pi\sqrt{LC}}\)
a) Determinar la frecuencia de resonancia en un circuito electrónico si la inductancia es\(9\) y la capacitancia es\(0.0001\). Uso\(\pi = 3.14\).
b) Determinar la inductancia en un circuito eléctrico si la frecuencia de resonancia es\(5.308\) y la capacitancia es\(0.0001\). Uso\(\pi = 3.14\).
Si dos polos magnéticos de fuerza\(m\) y\(m'\) están a una distancia\(r\) centímetros (cm) de distancia, la fuerza\ 9F\) de repulsión en el aire entre ellos viene dada por:
\(F = \dfrac{mm'}{r^2}\)
a) Determinar la fuerza de repulsión si dos polos magnéticos de resistencias 22 y 46 unidades están separados por 8 cm.
b) Determinar qué tan separados están dos polos magnéticos de intensidades 14 y 16 unidades si la fuerza de repulsión en el aire entre ellos es de 42 unidades.
- Responder
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a)\(F=15.8125\)
b)\(r=12.31\) cm