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((30)^2sin^2(30))/(2*9.81^2)

Solución

\frac{( 30 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 \cdot 9.8 1 ^{2}}

Solución

\frac{125000}{106929}

Notación decimal

1.16899 \dots

Pasos de solución

\frac{( 30 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 \cdot 9.8 1 ^{2}}

= \frac{3 0 ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 ( \frac{981}{100} ) ^{2}}

Utilizar la siguiente identidad trivial:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

Simplificar

\frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}} : \frac{125000}{106929}

\frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

Factorizar

3 0^{2} : 2^{2} \cdot 3^{2} \cdot 5^{2}

Factorizar

30 = 2 \cdot 3 \cdot 5

= (2 \cdot 3 \cdot 5)^{2}

Aplicar las leyes de los exponentes:

(ab)^{c} = a^{c} b^{c}

= 2^{2} \cdot 3^{2} \cdot 5^{2}

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 5 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

Eliminar los terminos comunes:

2

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 ( \frac{1}{2} ) ^{2}}{( \frac{981}{100} ) ^{2}}

(\frac{981}{100})^{2} = \frac{98 1 ^{2}}{10 0 ^{2}}

(\frac{981}{100})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{98 1 ^{2}}{10 0 ^{2}}

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 ( \frac{1}{2} ) ^{2}}{\frac{98 1 ^{2}}{10 0 ^{2}}}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

Aplicar la regla

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}}{\frac{98 1 ^{2}}{10 0 ^{2}}}

Aplicar las propiedades de las fracciones:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0 ^{2}}{98 1 ^{2}}

Simplificar

3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0^{2} : 5^{6} \cdot 3^{2} \cdot 4^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}

3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0^{2}

Factorizar entero

100 = 5^{2} \cdot 4

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} (5^{2} \cdot 4)^{2}

Aplicar las leyes de los exponentes:

(ab)^{c} = a^{c} b^{c}

(5^{2} \cdot 4)^{2} = (5^{2})^{2} \cdot 4^{2}

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} (5^{2})^{2} \cdot 4^{2}

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}

(5^{2})^{2} = 5^{2 \cdot 2}

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{2 \cdot 2} \cdot 4^{2}

Simplificar

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{4} \cdot 4^{2}

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

5^{2} \cdot 5^{4} = 5^{2 + 4}

= 3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{2 + 4} \cdot 4^{2}

Sumar:

2 + 4 = 6

= 3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2}

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}}{98 1 ^{2}}

Multiplicar

3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2} : 1125000

3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 3 ^{2} \cdot 2 \cdot 5 ^{6} \cdot 4 ^{2}}{2 ^{2}}

Multiplicar los numeros:

1 \cdot 2 = 2

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2} \cdot 2}{2 ^{2}}

Eliminar los terminos comunes:

2

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2}}{2}

Factorizar

4^{2} : 2^{4}

Factorizar

4 = 2^{2}

= (2^{2})^{2}

Simplificar

(2^{2})^{2} : 2^{4}

(2^{2})^{2}

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}

= 2^{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= 2^{4}

= 2^{4}

= \frac{5 ^{6} \cdot 2 ^{4} \cdot 3 ^{2}}{2}

Eliminar los terminos comunes:

2

= 5^{6} \cdot 2^{3} \cdot 3^{2}

5^{6} = 15625

= 2^{3} \cdot 3^{2} \cdot 15625

2^{3} = 8

= 3^{2} \cdot 15625 \cdot 8

3^{2} = 9

= 15625 \cdot 8 \cdot 9

Multiplicar los numeros:

15625 \cdot 8 \cdot 9 = 1125000

= 1125000

= \frac{1125000}{98 1 ^{2}}

Factorizar

1125000 : 5^{6} \cdot 2^{3} \cdot 3^{2}

Factorizar

1125000 = 5^{6} \cdot 2^{3} \cdot 3^{2}

Factorizar

98 1^{2} : 3^{4} \cdot 10 9^{2}

Factorizar

981 = 3^{2} \cdot 109

= (3^{2} \cdot 109)^{2}

Aplicar las leyes de los exponentes:

(ab)^{c} = a^{c} b^{c}

= 10 9^{2} (3^{2})^{2}

Simplificar

(3^{2})^{2} : 3^{4}

(3^{2})^{2}

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}

= 3^{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= 3^{4}

= 3^{4} \cdot 10 9^{2}

= \frac{5 ^{6} \cdot 2 ^{3} \cdot 3 ^{2}}{3 ^{4} \cdot 10 9 ^{2}}

Cancelar

\frac{2 ^{3} \cdot 3 ^{2} \cdot 5 ^{6}}{3 ^{4} \cdot 10 9 ^{2}} : \frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

\frac{2 ^{3} \cdot 3 ^{2} \cdot 5 ^{6}}{3 ^{4} \cdot 10 9 ^{2}}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{2}}{3 ^{4}} = \frac{1}{3 ^{4 - 2}}

= \frac{5 ^{6} \cdot 2 ^{3}}{10 9 ^{2} \cdot 3 ^{4 - 2}}

Restar:

4 - 2 = 2

= \frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

= \frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

5^{6} \cdot 2^{3} = 125000

5^{6} \cdot 2^{3}

5^{6} = 15625

= 2^{3} \cdot 15625

2^{3} = 8

= 15625 \cdot 8

Multiplicar los numeros:

15625 \cdot 8 = 125000

= 125000

= \frac{125000}{3 ^{2} \cdot 10 9 ^{2}}

3^{2} \cdot 10 9^{2} = 106929

3^{2} \cdot 10 9^{2}

3^{2} = 9

= 10 9^{2} \cdot 9

10 9^{2} = 11881

= 9 \cdot 11881

Multiplicar los numeros:

9 \cdot 11881 = 106929

= 106929

= \frac{125000}{106929}

= \frac{125000}{106929}

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