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simplificar 4pi^2(1.8s^{-1})^2[1130kg+4(72.4kg)]

Solución

simplificar

4 π^{2} (1.8 s^{- 1})^{2} [1130 k g + 4 (72.4 k g)]

\frac{181581.13968 \dots k g}{s ^{2}}

Pasos de solución

4 π^{2} (1.8 s^{- 1})^{2} [1130 k g + 4 (72.4 k g)]

Aplicar la siguiente propiedad de los exponentes:

a^{m} b^{m} = (ab)^{m},

asumiendo que

a \geq 0, b \geq 0

π^{2} (1.8 s^{- 1})^{2} = (1.8 π s^{- 1})^{2}

= 4 (1.8 π s^{- 1})^{2} [1130 k g + 4 \cdot 72.4 k g]

Simplificar

π 1.8 s^{- 1} : \frac{5.65486 \dots}{s}

= 4 (\frac{5.65486 \dots}{s})^{2} [1130 k g + 4 \cdot 72.4 k g]

(\frac{5.65486 \dots}{s})^{2} = \frac{5.65486 \dots ^{2}}{s ^{2}}

= 4 \cdot \frac{5.65486 \dots ^{2}}{s ^{2}} (1130 k g + 4 \cdot 72.4 k g)

Multiplicar los numeros:

4 \cdot 72.4 = 289.6

= 4 \cdot \frac{5.65486 \dots ^{2}}{s ^{2}} (1130 k g + 289.6 k g)

Sumar elementos similares:

1130 k g + 289.6 k g = 1419.6 k g

= 4 \cdot 1419.6 k g \frac{5.65486 \dots ^{2}}{s ^{2}}

Multiplicar fracciones:

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

= 1419.6 \cdot \frac{4 \cdot 5.65486 \dots ^{2} k g}{s ^{2}}

5.65486 \dots^{2} \cdot 4 k g = 127.91007 \dots k g

= 1419.6 \cdot \frac{127.91007 \dots k g}{s ^{2}}

Multiplicar fracciones:

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

= \frac{127.91007 \dots k g \cdot 1419.6}{s ^{2}}

Multiplicar los numeros:

127.91007 \dots \cdot 1419.6 = 181581.13968 \dots

= \frac{181581.13968 \dots k g}{s ^{2}}

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