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2 years ago

Find the distance between the points (7,-1) and (5,9)

Mathematics

1 answer:

Dmitry_Shevchenko [17]2 years ago

8 0

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Answer: $\textsf{10.198 units}$

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Given: $\textsf{Points (7, -1) and (5, 9)}$

Find: $\textsf{Determine the distance between the two points}$

Solution: In order to find the distance we need to use the distance formula, plug in the values, and simplify the expression.

<u>Plug in the values</u>

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$d = \sqrt{(5 - 7)^2 + (9 - (-1))^2}$

<u>Simplify the expression</u>

$d = \sqrt{(-2)^2 + (9 + 1)^2}$

$d = \sqrt{4+ (10)^2}$

$d = \sqrt{4 + 100}$

$d = \sqrt{104}$

$d = 10.198$

After simplifying the expression we were able to determine that the distance between the two points is 10.198 units.

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Step-by-step explanation:

The sum of the two shortest sides must exceed the length of the longest side. This is only the case for choice D.

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3 years ago

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3 years ago

De acuerdo con la tercera ley de movimiento planetario de Kepler, la masa de un planeta es directamente proporcional al cubo de

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Answer:

La masa del Sol es $2.509\times 10^{31}$ kilogramos.

Step-by-step explanation:

Tras una lectura cuidadosa al enunciado, tenemos que la Tercera Ley de Kepler queda descrita por la siguiente relación:

$M \propto \frac{r^{3}}{T^{2}}$

$M = k\cdot \frac{r^{3}}{T^{2}}$ (Eq. 1)

Donde:

$r$ - Distancia entre los centros del planeta y el satélite, medido en kilómetros.

$T$ - Período oribital del satélite, medido en días.

$k$ - Constante de proporcionalidad, medida en kilogramo-días cuadrados por kilómetro cúbico.

$M$ - Masa del planeta, medida en kilogramos.

Podemos obtener la masa del Sol mediante la siguiente relación:

$\frac{M_{S}}{M_{E}} = \frac{\frac{r_{E}^{3}}{T_{E}^{2}} }{\frac{r_{M}^{3}}{T_{M}^{2}} }$

$\frac{M_{S}}{M_{E}} = \left(\frac{T_{M}}{T_{E}} \right)^{2}\cdot \left(\frac{r_{E}}{r_{M}} \right)^{3}$ (Eq. 2)

Donde:

$T_{M}$ , $T_{E}$ - Períodos orbitales de la Luna y la Tierra, medidos en días.

$r_{E}$ , $r_{M}$ - Distancias entre la Tierra y el Sol, así como entre la Luna y la Tierra, medidas en kilómetros.

$M_{S}$ , $M_{E}$ - Masas del Sol y la Tierra, medidos en kilogramos.

Si $M_{E} = 75.97\times 10^{24}\,kg$ , $T_{E} = 365.3\,d$ , $T_{M} = 27.3\,d$ , $r_{M} = 3.84\times 10^{5}\,km$ y $r_{E} = 1.496\times 10^{8}\,km$ , entonces tenemos que la masa del Sol es:

$M_{S} = \left(\frac{T_{M}}{T_{E}} \right)^{2}\cdot \left(\frac{r_{E}}{r_{M}} \right)^{3}\cdot M_{E}$

$M_{S} = \left(\frac{27.3\,d}{365.3\,d} \right)^{2}\cdot \left(\frac{1.496\times 10^{8}\,km}{3.84\times 10^{5}\,km} \right)^{3}\cdot (75.97\times 10^{24}\,kg)$

$M_{S} = 2.509\times 10^{31}\,kg$

La masa del Sol es $2.509\times 10^{31}$ kilogramos.

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3 years ago