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n200080 [17]
2 years ago
8

Dana is training to run a marathon. On Monday, she ran 10.2 miles. On Tuesday, she ran 11.4 miles. On Wednesday and Thursday, sh

e ran 11.8 miles each day. On Friday, she ran 12.3 miles. Round each amount to the nearest whole mile to find a reasonable estimate of the total number of miles Dana ran over this five-day period.
Mathematics
1 answer:
Tema [17]2 years ago
6 0

Answer:

about 58 miles

Step-by-step explanation:

10+12+12+12+12= 58

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De acuerdo con la tercera ley de movimiento planetario de Kepler, la masa de un planeta es directamente proporcional al cubo de
Sunny_sXe [5.5K]

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.

7 0
3 years ago
Need help ASAP!! Write an informal proof to show triangles ABC and DEF are similar.
yaroslaw [1]

Answer:

Δ ABC and Δ DEF are similar because their corresponding sides are proportional

Step-by-step explanation:

Two triangles are similar if their corresponding sides are proportional which means the corresponding sides have equal ratios

In the two triangles ABC and DEF

∵ AB = 4 units

∵ DE = 2 units

∴ \frac{AB}{DE}=\frac{4}{2}=2

∵ BC = 6 units

∵ EF = 3 units

∴ \frac{BC}{EF}=\frac{6}{3}=2

∵ CA = 2 units

∵ FD = 1 units

∴ \frac{CA}{FD}=\frac{2}{1}=2

∴ \frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}=2

∵ All the ratios of the corresponding sides are equal

∴ The corresponding sides of the two triangles are proportional

∴ Δ ABC is similar to Δ DEF

6 0
2 years ago
Please help me answer the question in the picture
coldgirl [10]

Answer:

D. y-5 = 3(x+1)

Step-by-step explanation:

Slope of the perpendicular line is 3.

Slope intercept form is,

y-5 = 3 (x-(-1))

y-5 = 3(x+1)

4 0
3 years ago
Write 0.12 as a fraction
Sladkaya [172]

Answer: 6/50

Step-by-step explanation:

5 0
3 years ago
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What is the value of X?
Bingel [31]
I believe the answer either 4 or 6
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7 0
3 years ago
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