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barxatty [35]
4 years ago
15

The sun and a planet with a period of 5 years would have a distance of

Mathematics
1 answer:
Galina-37 [17]4 years ago
8 0
To solve the problem shown above you must apply the proccedure shown below:

 1. You must apply the Kepler's third law, as below:

 (T1/T2)²=(R1/R2)³

 T1 and T2 are the orbital periods. (T1=1 year; T2=5 years)
 R1 and R2 are the orbital radius. (R1=1 Astronomical unit)

 2. Now, you must substitute the values shown above into the formula and clear R2:

 (1/5)²=(1/R2)³
 1/25=1/R2³
 R2³/25=1
 R2³=25
 R2=∛25
 R2=2.92 AU

 Therefore, the answer is: 2.92 AU
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A girl can run 6 2/3 metres in one second. How long will it take her to run 100 metres?
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15 seconds

Step-by-step explanation:

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Solve the system of equations. 2x+2y+7z=9, 2x+6y+5z=7, 2x+5y+4z=9. a.z=3 y=-2 z=3 b.x=1 y=0 z=1 c.x=2 y=-1 z=0 d. x=0 y=1 z=2
I am Lyosha [343]
2x + 2y + 7z = 9.....multiply by -1
2x + 6y + 5z = 7
--------------------
-2x - 2y - 7z = -9 (result of multiplying by -1)
2x + 6y + 5z = 7
-------------------add
4y - 2z = -2

2x + 6y + 5z = 7....multiply by -1
2x + 5y + 4z = 9
-------------------
-2x - 6y - 5z = -7 (result of multiplying by -1)
2x + 5y + 4z = 9
-------------------add
-y - z = 2

4y - 2z = -2
-y - z = 2 ......multiply by -2
-----------------
4y - 2z = -2
2y + 2z = -4 (result of multiplying by -2)
----------------add
6y = -6
y = -6/6
y = -1

4y - 2z = -2
4(-1) - 2z = -2
-4 - 2z = -2
-2z = -2 + 4
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z = -2/2
z = -1

2x + 2y + 7z = 9
2x + 2(-1) + 7(-1) = 9
2x - 2 - 7 = 9
2x - 9 = 9
2x = 9 + 9
2x = 18
x = 18/2
x = 9

solution is : x = 9, y = -1, and z = -1

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