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Answer:
The asteroid requires 5.14 years to make one revolution around the Sun.
Explanation:
Kepler's third law establishes that the square of the period of a planet will be proportional to the cube of the semi-major axis of its orbit:
(1)
Where T is the period of revolution and a is the semi-major axis.
In the other hand, the distance between the Earth and the Sun has a value of . That value can be known as well as an astronomical unit (1AU).
But 1 year is equivalent to 1 AU according with Kepler's third law, since 1 year is the orbital period of the Earth.
For the special case of the asteroid the distance will be:
That distance will be expressed in terms of astronomical units:
⇒
Finally, from equation 1 the period T can be isolated:
Then, the period can be expressed in years:
Hence, the asteroid requires 5.14 years to make one revolution around the Sun.
Answer:
method I = 88 chairs
method II = 62 chairs
Explanation:
This problem can be modeled by a system of two linear equations.
Define x as the number of chairs refinished by method I and y by method II
The sum of hours spent on both methods should equal 199 and the sum of total material cost should equal $1226, therefore:
Multiplying the first equation by -18 and adding it to the second equation we can solve for the value of y:
We can now apply the value of y found to the first equation and solve for x:
Therefore, they should refinish 88 chairs with method I and 62 chairs with method II