Advanced Placement (AP)
07.11.2020 22:53
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1, -3, 9, -27, what is the seventh number in the sequence

1, -3, 9, -27, what is the seventh number in the sequence
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oVcper
oVcper
4,4(29 marks)
This sequence can be modeled by a_{n}=3^{(n-1)}, and that if n is even, the number becomes negative. So the seventh number would be 3^6, and that is 729, since 7 is odd.
meramera50
meramera50
4,8(68 marks)
We can use an equation to find the gravitational force exerted on the HST.
F = GMm / r² G is the gravitational constant, M is the mass of the Earth, m is the mass of the HST, r is the distance to the center of the Earth. This force, F, provides the centripetal force for the HST to move in a circle.

The equation we use for circular motion is: F = mv^2 / r, m is the mass of the HST, v is the tangential speed, r is the distance to the center of the Earth. Now we can equate these two equations to find v.

mv² / r = GMm / r² v² = GM / r v = √{GM / r } v = √{(6.67 x 10^{-11})(5.97 x 10^{24}) / 6,949,000 m} v = 7570 m/s which is equal to 7.570 km/s

HST's tangential speed is 7570 m/s or 7.570 km/s

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