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Halley's comet has an elliptical orbit with the sun at one focus. its orbit shown below is given approximately by r=(10.71)/(1+0.883sin\theta) in the formula, r is measured in astronomical units. (one astronomical unit is the average distance from earth to the sun, approximately 93 million miles.) find the distance from halley's comet to the sun at its greatest distance from the sun. round to the nearest hundredth of an astronomical unit and the nearest million miles.

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Answer:

8513.2 million miles.

Explanation:

The radio is given by equation,

[tex]r= \frac{10.71}{1+0.883sin\theta}[/tex]

We must look for the nearest number so that the difference in the denominator part becomes almost 0.

The greatest distance is when without the is equal to -1. The most biggest negative number for sin would be,

[tex]\theta = \frac{3\pi}{2}[/tex]

Replacing this value we have to,

[tex]r= \frac{10.71}{1+0.883*(-1)}[/tex]

[tex]r= 91.5387[/tex] Astronomical units.

1 astronomical unit is equal to [tex]93*10^6[/tex] miles, then

[tex]r=91.54*93*10^6=8513.2[/tex] million miles.

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