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PilotLPTM [1.2K]
2 years ago
10

Write an equation for the orbit of Saturn in the form x^2/a^2 + y^2/b^2 = 1

Mathematics
1 answer:
frozen [14]2 years ago
7 0

Answer:

  x²/2166784 +y²/2159989 = 1

Step-by-step explanation:

The relationship between the semi-axes and the eccentricity of an ellipse is ...

  e = √(1 -b²/a²)

In order to write the desired equation we need to find 'b' from 'e' and 'a'.

__

<h3>semi-minor axis</h3>

Squaring the equation for eccentricity gives ...

  e² = 1 -b²/a²

Solving for b², we have ...

  b²/a² = 1 -e²

  b² = a²(1 -e²)

<h3>ellipse equation</h3>

Using the given values, we find ...

  b² = 1472²(1 -0.056²) = 2166784(0.996864) ≈ 2159989

The desired equation is ...

  x²/2166784 +y²/2159989 = 1

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The cloth top of the gazebo in Mr. Chang’s backyard has ripped from weathering. He needs to know the area of the cloth so he can
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Answer:

<u>The correct answer is A. 60 square feet.</u>

Step-by-step explanation:

1. Let's review the data provided to us for solving the question:

The gazebo in Mr. Chang's backyard, according to the figure, is a square pyramid because its base is a square of 6 feet as length of its sides.

Length of the sides of the base = 6 feet

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2. How much cloth, in square feet, will Mr. Chang need, assuming he does not need to replace the cloth at the bottom of the figure?

Area of a square pyramid = Base area + 1/2 Perimeter * Slant length

Replacing with the real values, we have:

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Area of a square pyramid = 36 + 60

Area of a square pyramid = 96 feet ²

3. But remember than Mr. Chang doesn't need to replace the cloth at the bottom of the gazebo.

So we need to subtract the area of the base to the area of the square pyramid:

Area of the square pyramid - area of the base

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Answer:

Step-by-step explanation:

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