Question

PLEASE HELP!!!!!!!!!!!!!!!!!

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.
The formula for eccentricity, e, of an orbit is given below, where a is the length of the semi-major axis and b is the length of the major axis.

Answer 1

Answer: D and 4.62

Explanation:

Answer 2

D, 4.62

Explanation:

e = √(1 - b²/a²)

To solve for a, first square both sides:

e² = 1 - b²/a²

Then subtract 1 from both sides:

e² - 1 = -b²/a²

Multiply both sides by -1:

1 - e² = b²/a²

Multiply by a²:

(1 - e²) a² = b²

Divide by 1 - e²:

a² = b² / (1 - e²)

Take the square root:

a = b / √(1 - e²)

So the answer is D.

When b = 4 and e = ½:

a = 4 / √(1 - (½)²)

a = 4 / √(1 - ¼)

a = 4 / √¾

a = 8 / √3

a ≈ 4.62