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.

Solve the formula for eccentricity for the length of the semi-major axis.

The correct equation for the length of the semi-major axis is equation .

When the length of the major axis is 4 inches and the eccentricity of the orbit is , the length of the semi-major axis is inches (round to the nearest hundredth).

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Part 1)

Part 2)

Step-by-step explanation:

The correct question in the attached figure

Part 1)

we have the formula

where

e the eccentricity

a is the length of the semi-major axis

b is the length of the major axis

solve for a

That means

Isolate the variable a

squared both sides

subtract 1 both sides

Multiply both sides by a^2

Divide both sides by (e^2-1)

Rewrite

square root both sides

simplify

Part 2) we have

Solve for a

substitute in the formula of part 1)

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.

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