Determine the eccentricity, the type of conic, and the directrix for r=6/1+2cos theta.

Option c

Step-by-step explanation:

The general polar form of the conic with cosine in the denominator is:

Comparing the given equation (Denominator) with the general equation, we can write:

e = 2

This means eccentricity = 2. Since eccentricity is greater than 1, the given conic is a hyperbola.

The equation of directrix is x = p

Comparing the numerators of general and given equation, we can write:

ep = 6

Using the value of e, we get p = 3

Therefore, equation of directrix is x =3

Hence option c is the correct answer.

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours