The equation 7^2=a^3 shows the relationship between a planet’s orbital period, t, and the planet’s mean distance from the sun, a, in astronomical units, au. if planet y is k times the mean distance from the sun as planet x, by what factor is the orbital period increased?

The period of Y increases by a factor of with respect to the period of X

Step-by-step explanation:

The equation shows the relationship between the orbital period of a planet, T, and the average distance from the planet to the sun, A, in astronomical units, AU. If planet Y is k times the average distance from the sun as planet X, at what factor does the orbital period increase?

For the planet Y:

For planet X:

To know the factor of aumeto we compared with

We know that the distance "a" from planet Y is k times larger than the distance from planet X to the sun. So:

Finally the period of Y increases by a factor of with respect to the period of X

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

"exterior angles = 360 / number of sides.

60 = 360 / sides

sides = 360 / 60

sides = 6"