From Kepler's third law the square of orbital period of revolving celestial body is proportional to the cube of semi -major axis from the body it is revolving about.

P² =A³

Where, P is the orbital period in years and A is the semi-major axis in AU (Astronomical units)

It is given that, For Saturn, A = 9.5 AU. We need to find P

⇒P² = (9.5 AU)³

⇒P² = 857.38

⇒P = 29.28 years

Thus, the orbital period of Jupiter is 29.28 years around the Sun.

5 0

3 years ago

Brooke makes a design using 4-inch, 6-inch, and 9-inch pieces of string. Can Brooke make a triangle with her string?

Olin [163]

I really hope this is right, i don’t quite remember how to do these but i think c

6 0

3 years ago

(x³ + ³) / (x - y)<br> Do not include parentheses in your answer.

Lubov Fominskaja [6]

The simplified expression of $\frac{x^3 + (-y)^3}{(x - y}$ is $x^2+xy+y^2$

<h3>Complete question</h3>

Simplify the expression: (x³ + (-y)³) / (x - y)

Do not include parentheses in your answer.

<h3>How to simplify the expression?</h3>

The expression is given as:

$\frac{x^3 + (-y)^3}{(x - y}$

Open the inner bracket

$\frac{x^3 -y^3}{(x - y}$

Apply the difference of two cubes to the numerator

$\frac{(x-y)(x^2+xy+y^2)}{(x - y}$

Cancel out the common factors

$x^2+xy+y^2$

Hence, the simplified expression of $\frac{x^3 + (-y)^3}{(x - y}$ is $x^2+xy+y^2$