Question

The rings of Saturn are composed of chunks of ice that orbit the planet. The inner radius of the rings is 73,000 km, while the outer radius is 170,000 km. Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn’s mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.69 x 1026 kg.

Answer 1

Conditions

slope intercept equation that is perpendicular to $y = 5x + 3$ and containing (-4,5)

Solution

$y = 5x + 3$ is an equation of straight line.

We have to use formula, which gives us a straight line, which goes through a defined point perpendicularly a defined straight line.

The slope of our equation $k = 5$. If we want to find a straight line, which is perpendicular to our line, we must calculate its slope by using formula: $k' = -\frac{1}{k} = -\frac{1}{5}$

Now, equation for our perpendicular is:

$$y = - \frac {1}{5} x + b, b - \text{const}$$

To find $b$ we must use the condition that this perpendicular contains point (-4;5):

$$5 = - \frac {1}{5} (- 4) + b, \Rightarrow b = 5 - \frac {4}{5} = \frac {21}{5}$$

Answer

The slope $k' = -\frac{1}{5}$

Equation is: $y = -\frac{1}{5} x + \frac{21}{5}$