Question

PLEASE HELP, I NEED THIS DONE BY TODAY!!!!!!!!! Mercury is the closest planet to the Sun, with an average distance of 35,000,000 miles. It takes light about 3 minutes to travel from the Sun to Mercury.

Neptune is the farthest, with an average distance of 2.8 × 109 miles from the Sun.

How many times farther from the Sun is Neptune than Mercury? How long does it take light to reach Neptune? Follow the steps to find out.

1. Write the distance from the Sun to Mercury in scientific notation. Include units with your answer. (2 points)

2. Write and simplify an expression showing how many times farther Neptune is from the Sun than Mercury. Write the result in scientific notation. (2 points)

3. How many times longer does it take light from the Sun to reach Neptune than Mercury? Express this number in standard notation. Explain your reasoning. (3 points)

4. It takes light from the Sun about 3 minutes to reach Mercury. How many hours does it take light from the Sun to reach Neptune? Show your work. (3 points)

Answer 1

Explanation:

The distance from the Sun to Mercury is 35,000,000 miles. In scientific notation, this can be written as 3.5 x 10^7 miles.

To find out how many times farther Neptune is from the Sun than Mercury, you can set up the following expression:

Distance to Neptune / Distance to Mercury = (2.8 x 10^9 miles) / (3.5 x 10^7 miles)

Now, simplify this expression:

(2.8 x 10^9 miles) / (3.5 x 10^7 miles) = (2.8 / 3.5) x (10^9 / 10^7) = 0.8 x 10^(9 - 7) = 0.8 x 10^2

So, Neptune is 0.8 x 10^2 times farther from the Sun than Mercury, which is equivalent to 80 times farther in standard notation.

To find out how many times longer it takes light from the Sun to reach Neptune than Mercury, you can set up the following expression:

Time to reach Neptune / Time to reach Mercury = (Time for Neptune) / (Time for Mercury)

The time for Mercury is given as 3 minutes, and we want to find the time for Neptune.

Time for Neptune = (0.8 x 10^2) * (Time for Mercury) = 80 * 3 minutes

Now, calculate the time for Neptune:

Time for Neptune = 80 * 3 minutes = 240 minutes

To express this in hours, divide by 60 (since there are 60 minutes in an hour):

Time for Neptune = 240 minutes / 60 = 4 hours

So, it takes light from the Sun about 4 hours to reach Neptune, which is 80 times longer than the 3 minutes it takes to reach Mercury.

In summary:

Distance from the Sun to Mercury in scientific notation: 3.5 x 10^7 miles.

Neptune is 80 times farther from the Sun than Mercury, which is equivalent to 0.8 x 10^2 in scientific notation.

It takes light from the Sun about 4 hours to reach Neptune, which is 80 times longer than the 3 minutes it takes to reach Mercury.