The function d(t) = 300,000t represents the distance (in kilometers) that light travels in t seconds. The distance from the Sun to Earth varies from 91.4 million miles to 94.5 million miles. How long does it take light to travel from the Sun to Earth? Round answer to the nearest tenth. Between blank seconds and blank seconds.

Answer 1

To find out how long it takes for light to travel from the Sun to Earth, we need to convert the distances from miles to kilometers and then use the function \( d(t) = 300,000t \) to find the time.

First, let's convert the distances from miles to kilometers. There are approximately 1.60934 kilometers in a mile.

Given:

• Minimum distance from the Sun to Earth: 91.4 million miles
• Maximum distance from the Sun to Earth: 94.5 million miles

Step 1: Convert the distances to kilometers.

Minimum distance: \[ 91.4 \text{ million miles} = 91.4 \times 10^6 \text{ miles} \times 1.60934 \text{ km/mile} \approx 147.1 \text{ million kilometers} \]

Maximum distance: \[ 94.5 \text{ million miles} = 94.5 \times 10^6 \text{ miles} \times 1.60934 \text{ km/mile} \approx 152.1 \text{ million kilometers} \]

Step 2: Use the formula \( d(t) = 300,000t \) to find the time.

For the minimum distance of approximately 147.1 million kilometers:

\[ d(t) = 300,000t \] \[ 147,100,000 = 300,000t \] \[ t = \frac{147,100,000}{300,000} \approx 490.33 \text{ seconds} \]

For the maximum distance of approximately 152.1 million kilometers:

\[ d(t) = 300,000t \] \[ 152,100,000 = 300,000t \] \[ t = \frac{152,100,000}{300,000} \approx 507 \text{ seconds} \]

Step 3: Rounding the answers to the nearest tenth.

Minimum time: \[ 490.33 \text{ seconds} \approx 490.3 \text{ seconds} \]

Maximum time: \[ 507 \text{ seconds} \approx 507.0 \text{ seconds} \]

Final Answer: Light takes between 490.3 seconds and 507.0 seconds to travel from the Sun to Earth.

Answer 2

wrong

Answer 3

Let’s go through the calculations step by step to ensure we have the right answer.

Step 1: Convert the distances from miles to kilometers

1 mile is approximately 1.60934 kilometers.

• Minimum distance from the Sun to Earth: 91.4 million miles \[ 91.4 \text{ million miles} = 91.4 \times 10^6 \text{ miles} \times 1.60934 \text{ km/mile} \] Calculating this: \[ = 91.4 \times 1.60934 \times 10^6 \approx 147.1 \text{ million kilometers} \]

• Maximum distance from the Sun to Earth: 94.5 million miles \[ 94.5 \text{ million miles} = 94.5 \times 10^6 \text{ miles} \times 1.60934 \text{ km/mile} \] Calculating this: \[ = 94.5 \times 1.60934 \times 10^6 \approx 152.1 \text{ million kilometers} \]

Step 2: Calculate the time it takes for light to travel these distances

The formula for the distance light travels is: \[ d(t) = 300,000t \] where \(d(t)\) is the distance in kilometers, and \(t\) is the time in seconds.

For the minimum distance (147.1 million kilometers):

\[ d(t) = 147,100,000 \text{ kilometers} \] Setting this equal to the distance formula: \[ 147,100,000 = 300,000t \] Now solving for \(t\): \[ t = \frac{147,100,000}{300,000} \approx 490.33 \text{ seconds} \]

For the maximum distance (152.1 million kilometers):

\[ d(t) = 152,100,000 \text{ kilometers} \] Setting this equal to the distance formula: \[ 152,100,000 = 300,000t \] Now solving for \(t\): \[ t = \frac{152,100,000}{300,000} \approx 507 \text{ seconds} \]

Final Time Values

• Minimum time: Approximately \(490.3\) seconds
• Maximum time: Approximately \(507.0\) seconds

Final Answer

The light takes between approximately 490.3 seconds and 507.0 seconds to travel from the Sun to Earth.

If there’s any misunderstanding or specific part you would like to review, please let me know!

Answer 4

still wrong

Answer 5

Let's go through the calculation again carefully.

Step 1: Convert distances from miles to kilometers

1 mile = 1.60934 kilometers.

1. Minimum Distance from the Sun to Earth: \[ 91.4 \text{ million miles} = 91.4 \times 10^6 \text{ miles} \] \[ = 91.4 \times 10^6 \times 1.60934 \approx 147.1 \text{ million kilometers} \]

2. Maximum Distance from the Sun to Earth: \[ 94.5 \text{ million miles} = 94.5 \times 10^6 \text{ miles} \] \[ = 94.5 \times 10^6 \times 1.60934 \approx 152.1 \text{ million kilometers} \]

Step 2: Calculate the time it takes for light to travel these distances

Using the formula \( d(t) = 300,000t \), where \( d(t) \) is the distance in kilometers and \( t \) is the time in seconds.

1. For Minimum Distance (147.1 million kilometers): \[ d(t) = 147,100,000 \text{ kilometers} \] Setting this equal to the light travel equation: \[ 147,100,000 = 300,000t \] Solving for \( t \): \[ t = \frac{147,100,000}{300,000} \approx 490.33 , \text{seconds} \]

2. For Maximum Distance (152.1 million kilometers): \[ d(t) = 152,100,000 \text{ kilometers} \] Setting this equal to the light travel equation: \[ 152,100,000 = 300,000t \] Solving for \( t \): \[ t = \frac{152,100,000}{300,000} \approx 507 , \text{seconds} \]

Final Answer

So, light takes approximately between 490.3 seconds and 507.0 seconds to travel from the Sun to Earth.

Alternative Conversion Checking

Let’s check the conversion and calculations step-by-step again.

1. Minimum distance:
   • \( 91.4 \times 1.60934 \approx 147.1 , \text{million km} \)
2. Maximum distance:
   • \( 94.5 \times 1.60934 \approx 152.1 , \text{million km} \)

Both conversions look correct.

The times calculated as:

1. Minimum: \( \frac{147,100,000}{300,000} \approx 490.33 \)
2. Maximum: \( \frac{152,100,000}{300,000} \approx 507 \)

Final Rounding:

• Between 490.3 seconds and 507.0 seconds.

If there’s a specific difference in expected results or additional information regarding the nature of the error, please clarify, and I'll seek to address it!