To determine if you have been alive for a billion seconds, it’s crucial to find a setup that correctly converts your age from years to seconds. We follow these steps:
1. Convert years to days:
- [tex]\( \frac{365 \text{ days}}{1 \text{ year}} \)[/tex]
2. Convert days to hours:
- [tex]\( \frac{24 \text{ hours}}{1 \text{ day}} \)[/tex]
3. Convert hours to minutes:
- [tex]\( \frac{60 \text{ minutes}}{1 \text{ hour}} \)[/tex]
4. Convert minutes to seconds:
- [tex]\( \frac{60 \text{ seconds}}{1 \text{ minute}} \)[/tex]
The correct setup would be:
[tex]\[ \frac{\text{ Your age (in years) }}{1} \times \frac{365 \text{ days}}{1 \text{ year}} \times \frac{24 \text{ hours}}{1 \text{ day}} \times \frac{60 \text{ minutes}}{1 \text{ hour}} \times \frac{60 \text{ seconds}}{1 \text{ minute}} \][/tex]
Examining the given options:
1.
[tex]\[ \frac{\text{ Your age (in years) }}{1} \cdot \frac{365 \text{ days }}{1 \text{ year }} \cdot \frac{1 \text{ hour }}{24 \text{ days }} \cdot \frac{60 \text{ min }}{1 \text{ hr }} \cdot \frac{1 \text{ sec }}{60 \text{ min }} \][/tex]
- This option incorrectly converts days to hours (should be [tex]\(\frac{24 \text{ hours}}{1 \text{ day}}\)[/tex]).
2.
[tex]\[ \frac{\text { Your age(in years) }}{1} \cdot \frac{1 \text { year }}{365 \text { days }} \cdot \frac{24 \text { hrs }}{1 \text { day }} \cdot \frac{1 \text { hour }}{60 \text { min }} \cdot \frac{60 \text { sec }}{1 \text { nin }} \][/tex]
- This option actually has the correct unit conversions, despite the typo “nin” which was likely meant to be "min".
3.
[tex]\[ \frac{\text { Your age (in years) }}{1} \cdot \frac{1 \text { year }}{36 \text { days }} \cdot \frac{1 \text { day }}{24 \text { hrs }} \cdot \frac{1 \text { hour }}{60 \text { min }} \cdot \frac{1 \text { unin }}{80 \text { sec }} \][/tex]
- This option has incorrect conversion factors (36 days in a year, "unin" for unit conversion).
4.
[tex]\[ \frac{\text { Your age (in years) }}{1} \cdot \frac{365 \text { days }}{1 \text { year }} \cdot \frac{24 \text { hours }}{1 \text { day }} \cdot \frac{60 \text { min }}{1 \text { howr }} \frac{60 \text { soc }}{1 \text { min }} \][/tex]
- This option has typos ("howr" and "soc" instead of hour and sec).
Given these observations, none of these options are entirely correct due to various issues like incorrect conversion factors and typographical errors.
Answer: None of these are correct.
