Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Let's tackle this problem by examining each given expression to determine which one correctly converts the erosion rate from centimeters per year to millimeters per day.
### Given Erosion Rate
The initial erosion rate is given as [tex]\( 4 \text{ centimeters per year} \)[/tex].
### Conversion Factors
- We need to convert centimeters to millimeters. Since [tex]\( 1 \text{ centimeter} = 10 \text{ millimeters} \)[/tex], the conversion factor is [tex]\( \frac{10 \text{ mm}}{1 \text{ cm}} \)[/tex].
- We also need to convert years to days. Since [tex]\( 1 \text{ year} = 365 \text{ days} \)[/tex], the conversion factor is [tex]\( \frac{1 \text{ year}}{365 \text{ days}} \)[/tex].
Now let's evaluate each of the given expressions step-by-step.
### Option 1
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{1 \text{ year}}{365 \text{ days}} \][/tex]
- First, convert centimeters to millimeters: [tex]\( 4 \text{ cm} \times \frac{10 \text{ mm}}{1 \text{ cm}} = 40 \text{ mm} \)[/tex].
- Then convert years to days: [tex]\( 40 \text{ mm per year} \times \frac{1 \text{ year}}{365 \text{ days}} = \frac{40 \text{ mm}}{365 \text{ days}} \approx 0.1095890410958904 \text{ mm per day} \)[/tex].
### Option 2
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{1 \text{ mm}}{10 \text{ cm}} \times \frac{1 \text{ year}}{365 \text{ days}} \][/tex]
- First, convert centimeters to millimeters incorrectly: [tex]\( 4 \text{ cm} \times \frac{1 \text{ mm}}{10 \text{ cm}} = 0.4 \text{ mm} \)[/tex].
- Then convert years to days: [tex]\( 0.4 \text{ mm per year} \times \frac{1 \text{ year}}{365 \text{ days}} = \frac{0.4 \text{ mm}}{365 \text{ days}} \approx 0.0010958904109589042 \text{ mm per day} \)[/tex].
### Option 3
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{1 \text{ cm}}{10 \text{ mm}} \times \frac{365 \text{ days}}{1 \text{ year}} \][/tex]
- First, the conversion factor for millimeters and centimeters is inverted: [tex]\( 4 \text{ cm} \times \frac{1 \text{ cm}}{10 \text{ mm}} = 0.4 \text{ cm} \)[/tex].
- Then multiply by the number of days per year [tex]\( 0.4 \text{ mm} \times 365 \approx 146 \text{ mm per day} \)[/tex], which is logically incorrect because it increases the rate significantly.
### Option 4
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{365 \text{ days}}{1 \text{ year}} \][/tex]
- First, convert centimeters to millimeters [tex]\( 4 \text{ cm} \times \frac{10 \text{ mm}}{1 \text{ cm}} = 40 \text{ mm} \)[/tex].
- Then multiply by the number of days per year [tex]\( 40 \text{ mm} \times 365 = 14600 \text{ mm per day} \)[/tex], which again significantly increases the rate, hence incorrect.
### Conclusion
The expression that gives the correct unit and the numerical value is:
[tex]\[ \frac{4 \text{ cm }}{1 \text{ year }} \times \frac{10 \text{ mm }}{1 \text{ cm }} \times \frac{1 \text{ year }}{365 \text{ days }} \][/tex]
This results in an erosion rate of approximately [tex]\( 0.1096 \text{ mm per day} \)[/tex], thus confirming that the correct option is Option 1.
### Given Erosion Rate
The initial erosion rate is given as [tex]\( 4 \text{ centimeters per year} \)[/tex].
### Conversion Factors
- We need to convert centimeters to millimeters. Since [tex]\( 1 \text{ centimeter} = 10 \text{ millimeters} \)[/tex], the conversion factor is [tex]\( \frac{10 \text{ mm}}{1 \text{ cm}} \)[/tex].
- We also need to convert years to days. Since [tex]\( 1 \text{ year} = 365 \text{ days} \)[/tex], the conversion factor is [tex]\( \frac{1 \text{ year}}{365 \text{ days}} \)[/tex].
Now let's evaluate each of the given expressions step-by-step.
### Option 1
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{1 \text{ year}}{365 \text{ days}} \][/tex]
- First, convert centimeters to millimeters: [tex]\( 4 \text{ cm} \times \frac{10 \text{ mm}}{1 \text{ cm}} = 40 \text{ mm} \)[/tex].
- Then convert years to days: [tex]\( 40 \text{ mm per year} \times \frac{1 \text{ year}}{365 \text{ days}} = \frac{40 \text{ mm}}{365 \text{ days}} \approx 0.1095890410958904 \text{ mm per day} \)[/tex].
### Option 2
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{1 \text{ mm}}{10 \text{ cm}} \times \frac{1 \text{ year}}{365 \text{ days}} \][/tex]
- First, convert centimeters to millimeters incorrectly: [tex]\( 4 \text{ cm} \times \frac{1 \text{ mm}}{10 \text{ cm}} = 0.4 \text{ mm} \)[/tex].
- Then convert years to days: [tex]\( 0.4 \text{ mm per year} \times \frac{1 \text{ year}}{365 \text{ days}} = \frac{0.4 \text{ mm}}{365 \text{ days}} \approx 0.0010958904109589042 \text{ mm per day} \)[/tex].
### Option 3
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{1 \text{ cm}}{10 \text{ mm}} \times \frac{365 \text{ days}}{1 \text{ year}} \][/tex]
- First, the conversion factor for millimeters and centimeters is inverted: [tex]\( 4 \text{ cm} \times \frac{1 \text{ cm}}{10 \text{ mm}} = 0.4 \text{ cm} \)[/tex].
- Then multiply by the number of days per year [tex]\( 0.4 \text{ mm} \times 365 \approx 146 \text{ mm per day} \)[/tex], which is logically incorrect because it increases the rate significantly.
### Option 4
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{365 \text{ days}}{1 \text{ year}} \][/tex]
- First, convert centimeters to millimeters [tex]\( 4 \text{ cm} \times \frac{10 \text{ mm}}{1 \text{ cm}} = 40 \text{ mm} \)[/tex].
- Then multiply by the number of days per year [tex]\( 40 \text{ mm} \times 365 = 14600 \text{ mm per day} \)[/tex], which again significantly increases the rate, hence incorrect.
### Conclusion
The expression that gives the correct unit and the numerical value is:
[tex]\[ \frac{4 \text{ cm }}{1 \text{ year }} \times \frac{10 \text{ mm }}{1 \text{ cm }} \times \frac{1 \text{ year }}{365 \text{ days }} \][/tex]
This results in an erosion rate of approximately [tex]\( 0.1096 \text{ mm per day} \)[/tex], thus confirming that the correct option is Option 1.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
