Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To determine the range of acceptable lengths for the metal rod given that its ideal length is [tex]$20.5 \, \text{cm}$[/tex] and it may vary by at most [tex]$0.045 \, \text{cm}$[/tex], follow these steps:
1. Determine the maximum allowed deviation:
The measured length can vary from the ideal length by [tex]$0.045 \, \text{cm}$[/tex].
2. Calculate the lower limit of the range:
Subtract the maximum deviation from the ideal length:
[tex]\[ 20.5 \, \text{cm} - 0.045 \, \text{cm} = 20.455 \, \text{cm} \][/tex]
3. Calculate the upper limit of the range:
Add the maximum deviation to the ideal length:
[tex]\[ 20.5 \, \text{cm} + 0.045 \, \text{cm} = 20.545 \, \text{cm} \][/tex]
4. Express the range of acceptable lengths:
The acceptable length of the rod should be at least [tex]$20.455 \, \text{cm}$[/tex] and at most [tex]$20.545 \, \text{cm}$[/tex].
Therefore, the range of acceptable lengths for the rod is:
[tex]\[ 20.455 \leq x \leq 20.545 \][/tex]
By comparing this result to the given choices, the correct answer is:
[tex]\[ \boxed{D. \, 20.455 \leq x \leq 20.545} \][/tex]
1. Determine the maximum allowed deviation:
The measured length can vary from the ideal length by [tex]$0.045 \, \text{cm}$[/tex].
2. Calculate the lower limit of the range:
Subtract the maximum deviation from the ideal length:
[tex]\[ 20.5 \, \text{cm} - 0.045 \, \text{cm} = 20.455 \, \text{cm} \][/tex]
3. Calculate the upper limit of the range:
Add the maximum deviation to the ideal length:
[tex]\[ 20.5 \, \text{cm} + 0.045 \, \text{cm} = 20.545 \, \text{cm} \][/tex]
4. Express the range of acceptable lengths:
The acceptable length of the rod should be at least [tex]$20.455 \, \text{cm}$[/tex] and at most [tex]$20.545 \, \text{cm}$[/tex].
Therefore, the range of acceptable lengths for the rod is:
[tex]\[ 20.455 \leq x \leq 20.545 \][/tex]
By comparing this result to the given choices, the correct answer is:
[tex]\[ \boxed{D. \, 20.455 \leq x \leq 20.545} \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.