The dimensions of Roy and Roger's sandbox are t² meters by t5 meters. One cubic meter of the sandbox contains 3821 grains of sand. Which of the following expressions represent the amount of grains of sand in the sandbox? O 27t ¹07,21 ○ 9t7²,21 O t¹0², 21 31² ²²1
The dimensions of Roy and Roger's sandbox are t² meters by t5 meters. One cubic meter of the sandbox contains 3821 grains of sand. Which of the following expressions represent the amount of grains of sand in the sandbox? O 27t ¹07,21 ○ 9t7²,21 O t¹0², 21 31² ²²1
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Sandbox Volume and Grain Count Calculation
The dimensions of Roy and Roger’s sandbox are \( t^2 \) meters by \( t^5 \) meters. One cubic meter of the sandbox contains \( 3t^{21} \) grains of sand. Which of the following expressions represent the amount of grains of sand in the sandbox?
#### Options:
1. \( 27t^{10-7}t^{21} \)
2. \( 9t^7t^{21} \)
3. \( t^{10-7}t^{21} \)
4. \( 3t^7t^{21} \) **(Selected)**
#### Explanation:
To determine the correct expression, consider the following steps:
1. Calculate the volume of the sandbox:
- Volume = \( t^2 \times t^5 \)
- Simplified, this is \( t^{2+5} = t^7 \) cubic meters.
2. Calculate the grains of sand in the sandbox:
- Given that 1 cubic meter contains \( 3t^{21} \) grains, the total grains in \( t^7 \) cubic meters is:
\[ \text{Total Grains} = t^7 \times 3t^{21} = 3t^{7+21} = 3t^{28} \]
Therefore, the correct expression representing the amount of grains of sand in the sandbox is \( 3t^{28} \), matching the choice labeled under option 4: \( 3t^7t^{21} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a31e81a-24d8-4563-9559-816217592977%2Fe06b2420-0390-4f41-ba10-e058021d8f33%2Fk9aopts_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Sandbox Volume and Grain Count Calculation
The dimensions of Roy and Roger’s sandbox are \( t^2 \) meters by \( t^5 \) meters. One cubic meter of the sandbox contains \( 3t^{21} \) grains of sand. Which of the following expressions represent the amount of grains of sand in the sandbox?
#### Options:
1. \( 27t^{10-7}t^{21} \)
2. \( 9t^7t^{21} \)
3. \( t^{10-7}t^{21} \)
4. \( 3t^7t^{21} \) **(Selected)**
#### Explanation:
To determine the correct expression, consider the following steps:
1. Calculate the volume of the sandbox:
- Volume = \( t^2 \times t^5 \)
- Simplified, this is \( t^{2+5} = t^7 \) cubic meters.
2. Calculate the grains of sand in the sandbox:
- Given that 1 cubic meter contains \( 3t^{21} \) grains, the total grains in \( t^7 \) cubic meters is:
\[ \text{Total Grains} = t^7 \times 3t^{21} = 3t^{7+21} = 3t^{28} \]
Therefore, the correct expression representing the amount of grains of sand in the sandbox is \( 3t^{28} \), matching the choice labeled under option 4: \( 3t^7t^{21} \).
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