At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine which equation correctly models the situation where the time [tex]\( t \)[/tex] it takes to clean up a park varies inversely with the number of volunteers [tex]\( v \)[/tex], we need to follow these steps:
1. Understand inverse variation: When two variables vary inversely, their product is constant. In this case, the time [tex]\( t \)[/tex] and the number of volunteers [tex]\( v \)[/tex] vary inversely, so [tex]\( t \cdot v \)[/tex] is a constant.
Mathematically, [tex]\( t \cdot v = k \)[/tex], where [tex]\( k \)[/tex] is the constant of variation.
2. Use the given values: We are given that it takes 7 volunteers [tex]\( v = 7 \)[/tex] to clean up the park in 1.25 hours [tex]\( t = 1.25 \)[/tex].
3. Calculate the constant [tex]\( k \)[/tex]:
[tex]\[ k = t \cdot v = 1.25 \cdot 7 = 8.75 \][/tex]
4. Formulate the equation: Since [tex]\( t \cdot v = 8.75 \)[/tex], we can write [tex]\( t \)[/tex] in terms of [tex]\( v \)[/tex]:
[tex]\[ t = \frac{8.75}{v} \][/tex]
5. Compare with the given options:
- A. [tex]\( t = \frac{8.25}{v} \)[/tex]
- B. [tex]\( t = \frac{8.75}{v} \)[/tex]
- C. [tex]\( t = \frac{7.25}{v} \)[/tex]
- D. [tex]\( t = \frac{5.75}{v} \)[/tex]
From our calculation, the correct equation that models the situation is:
[tex]\[ t = \frac{8.75}{v} \][/tex]
Thus, the correct option is [tex]\( \boxed{B} \)[/tex].
1. Understand inverse variation: When two variables vary inversely, their product is constant. In this case, the time [tex]\( t \)[/tex] and the number of volunteers [tex]\( v \)[/tex] vary inversely, so [tex]\( t \cdot v \)[/tex] is a constant.
Mathematically, [tex]\( t \cdot v = k \)[/tex], where [tex]\( k \)[/tex] is the constant of variation.
2. Use the given values: We are given that it takes 7 volunteers [tex]\( v = 7 \)[/tex] to clean up the park in 1.25 hours [tex]\( t = 1.25 \)[/tex].
3. Calculate the constant [tex]\( k \)[/tex]:
[tex]\[ k = t \cdot v = 1.25 \cdot 7 = 8.75 \][/tex]
4. Formulate the equation: Since [tex]\( t \cdot v = 8.75 \)[/tex], we can write [tex]\( t \)[/tex] in terms of [tex]\( v \)[/tex]:
[tex]\[ t = \frac{8.75}{v} \][/tex]
5. Compare with the given options:
- A. [tex]\( t = \frac{8.25}{v} \)[/tex]
- B. [tex]\( t = \frac{8.75}{v} \)[/tex]
- C. [tex]\( t = \frac{7.25}{v} \)[/tex]
- D. [tex]\( t = \frac{5.75}{v} \)[/tex]
From our calculation, the correct equation that models the situation is:
[tex]\[ t = \frac{8.75}{v} \][/tex]
Thus, the correct option is [tex]\( \boxed{B} \)[/tex].
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.