Question
HINT: the constant of proportionality means you are solving for how many feet a diver descends in 1 minute. Set up your equation as "feet(y)/minutes(x)" to find the constant of proportionality.
*
10 points
Captionless Image
3/2
1/16
24
16
*
10 points
Captionless Image
3/2
1/16
24
16
Answers
GPT-4o mini
To find the constant of proportionality for how many feet a diver descends in 1 minute, we need to set up a ratio based on the information you've provided.
The format you've suggested is \[ \text{feet}(y) / \text{minutes}(x) \]. In this case, we can denote \( y \) as the feet descended and \( x \) as the time in minutes.
If we assume that the diver descends \( y \) feet in \( x \) minutes, then the constant of proportionality \( k \) is given by the equation:
\[
k = \frac{y}{x}
\]
To solve for \( k \), we need specific values of \( y \) (feet descended) and \( x \) (time in minutes). However, as per the hints you've provided:
- **3/2**
- **1/16**
- **24**
- **16**
It looks like these numbers might be providing possible values for \( y \) or \( x \).
If we interpret the hint as saying the diver descends 24 feet (likely \( y = 24 \)) in some number of minutes (let's hypothesize \( x = 1 \) minute for simplicity), then we can compute the constant:
1. If \( x = 1 \):
\[
k = \frac{24}{1} = 24
\]
In this example, the diver descends 24 feet in 1 minute, and the constant of proportionality is 24.
If the diver descended 16 feet in 1 minute instead, then:
\[
k = \frac{16}{1} = 16
\]
Without more specific guidance on which values correspond to feet or minutes, please let me know if you have additional information or want to explore more scenarios or combinations.
The format you've suggested is \[ \text{feet}(y) / \text{minutes}(x) \]. In this case, we can denote \( y \) as the feet descended and \( x \) as the time in minutes.
If we assume that the diver descends \( y \) feet in \( x \) minutes, then the constant of proportionality \( k \) is given by the equation:
\[
k = \frac{y}{x}
\]
To solve for \( k \), we need specific values of \( y \) (feet descended) and \( x \) (time in minutes). However, as per the hints you've provided:
- **3/2**
- **1/16**
- **24**
- **16**
It looks like these numbers might be providing possible values for \( y \) or \( x \).
If we interpret the hint as saying the diver descends 24 feet (likely \( y = 24 \)) in some number of minutes (let's hypothesize \( x = 1 \) minute for simplicity), then we can compute the constant:
1. If \( x = 1 \):
\[
k = \frac{24}{1} = 24
\]
In this example, the diver descends 24 feet in 1 minute, and the constant of proportionality is 24.
If the diver descended 16 feet in 1 minute instead, then:
\[
k = \frac{16}{1} = 16
\]
Without more specific guidance on which values correspond to feet or minutes, please let me know if you have additional information or want to explore more scenarios or combinations.