Question
the function m = 25
x+50
gives the saline concentrate of a solution in milliliters when x milliliters of water is mixed with 50 milliliters of a 50% saline solution.
what are the constraints on the variable m in the function
the value of m is restricted to ''blank'' numbers
the constraint on the variable m is written as ''blank''
answer the blank spots with the correct answer.
x+50
gives the saline concentrate of a solution in milliliters when x milliliters of water is mixed with 50 milliliters of a 50% saline solution.
what are the constraints on the variable m in the function
the value of m is restricted to ''blank'' numbers
the constraint on the variable m is written as ''blank''
answer the blank spots with the correct answer.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the function \( m = \frac{25}{x + 50} \), we need to determine the constraints on the variable \( m \).
1. **Identifying the domain of \( x \)**:
- \( x \) represents the amount of water in milliliters. Since volume cannot be negative, \( x \) should be greater than or equal to 0:
\[
x \geq 0
\]
2. **Behavior of the function**:
- As \( x \) increases, \( x + 50 \) also increases, which means \( m \) decreases.
- When \( x = 0 \):
\[
m = \frac{25}{0 + 50} = \frac{25}{50} = 0.5
\]
- As \( x \) approaches infinity, the term \( x + 50 \) increases without bound, which means \( m \) approaches 0:
\[
\lim_{x \to \infty} m = 0
\]
3. **Conclusion on the variable \( m \)**:
- The values of \( m \) are restricted between \( 0 \) and \( 0.5 \).
Given this analysis, we can fill in the blanks:
- The value of \( m \) is restricted to **non-negative numbers** (since \( m \) cannot be negative).
- The constraint on the variable \( m \) is written as **\( 0 < m \leq 0.5 \)**.
Thus, the final answers are:
- The value of \( m \) is restricted to **non-negative numbers**.
- The constraint on the variable \( m \) is written as **\( 0 < m \leq 0.5 \)**.
1. **Identifying the domain of \( x \)**:
- \( x \) represents the amount of water in milliliters. Since volume cannot be negative, \( x \) should be greater than or equal to 0:
\[
x \geq 0
\]
2. **Behavior of the function**:
- As \( x \) increases, \( x + 50 \) also increases, which means \( m \) decreases.
- When \( x = 0 \):
\[
m = \frac{25}{0 + 50} = \frac{25}{50} = 0.5
\]
- As \( x \) approaches infinity, the term \( x + 50 \) increases without bound, which means \( m \) approaches 0:
\[
\lim_{x \to \infty} m = 0
\]
3. **Conclusion on the variable \( m \)**:
- The values of \( m \) are restricted between \( 0 \) and \( 0.5 \).
Given this analysis, we can fill in the blanks:
- The value of \( m \) is restricted to **non-negative numbers** (since \( m \) cannot be negative).
- The constraint on the variable \( m \) is written as **\( 0 < m \leq 0.5 \)**.
Thus, the final answers are:
- The value of \( m \) is restricted to **non-negative numbers**.
- The constraint on the variable \( m \) is written as **\( 0 < m \leq 0.5 \)**.
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