Find the constant of variation k. Write the answer as an integer or simplified fraction. N varies jointly as t and p. When t is 20 and p is 0.2, N is 80. k = k-0
Find the constant of variation k. Write the answer as an integer or simplified fraction. N varies jointly as t and p. When t is 20 and p is 0.2, N is 80. k = k-0
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 48SE: A conductor needs 5 cellists and 5 violinists to play at a diplomatic event. 10 do this, he ranks...
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## Finding the Constant of Variation
**Objective:** Determine the constant of variation \( k \). Provide the answer as either an integer or a simplified fraction.
### Problem Statement
The variable \( N \) varies jointly as \( t \) and \( p \). Given the values:
- \( t = 20 \)
- \( p = 0.2 \)
- \( N = 80 \)
### Solution
To find the constant \( k \), use the relationship:
\[ N = k \cdot t \cdot p \]
Given:
\[ N = 80 \]
\[ t = 20 \]
\[ p = 0.2 \]
Substitute the values into the equation:
\[ 80 = k \cdot 20 \cdot 0.2 \]
Solve for \( k \):
\[ 80 = k \cdot 4 \]
\[ k = \frac{80}{4} \]
\[ k = 20 \]
Thus, the constant of variation \( k \) is:
\[ k = 20 \]
### Interactive Component
Below the problem statement, there is an interactive box where you can input your answer for \( k \):
\[ k = \boxed{20} \]
For detailed steps and additional practice problems, please refer to the attached exercises.
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Transcribed Image Text:---
## Finding the Constant of Variation
**Objective:** Determine the constant of variation \( k \). Provide the answer as either an integer or a simplified fraction.
### Problem Statement
The variable \( N \) varies jointly as \( t \) and \( p \). Given the values:
- \( t = 20 \)
- \( p = 0.2 \)
- \( N = 80 \)
### Solution
To find the constant \( k \), use the relationship:
\[ N = k \cdot t \cdot p \]
Given:
\[ N = 80 \]
\[ t = 20 \]
\[ p = 0.2 \]
Substitute the values into the equation:
\[ 80 = k \cdot 20 \cdot 0.2 \]
Solve for \( k \):
\[ 80 = k \cdot 4 \]
\[ k = \frac{80}{4} \]
\[ k = 20 \]
Thus, the constant of variation \( k \) is:
\[ k = 20 \]
### Interactive Component
Below the problem statement, there is an interactive box where you can input your answer for \( k \):
\[ k = \boxed{20} \]
For detailed steps and additional practice problems, please refer to the attached exercises.
---
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