the water level of a tank every minute since ...
the water level of a tank every minute since it began filling is indicated by segments a, b, and c on the graph below. place the segments in the correct order from the least to the greatest rate of increase in the water level.
Answer
# Explanation:
## Step1: Recall slope formula
The rate of increase is the slope of the line - segment. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
## Step2: Find slope of segment A
For segment A, assume the starting - point is $(0,10)$ and the ending - point is $(2,60)$. Then $m_A=\frac{60 - 10}{2-0}=\frac{50}{2}=25$.
## Step3: Find slope of segment B
For segment B, assume the starting - point is $(2,60)$ and the ending - point is $(6,80)$. Then $m_B=\frac{80 - 60}{6 - 2}=\frac{20}{4}=5$.
## Step4: Find slope of segment C
For segment C, assume the starting - point is $(6,80)$ and the ending - point is $(9,100)$. Then $m_C=\frac{100 - 80}{9 - 6}=\frac{20}{3}\approx6.67$.
## Step5: Compare slopes
Comparing the slopes $m_B = 5$, $m_C\approx6.67$, $m_A = 25$, we have $m_B<m_C<m_A$.
# Answer:
B, C, A