To answer the questions, we can use the line of best fit equation provided:
y = 6.2x + 0.2
where:
- \( y \) represents the distance the sloth has moved in feet,
- \( x \) represents the time in minutes.
Question 9
To find how far the sloth has moved after 3 minutes, substitute \( x = 3 \) into the equation:
\[ y = 6.2(3) + 0.2 \]
Calculating this:
\[ y = 18.6 + 0.2 = 18.8 \]
Rounding to the nearest foot:
The sloth will have moved 19 feet in 3 minutes.
Question 10
To determine how many minutes it will take for the sloth to travel 37 feet, we need to solve for \( x \) when \( y = 37 \):
\[ 37 = 6.2x + 0.2 \]
First, subtract 0.2 from both sides:
\[ 37 - 0.2 = 6.2x \] \[ 36.8 = 6.2x \]
Now, divide both sides by 6.2 to solve for \( x \):
\[ x = \frac{36.8}{6.2} \approx 5.903225806451613 \]
Rounding to the nearest tenth:
It will take the sloth approximately 5.9 minutes to travel 37 feet.
Summary of Answers:
- Question 9: The sloth will have moved 19 feet in 3 minutes.
- Question 10: It will take the sloth approximately 5.9 minutes to travel 37 feet.
1 answer