Podcast
Questions and Answers
What does the slope of -3/10 indicate in the context of windchill calculations?
What does the slope of -3/10 indicate in the context of windchill calculations?
- Windchill increases by 3 degrees Fahrenheit for every 10 mph increase in windspeed.
- Windchill remains constant regardless of the windspeed.
- Windchill decreases by 10 degrees Fahrenheit for every 3 mph increase in windspeed.
- Windchill decreases by 3 degrees Fahrenheit for every 10 mph increase in windspeed. (correct)
What is the first step in calculating the linear equation for windchill?
What is the first step in calculating the linear equation for windchill?
- Finding the slope using two data points. (correct)
- Calculating windchill for a specific value.
- Interpreting the slope.
- Determining the reasonable range of windspeed.
How is the y-intercept determined in the windchill calculation process?
How is the y-intercept determined in the windchill calculation process?
- By averaging the two windspeed values provided.
- By setting the slope equal to zero in the model.
- By substituting the slope and a data point into the equation y = mx + b. (correct)
- By calculating the difference between two y-values.
What windchill value is calculated for a windspeed of 60 mph using the model?
What windchill value is calculated for a windspeed of 60 mph using the model?
What difficulty does the document express regarding the topic of linear equations?
What difficulty does the document express regarding the topic of linear equations?
Flashcards
Windchill Calculation
Windchill Calculation
A method to estimate how cold it feels based on temperature and wind speed.
Linear Equation
Linear Equation
An equation that forms a straight line on a graph, modelling a relationship between two variables.
Slope (m)
Slope (m)
The rate of change of one variable with respect to another, in a linear equation (y=mx+b).
Windchill at 60 mph
Windchill at 60 mph
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Reasonable Range of Wind Speeds
Reasonable Range of Wind Speeds
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Study Notes
Linear Equations - Word Problems
- Windchill Example: Windchill is dependent on windspeed.
- Given a windchill of -15°F with 20 mph wind and -24°F with 50 mph wind.
- Find the linear model for windchill.
- Calculate the slope: m = (-24 - (-15))/(50 - 20) = -9/30 = -3/10
- Find the y-intercept (b): Substitute one point into the equation y = mx + b. -15 = (-3/10)(20) + b. Solve for b, which equals -9
- Equation: y = -3/10 x - 9
- Interpretation of slope: For every 10 mph increase in windspeed, windchill decreases by 3°F. The y-intercept represents the windchill when the windspeed is 0 mph.
- Reasonable range: The reasonable range for windspeed could be from 0 to 60 mph.
- Find the windchill for 60 mph wind: Substitute x = 60 into y = -3/10 x - 9. y = -27°F.
Additional Information
- Quiz on Thursday, covering linear equations.
- Office hours for additional help.
- Student expressed difficulty with the material.
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