n certain conditions, the air temperature drops about 3.6F for each 1,000-foot rise in altitude.
(A) If the temperature at sea level is 65F, write a linear equation that expresses the temperature T in terms of altitude A in thousands of feet.
(B) At what altitude is the temperature 11
F?
(A) To write a linear equation that expresses the temperature T in terms of altitude A in thousands of feet, we can use the given condition that the temperature drops about 3.6F for each 1,000-foot rise in altitude.
Let's assume that at sea level (A = 0), the temperature is T = 65F. As the altitude increases by 1,000 feet (A = 1), the temperature drops by 3.6F.
Therefore, the equation that expresses the temperature in terms of altitude is:
T = 65 - 3.6A
(B) To find the altitude at which the temperature is 11F, we can substitute T = 11 into the equation we obtained in part (A) and solve for A.
11 = 65 - 3.6A
Rearranging the equation, we get:
3.6A = 65 - 11
3.6A = 54
Dividing both sides by 3.6, we have:
A = 54/3.6
A = 15
Therefore, the altitude at which the temperature is 11F is 15,000 feet.
(A) To write a linear equation to express the temperature T in terms of altitude A, we can use the equation of a straight line: y = mx + b, where y is the dependent variable (temperature), x is the independent variable (altitude in thousands of feet), m is the slope of the line, and b is the y-intercept.
Given that the air temperature drops 3.6F for every 1,000-foot rise in altitude, the slope (m) would be -3.6F/1000ft.
At sea level (A = 0), the temperature is 65F. This gives us the y-intercept (b) value of 65.
Therefore, the linear equation that expresses the temperature T in terms of altitude A in thousands of feet is:
T = -3.6A + 65
(B) To find at what altitude the temperature is 11F, we substitute T = 11 into the equation and solve for A:
11 = -3.6A + 65
Subtracting 65 from both sides:
-54 = -3.6A
Dividing both sides by -3.6:
A = 15
Therefore, the altitude at which the temperature is 11F is 15,000 feet.
To write a linear equation expressing the temperature T in terms of the altitude A in thousands of feet, we can use the slope-intercept form of a linear equation: y = mx + b, where y represents the dependent variable (temperature), x represents the independent variable (altitude), m represents the slope of the line, and b represents the y-intercept.
(A) The slope, m, is given as -3.6F per 1,000-foot rise in altitude. This means that for each 1,000-foot increase in altitude, the temperature decreases by 3.6 degrees Fahrenheit. Therefore, the slope, m, is -3.6.
The y-intercept, b, is the value of T when A is 0. In this case, at sea level (A = 0), the temperature is 65°F. Therefore, the y-intercept, b, is 65.
Putting this information together, the linear equation that expresses the temperature T in terms of altitude A is:
T = -3.6A + 65
(B) To find the altitude at which the temperature is 11°F, we can substitute T = 11 into the equation T = -3.6A + 65 and solve for A:
11 = -3.6A + 65
Subtracting 65 from both sides gives:
-54 = -3.6A
Dividing both sides by -3.6 gives:
A = 15
Therefore, the altitude at which the temperature is 11°F is 15,000 feet.