Amy is backpacking with her friends. At the base of a hill, they find the temperature to be 22.8°C. As they reach the summit situated at a height of one kilometer, they notice that the temperature has dipped to 15.2°C.
The temperature decrease with the increase in height is known as the lapse rate. To calculate the lapse rate, we can use the formula:
Lapse Rate = (Temperature at higher point - Temperature at lower point) / Height difference
In this case, the temperature at the base is 22.8°C, the temperature at the summit is 15.2°C, and the height difference is 1 kilometer.
Lapse Rate = (15.2°C - 22.8°C) / 1 km
Lapse Rate = -7.6°C / 1 km
Lapse Rate = -7.6°C/km
Therefore, the lapse rate is -7.6°C per kilometer.
Amy is backpacking with her friends. At the base of a hill, they find the temperature to be 22.8°C. As they reach the summit situated at a height of one kilometer, they notice that the temperature has dipped to 15.2°C.
If h represents the height and T represents the temperature, which of the following equations can be used to model this situation?
To model this situation, we can use a linear equation in the form of:
T = m * h + b
where T represents the temperature, h represents the height, m represents the slope (lapse rate), and b represents the y-intercept (temperature at the base).
In this case, we have the base temperature (T1) as 22.8°C and the summit temperature (T2) as 15.2°C, with a height difference of 1 kilometer (h2 - h1 = 1km). Plugging these values into the equation, we get:
T1 = m * h1 + b
T2 = m * h2 + b
22.8°C = m * h1 + b ...(1)
15.2°C = m * h2 + b ...(2)
From equation (1), we can solve for b:
b = 22.8°C - m * h1
Substituting this value of b into equation (2), we get:
15.2°C = m * h2 + (22.8°C - m * h1)
15.2°C = m * h2 + 22.8°C - m * h1
Simplifying further:
15.2°C - 22.8°C = m * h2 - m * h1
-7.6°C = m * (h2 - h1)
-7.6°C = m * 1km
-7.6°C/km = m
Therefore, the equation that can be used to model this situation is:
T = -7.6°C/km * h + (22.8°C - (-7.6°C/km) * h1)
Amy is backpacking with her friends. At the base of a hill, they find the temperature to be 22.8°C. As they reach the summit situated at a height of one kilometer, they notice that the temperature has dipped to 15.2°C.
If h represents the height and Trepresents the temperature, which of the following equations can be used to model this situation?
A. T-7.6 22.8h
B. T-7.6 + 22.8h
C. T 22.8h + 7.6
D. T-7.6h + 22.8
To model this situation, we can use a linear equation in the form of:
T = m*h + b
where T represents the temperature, h represents the height, m represents the slope (lapse rate), and b represents the y-intercept (temperature at the base).
In this case, we have the base temperature (T1) as 22.8°C and the summit temperature (T2) as 15.2°C, with a height difference of 1 kilometer (h2 - h1 = 1km).
To find the slope (m), we can use the formula:
m = (T2 - T1)/(h2 - h1)
Substituting the given values, we have:
m = (15.2°C - 22.8°C)/(1km)
m = -7.6°C/km
Now, let's substitute the value of m in the equation:
T = -7.6°C/km * h + b
To find the value of b, we can substitute the base temperature (T1) and the height at the base (h1):
22.8°C = -7.6°C/km * h1 + b
Now, let's rearrange the equation to solve for b:
b = 22.8°C + 7.6°C/km * h1
b = 22.8°C - 7.6°C * h1
Therefore, the equation that can be used to model this situation is:
T = -7.6°C/km * h + (22.8°C - 7.6°C * h1)
None of the given options A, B, C, D match the correct equation.