The temperature in degrees Celsius (C) can be converted to degrees Fahrenheit (F) using the formula F(C)= 9/5 C+k, where k is a constant. Find k, if to C=−40ºC corresponds F=−40ºF.
F(C) = 9 / 5 C + k
− 40º F = 9 / 5 ∙ ( - 40°C ) + k
Mathematically:
− 40 = 9 / 5 ∙ ( - 40 ) + k
− 40 = 9 ∙ ( - 40 ) / 5 + k
− 40 = - 360 / 5 + k
− 40 = - 72 + k
Add 72 to both sides
− 40 + 72 = - 72 + k + 72
32 = k
k = 32
To find the value of k, we need to set up and solve an equation using the given information.
From the formula F(C) = (9/5)C + k, we know that if C = -40ºC, then F = -40ºF.
Substituting these values into the formula, we have:
-40 = (9/5)(-40) + k
Simplifying the equation, we get:
-40 = -72 + k
To isolate k, we can add 72 to both sides of the equation:
32 = k
Therefore, the value of k is 32.
To find the value of k in the given formula, we can substitute the given values for Celsius and Fahrenheit into the equation and solve for k.
Given:
C = -40°C
F = -40°F
Using the formula F(C) = (9/5)C + k, we substitute the given values:
-40°F = (9/5)(-40°C) + k
Next, we simplify the equation:
-40°F = -72°C + k
To isolate the variable k, we need to move -72°C to the other side of the equation:
-40°F + 72°C = k
We can convert -40°F to Celsius by using the formula C = (5/9)(F - 32):
C = (5/9)(-40 - 32)
C = (5/9)(-72)
C = -40
Substituting the value of C back into the equation:
-40°F + 72(-40°C) = k
-40°F + (-2880°C) = k
-40°F - 2880°C = k
Therefore, the value of k is -40°F - 2880°C.