Temperature readings on the Fahrenheit and Celsius scales are related by the formula 𝐶 =
5
9
(𝐹 − 32).
Determine when the temperature reading on the Celsius scale is twice the temperature reading on the
Fahrenheit scale.
C=(F-32)×5/9
Since, C=2F(given)
Hence,
2F=(F-32)×5/9
18F=(F-32)×5
18F=5F-160
13F=-160
F=-160/13
To determine when the temperature reading on the Celsius scale is twice the temperature reading on the Fahrenheit scale, we can use the given formula:
C = (5/9)(F - 32)
We want to find when C is twice the value of F.
Therefore, we can set up the equation:
C = 2F
Substituting the value of C from the first equation into the second equation, we have:
(5/9)(F - 32) = 2F
Now, let's solve for F:
First, distribute the (5/9) to both terms in parentheses:
(5F/9) - (160/9) = 2F
Next, bring all the F terms to one side and the constant terms to the other side:
(5F/9) - 2F = 160/9
Multiply all terms by 9 to eliminate the denominators:
5F - 18F = 160
Combine like terms:
-13F = 160
Divide both sides by -13 to isolate F:
F = 160 / -13
F ≈ -12.308
Therefore, when the temperature reading on the Fahrenheit scale is approximately -12.308 degrees Fahrenheit, the temperature reading on the Celsius scale will be twice that value.
To determine when the temperature reading on the Celsius scale is twice the temperature reading on the Fahrenheit scale, we need to set up an equation using the given formula and solve for the values of Fahrenheit and Celsius.
Let's assume the temperature reading on the Fahrenheit scale is represented by the variable F, and the temperature reading on the Celsius scale is represented by the variable C.
According to the given formula, we have:
C = 5/9 * (F - 32)
To find when the temperature reading on the Celsius scale is twice that of the Fahrenheit scale, we can set up the equation:
C = 2F
Substituting the value of C from the first equation into the second equation, we have:
5/9 * (F - 32) = 2F
We can now solve this equation to find the value of F.
First, let's distribute the 5/9 to F and -32:
5/9 * F - 5/9 * 32 = 2F
Next, let's simplify the equation:
5F/9 - 160/9 = 2F
To get rid of the fractions, we can multiply the entire equation by 9:
9 * (5F/9) - 9 * (160/9) = 9 * (2F)
This simplifies to:
5F - 160 = 18F
Now, let's isolate F by moving the terms with F to one side:
5F - 18F = 160
Simplifying this equation further gives us:
-13F = 160
To solve for F, we'll divide by -13 on both sides:
F = 160 / -13
Using a calculator or doing the division manually, we find that F ≈ -12.3077.
Now that we have the value of F, we can substitute it back into the equation C = 5/9 * (F - 32) to find the value of C.
C = 5/9 * (-12.3077 - 32)
Simplifying this equation gives:
C ≈ -24.6154
Therefore, when the temperature reading on the Celsius scale is twice the temperature reading on the Fahrenheit scale, the Fahrenheit temperature reading is approximately -12.3077 degrees, and the Celsius temperature reading is approximately -24.6154 degrees.