A metal stays solid at Fahrenheit temperatures below 1796.4 degrees. Determine (in terms of an inequality) those Celsius temperatures for which the metal stays solid. Use the formula F= 9/5 C + 32.
To determine the Celsius temperatures for which the metal stays solid, we need to convert the given Fahrenheit temperature of 1796.4 degrees into Celsius. We can use the formula F = (9/5)C + 32 to do this.
First, we subtract 32 from both sides of the formula:
F - 32 = (9/5)C
Next, we multiply both sides by (5/9) to isolate C:
(5/9)(F - 32) = C
Now, we substitute the given Fahrenheit temperature of 1796.4 degrees into the equation:
(5/9)(1796.4 - 32) = C
Simplifying the equation, we get:
(5/9)(1764.4) = C
C ≈ 980.22
Therefore, the Celsius temperature for which the metal stays solid is approximately 980.22 degrees.
In terms of an inequality, the Celsius temperatures for which the metal stays solid can be expressed as:
C ≤ 980.22
To determine the Celsius temperatures for which the metal stays solid, we need to translate the given Fahrenheit temperature into Celsius using the formula F = (9/5)C + 32.
To find the Celsius temperature, we need to isolate C in the formula.
First, subtract 32 from both sides of the equation:
F - 32 = (9/5)C
Next, multiply both sides of the equation by 5/9 to solve for C:
(5/9)(F - 32) = C
Now, we can substitute the Fahrenheit temperature below which the metal stays solid, which is 1796.4 degrees Fahrenheit, into the equation:
C < (5/9)(1796.4 - 32)
Simplifying:
C < (5/9)(1764.4)
Let's evaluate the inequality further:
C < (5/9) * 1764.4
C < 980.222...
Therefore, the Celsius temperatures for which the metal stays solid can be expressed as C < 980.