A metal stays solid at Fahrenheit temperatures below 1639.8. Determine in terms of an inequality those celsius temperatures for which the metal stays solid. Use the formula F=9/5C+23.
Thank you so very much!
CM<5/9 (1639-32)
To determine the Celsius temperatures for which the metal stays solid, we need to convert the Fahrenheit temperature of 1639.8 to Celsius using the formula F = (9/5)C + 32.
Given: F ≤ 1639.8
Convert the inequality to Celsius:
(9/5)C + 32 ≤ 1639.8
Subtract 32 from both sides:
(9/5)C ≤ 1639.8 - 32
Simplify:
(9/5)C ≤ 1607.8
To isolate C, divide both sides by 9/5:
C ≤ (1607.8) / (9/5)
Simplify:
C ≤ (1607.8) * (5/9)
C ≤ 893.22
So, in terms of an inequality, the Celsius temperatures for which the metal stays solid are C ≤ 893.22.
To determine the Celsius temperatures for which the metal stays solid, we need to convert the given Fahrenheit temperature into Celsius using the formula F = (9/5)C + 23.
First, let's solve the equation for Celsius:
F = (9/5)C + 23
To isolate C, we'll subtract 23 from both sides:
F - 23 = (9/5)C
Now, let's multiply both sides by (5/9) to solve for C:
C = (5/9)(F - 23)
To find the Celsius temperatures, we substitute the inequality F < 1639.8 into the equation above:
C = (5/9)(1639.8 - 23)
Simplifying the equation gives us:
C = (5/9)(1616.8)
We can further simplify by dividing 1616.8 by 9:
C ≈ 179.64
Therefore, the Celsius temperatures for which the metal stays solid are below approximately 179.64 degrees Celsius. In terms of an inequality, this can be written as C < 179.64.