The formula C = 5/9(F-32) can be used to convert Fahrenheit temperatures to Celsius temperatures.
a. Gold is liquid for Celsius temperatures C such that 1063 degrees (less than or equal to) C < 2660 degrees. Find a comparable inequality for Fahrenheit temperatures.
b. Silver is liquid for Celsius temperatures C such that 960.8 degrees (less than or equal to) C < 2180 degrees. Find a comparable inequality for Fahrenheit temperatures.
I am not sure how to solve either of these, so please walk me through the process. Thank you!
Silver is liquid for Celsius temperatures C such that 960.8 degrees (less than or equal to) C < 2180 degrees. Find such an inequality for for the corresponding Fahrenheit temperatures.
To find a comparable inequality for Fahrenheit temperatures for each scenario, we need to solve the given inequality by substituting the Celsius temperature range into the formula C = 5/9(F-32) and then isolating the variable F in each case.
a. Gold is liquid for Celsius temperatures C such that 1063 degrees ≤ C < 2660 degrees.
First, we'll substitute the lower bound of 1063 degrees into the formula:
1063 = 5/9(F - 32)
Next, we'll solve for F:
Multiply both sides by 9/5 to eliminate the fraction:
9/5 * 1063 = F - 32
1913.4 = F - 32
Add 32 to both sides:
F = 1913.4 + 32
F ≈ 1945.4 degrees
Therefore, the lower bound of the comparable inequality for Fahrenheit temperatures is approximately 1945.4 degrees.
Next, we'll substitute the upper bound of 2660 degrees into the formula:
2660 = 5/9(F - 32)
Solving for F:
Multiply both sides by 9/5:
9/5 * 2660 = F - 32
4772 = F - 32
Add 32 to both sides:
F = 4772 + 32
F ≈ 4804 degrees
Therefore, the upper bound of the comparable inequality for Fahrenheit temperatures is approximately 4804 degrees.
Combining the results, the comparable inequality for Fahrenheit temperatures is:
1945.4 degrees ≤ F < 4804 degrees.
b. Silver is liquid for Celsius temperatures C such that 960.8 degrees ≤ C < 2180 degrees.
Using a similar process, we can find the comparable inequality for Fahrenheit temperatures.
First, substitute the lower bound of 960.8 degrees into the formula:
960.8 = 5/9(F - 32)
Solving for F:
Multiply both sides by 9/5:
9/5 * 960.8 = F - 32
1730.56 = F - 32
Add 32 to both sides:
F = 1730.56 + 32
F ≈ 1762.56 degrees
Therefore, the lower bound of the comparable inequality for Fahrenheit temperatures is approximately 1762.56 degrees.
Next, substitute the upper bound of 2180 degrees into the formula:
2180 = 5/9(F - 32)
Solving for F:
Multiply both sides by 9/5:
9/5 * 2180 = F - 32
3924 = F - 32
Add 32 to both sides:
F = 3924 + 32
F ≈ 3956 degrees
Therefore, the upper bound of the comparable inequality for Fahrenheit temperatures is approximately 3956 degrees.
Combining the results, the comparable inequality for Fahrenheit temperatures is:
1762.56 degrees ≤ F < 3956 degrees.
To find the comparable inequality for Fahrenheit temperatures, we can use the given formula:
C = 5/9(F-32)
a. First, let's consider the range for Celsius temperatures: 1063 degrees ≤ C < 2660 degrees.
Step 1: Substitute the lower Celsius temperature (1063 degrees) into the formula to find the corresponding Fahrenheit temperature.
1063 = 5/9(F-32)
Step 2: Simplify the equation.
Multiply both sides by 9/5 to get rid of the fraction.
(9/5)(1063) = F - 32
Step 3: Calculate the Fahrenheit temperature.
(9/5)(1063) = F - 32
1913.4 = F - 32
Step 4: Add 32 to both sides to isolate F.
1913.4 + 32 = F
1945.4 = F
So, the lower Fahrenheit temperature is 1945.4 degrees.
b. Repeat the same steps for the upper range of Celsius temperatures: 960.8 degrees ≤ C < 2180 degrees.
Step 1: Substitute the upper Celsius temperature (2180 degrees) into the formula.
2180 = 5/9(F-32)
Step 2: Simplify the equation.
Multiply both sides by 9/5.
(9/5)(2180) = F - 32
Step 3: Calculate the Fahrenheit temperature.
(9/5)(2180) = F - 32
3944 = F - 32
Step 4: Add 32 to both sides.
3944 + 32 = F
3976 = F
So, the upper Fahrenheit temperature is 3976 degrees.
Combining the results, the comparable inequality for Fahrenheit temperatures is:
1945.4 degrees ≤ F < 3976 degrees.
I will start you on the second.
find the F that is equivalent t0 960.8, then find F that is equivalent to 2180C
C=5/9(F-32)
9/5C=F-32
F= 9.5C+32
Put C in, solve for F