In a certain city, the temperature normally ranges from 20 degrees Fahrenheit and 80 degrees Fahrenheit. Write a compound inequality that describes abnormal temperature ranges for this city and then convert that inequality to degrees Celsius. F=9/5C+32
explain how the inequality -4'c> -9'c describes how the temperatures are related
Well, in this certain city, the abnormal temperature range can be described using a compound inequality as follows:
-80 ≤ F ≤ 20 or 80 ≤ F ≤ 212
Now, let's convert this inequality to degrees Celsius:
Using the formula F = (9/5)C + 32, we can rearrange it to get C = (5/9)(F - 32).
So, the abnormal temperature range in degrees Celsius would be:
-62.2 ≤ C ≤ -6.7 or 26.7 ≤ C ≤ 100
To write a compound inequality that describes abnormal temperature ranges for this city, we need to consider that abnormal temperatures fall outside the normal temperature range of 20 to 80 degrees Fahrenheit.
Let's say that x represents the temperature in degrees Fahrenheit. The compound inequality can be written as:
x < 20 or x > 80
This represents temperatures that are either less than 20 degrees Fahrenheit or greater than 80 degrees Fahrenheit, which fall outside the normal range.
Now, to convert this inequality to degrees Celsius, we can use the formula F = (9/5)C + 32, where F represents degrees Fahrenheit and C represents degrees Celsius.
Let's solve the formula for C, which will help us convert the inequality.
F = (9/5)C + 32
Subtract 32 from both sides:
F - 32 = (9/5)C
Multiply both sides by 5/9 to isolate C:
(5/9)(F - 32) = C
Now we can substitute the compound inequality for F and solve for C:
(5/9)(x - 32) = C
Therefore, the compound inequality in degrees Celsius would be:
(5/9)(x - 32) < (5/9)(20 - 32) or (5/9)(x - 32) > (5/9)(80 - 32) [Converting the inequality]
Simplifying the inequality further is possible, but this is the general form of the compound inequality in degrees Celsius.
20 < T < 80 , where T is temperature in Fahrenheit
Since C = (5/9)(F - 32) , I will let you do the conversion