Each of the following temperature ranges is in degrees Fahrenheit. Use the formula 𝐹=95𝐶+32 to find the corresponding temperature range in degrees Celsius (using interval notation and assume inclusion).𝑎. at or below 95°F(−∞,663] 𝑏. at or above -13°F 𝑐. at or below 131°F 𝑑. at or above 32°F
Question
Each of the following temperature ranges is in degrees Fahrenheit. Use the formula 𝐹=95𝐶+32 to find the corresponding temperature range in degrees Celsius (using interval notation and assume inclusion).𝑎. at or below 95°F(−∞,663] 𝑏. at or above -13°F 𝑐. at or below 131°F 𝑑. at or above 32°F
Solution
a. To convert 95°F to Celsius using the formula 𝐹=95𝐶+32, we first subtract 32 from 95, which gives us 63. Then we divide 63 by 95, which gives us approximately 0.663. So, the corresponding temperature range in degrees Celsius for at or below 95°F is (-∞, 0.663].
b. To convert -13°F to Celsius, we subtract 32 from -13, which gives us -45. Then we divide -45 by 95, which gives us approximately -0.474. So, the corresponding temperature range in degrees Celsius for at or above -13°F is [-0.474, ∞).
c. To convert 131°F to Celsius, we subtract 32 from 131, which gives us 99. Then we divide 99 by 95, which gives us approximately 1.042. So, the corresponding temperature range in degrees Celsius for at or below 131°F is (-∞, 1.042].
d. To convert 32°F to Celsius, we subtract 32 from 32, which gives us 0. Then we divide 0 by 95, which gives us 0. So, the corresponding temperature range in degrees Celsius for at or above 32°F is [0, ∞).
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