QuestionConvert Celsius $C$ in the range $[-16^{\circ}C, 17^{\circ}C]$ to Fahrenheit $F$ using $C=\frac{5}{9}(F-32)$ . What is the range for $F$ ?

Studdy Solution

STEP 1

Assumptions1. The formula for converting Fahrenheit temperature, F, to Celsius, C, is $C=\frac{5}{9}(-32)$ . . The Celsius temperature ranges from $-16^{\circ}C$ to $17^{\circ}C$ , inclusive.
3. We need to find the range for the Fahrenheit temperature using interval notation.

STEP 2

First, we need to find the Fahrenheit equivalent for the lower limit of the Celsius range, which is $-16^{\circ}C$ . We can do this by rearranging the conversion formula to solve for F.
$= \frac{9}{5}C +32$

STEP 3

Now, plug in the value for the lower limit of the Celsius range to calculate the corresponding Fahrenheit temperature.
$= \frac{9}{5}(-16) +32$

STEP 4

Calculate the Fahrenheit temperature for the lower limit of the Celsius range.
$= \frac{9}{}(-16) +32 =3.2^{\circ}$

STEP 5

Next, we need to find the Fahrenheit equivalent for the upper limit of the Celsius range, which is $17^{\circ}C$ . We can do this by plugging in the value for the upper limit of the Celsius range into the rearranged conversion formula.
$= \frac{9}{5}(17) +32$

STEP 6

Calculate the Fahrenheit temperature for the upper limit of the Celsius range.
$= \frac{9}{5}(17) +32 =62.6^{\circ}$

STEP 7

Now that we have the Fahrenheit equivalents for the lower and upper limits of the Celsius range, we can express the range for the Fahrenheit temperature using interval notation.
The range for the Fahrenheit temperature is $[3.2,62.6]$ .

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QuestionConvert Celsius $C$ in the range $[-16^{\circ}C, 17^{\circ}C]$ to Fahrenheit $F$ using $C=\frac{5}{9}(F-32)$ . What is the range for $F$ ?

Studdy Solution

STEP 1

Assumptions1. The formula for converting Fahrenheit temperature, F, to Celsius, C, is $C=\frac{5}{9}(-32)$ . . The Celsius temperature ranges from $-16^{\circ}C$ to $17^{\circ}C$ , inclusive.
3. We need to find the range for the Fahrenheit temperature using interval notation.

STEP 2

First, we need to find the Fahrenheit equivalent for the lower limit of the Celsius range, which is $-16^{\circ}C$ . We can do this by rearranging the conversion formula to solve for F.
$= \frac{9}{5}C +32$

STEP 3

Now, plug in the value for the lower limit of the Celsius range to calculate the corresponding Fahrenheit temperature.
$= \frac{9}{5}(-16) +32$

STEP 4

Calculate the Fahrenheit temperature for the lower limit of the Celsius range.
$= \frac{9}{}(-16) +32 =3.2^{\circ}$

STEP 5

Next, we need to find the Fahrenheit equivalent for the upper limit of the Celsius range, which is $17^{\circ}C$ . We can do this by plugging in the value for the upper limit of the Celsius range into the rearranged conversion formula.
$= \frac{9}{5}(17) +32$

STEP 6

Calculate the Fahrenheit temperature for the upper limit of the Celsius range.
$= \frac{9}{5}(17) +32 =62.6^{\circ}$

STEP 7

Now that we have the Fahrenheit equivalents for the lower and upper limits of the Celsius range, we can express the range for the Fahrenheit temperature using interval notation.
The range for the Fahrenheit temperature is $[3.2,62.6]$ .

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QuestionConvert Celsius CCC in the range [−16∘C,17∘C][-16^{\circ}C, 17^{\circ}C][−16∘C,17∘C] to Fahrenheit FFF using C=59(F−32)C=\frac{5}{9}(F-32)C=95​(F−32). What is the range for FFF?

Studdy Solution

STEP 1

STEP 2

First, we need to find the Fahrenheit equivalent for the lower limit of the Celsius range, which is −16∘C-16^{\circ}C−16∘C. We can do this by rearranging the conversion formula to solve for F.=95C+32 = \frac{9}{5}C +32=59​C+32

STEP 3

Now, plug in the value for the lower limit of the Celsius range to calculate the corresponding Fahrenheit temperature.=95(−16)+32 = \frac{9}{5}(-16) +32=59​(−16)+32

STEP 4

Calculate the Fahrenheit temperature for the lower limit of the Celsius range.=9(−16)+32=3.2∘ = \frac{9}{}(-16) +32 =3.2^{\circ}=9​(−16)+32=3.2∘

STEP 5

Next, we need to find the Fahrenheit equivalent for the upper limit of the Celsius range, which is 17∘C17^{\circ}C17∘C. We can do this by plugging in the value for the upper limit of the Celsius range into the rearranged conversion formula.=95(17)+32 = \frac{9}{5}(17) +32=59​(17)+32

STEP 6

Calculate the Fahrenheit temperature for the upper limit of the Celsius range.=95(17)+32=62.6∘ = \frac{9}{5}(17) +32 =62.6^{\circ}=59​(17)+32=62.6∘

STEP 7

Now that we have the Fahrenheit equivalents for the lower and upper limits of the Celsius range, we can express the range for the Fahrenheit temperature using interval notation.The range for the Fahrenheit temperature is [3.2,62.6][3.2,62.6][3.2,62.6].

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QuestionConvert Celsius $C$ in the range $[-16^{\circ}C, 17^{\circ}C]$ to Fahrenheit $F$ using $C=\frac{5}{9}(F-32)$ . What is the range for $F$ ?

First, we need to find the Fahrenheit equivalent for the lower limit of the Celsius range, which is $-16^{\circ}C$ . We can do this by rearranging the conversion formula to solve for F.
$= \frac{9}{5}C +32$

Now, plug in the value for the lower limit of the Celsius range to calculate the corresponding Fahrenheit temperature.
$= \frac{9}{5}(-16) +32$

Calculate the Fahrenheit temperature for the lower limit of the Celsius range.
$= \frac{9}{}(-16) +32 =3.2^{\circ}$

Next, we need to find the Fahrenheit equivalent for the upper limit of the Celsius range, which is $17^{\circ}C$ . We can do this by plugging in the value for the upper limit of the Celsius range into the rearranged conversion formula.
$= \frac{9}{5}(17) +32$

Calculate the Fahrenheit temperature for the upper limit of the Celsius range.
$= \frac{9}{5}(17) +32 =62.6^{\circ}$

Now that we have the Fahrenheit equivalents for the lower and upper limits of the Celsius range, we can express the range for the Fahrenheit temperature using interval notation.
The range for the Fahrenheit temperature is $[3.2,62.6]$ .