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Answer :
To find the Celsius temperature when the Fahrenheit temperature is [tex]\(-30^\circ\)[/tex], you can use the formula that relates Fahrenheit ([tex]\(F\)[/tex]) and Celsius ([tex]\(C\)[/tex]) temperatures:
[tex]\[ F = 1.8 \cdot C + 32 \][/tex]
Here, we need to find [tex]\(C\)[/tex] when [tex]\(F = -30\)[/tex].
1. Start with the formula:
[tex]\[ F = 1.8 \cdot C + 32 \][/tex]
2. Substitute [tex]\(-30\)[/tex] for [tex]\(F\)[/tex] in the formula:
[tex]\[ -30 = 1.8 \cdot C + 32 \][/tex]
3. Solve for [tex]\(C\)[/tex] by isolating it on one side of the equation. First, subtract 32 from both sides:
[tex]\[ -30 - 32 = 1.8 \cdot C \][/tex]
[tex]\[ -62 = 1.8 \cdot C \][/tex]
4. Divide both sides by 1.8 to solve for [tex]\(C\)[/tex]:
[tex]\[ C = \frac{-62}{1.8} \][/tex]
5. Calculate the division:
[tex]\[ C \approx -34.444\][/tex]
6. Round the result to the nearest tenth:
[tex]\[ C \approx -34.4 \][/tex]
So, the Celsius temperature is approximately [tex]\(-34.4^\circ\)[/tex].
[tex]\[ F = 1.8 \cdot C + 32 \][/tex]
Here, we need to find [tex]\(C\)[/tex] when [tex]\(F = -30\)[/tex].
1. Start with the formula:
[tex]\[ F = 1.8 \cdot C + 32 \][/tex]
2. Substitute [tex]\(-30\)[/tex] for [tex]\(F\)[/tex] in the formula:
[tex]\[ -30 = 1.8 \cdot C + 32 \][/tex]
3. Solve for [tex]\(C\)[/tex] by isolating it on one side of the equation. First, subtract 32 from both sides:
[tex]\[ -30 - 32 = 1.8 \cdot C \][/tex]
[tex]\[ -62 = 1.8 \cdot C \][/tex]
4. Divide both sides by 1.8 to solve for [tex]\(C\)[/tex]:
[tex]\[ C = \frac{-62}{1.8} \][/tex]
5. Calculate the division:
[tex]\[ C \approx -34.444\][/tex]
6. Round the result to the nearest tenth:
[tex]\[ C \approx -34.4 \][/tex]
So, the Celsius temperature is approximately [tex]\(-34.4^\circ\)[/tex].
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