If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C = 5(F – 32). On a day when the temperature extremes recorded at a certain weather station differed by 45 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?

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whitneytr12 whitneytr12 · Answer 1 · 2020-04-15T04:56:31+02:00

Answer:

The temperature differs in 25 degrees on the Celsius scale

Explanation:

The relationship between temperatures on the two scales is:

[tex] 9C = 5(F - 32) [/tex]

So, if the temperature recorded differed by 45, then the degrees on the Celsius scale can be calculated as follows:

[tex] F_{1} = \frac{9}{5}(C_{1} + 32) [/tex]

[tex] F_{2} = \frac{9}{5}(C_{2} + 32) [/tex]

Since F₂ - F₁ = 45, we have:

[tex] 45 = \frac{9}{5}(C_{2} + 32) - \frac{9}{5}(C_{1} + 32) [/tex]

[tex] 45 = \frac{9}{5}(C_{2} - C_{1} + 32 - 32) [/tex]

[tex] 45*\frac{5}{9} = C_{2} - C_{1} [/tex]

[tex]C_{2} - C_{1} = 25[/tex]

Therefore, the temperature extremes differ in 25 degrees on the Celsius scale.

I hope it helps you!

oeerivona oeerivona · Answer 2 · 2020-04-15T05:35:43+02:00

Answer:

The number of degrees the temperature extremes differ on the Celsius sale 25 °

Explanation:

Here we have

9 °C = 5(F-32)

On the day the temperature extremes recorded at the weather station differed by 45 ° F we then have

F₂ - F₁ = 45

F₂ = F₁ + 45

C₁ = 5(F₁-32)/9

C₂ = 5(F₂-32)/9

C₂ - C₁ = 5(F₂-32)/9 - 5(F₁-32)/9 = 5(F₂ - F₁)/9 = 5×45/9 = 25

Therefore, the number of degrees the temperature extremes differ on the Celsius sale = 25 °

That is the temperature on the Celsius scale increased by 25 °.