What's the relationship between C and F?

Algebra Level 1

In middle school, I was taught that -40 degrees Celsius is -40 degrees Fahrenheit. Is there any other temperature such that the two scales have the same numerical value?

Yes No

View wiki
Pi Han Goh by Pi Han Goh , 30, Malaysia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Munem Shahriar
Aug 30, 2018

We know that T C 5 = T F − 32 9 \dfrac{T_C}5 = \dfrac{T_F - 32}9 . Assume that T C = T F = x T_C = T_F = x .

x 5 = x − 32 9 ⇒ 9 x = 5 x − 160 ⇒ 4 x = − 160 ⟹ x = − 40 \begin{aligned} \dfrac x5 & = \dfrac{x - 32}9 \\ \Rightarrow 9x & = 5x - 160 \\ \Rightarrow 4x & = - 160 \\ \implies x & = - 40 \\ \end{aligned}

Hence x = − 4 0 ∘ C = − 4 0 ∘ F x = - 40^\circ C = -40^\circ F is unique.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
David Vreken
Jun 6, 2018

The conversion formula between Fahrenheit F F and Celsius C C is C = 5 9 ( F − 32 ) C = \frac{5}{9}(F - 32) . To have the same numerical value, F = C F = C , so C = 5 9 ( C − 32 ) C = \frac{5}{9}(C - 32) , which solves to C = − 40 C = -40 (and no other value).

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...