Respuesta :
Answer:
(a) [tex]F=1.8C+32[/tex]
(b) [tex]C=\frac{F-32}{1.8}[/tex]
(c) -40 degree
Step-by-step explanation:
(a)
A linear function is of the form [tex]y=mx+b[/tex]
Given:
Temperature in Fahrenheit is given as 'F' and in Celsius is 'C'.
So, the linear relation is of the form [tex]F = mC + b[/tex], where, 'm' and 'b' are real numbers.
Now, when [tex]C=15,F=59[/tex]
When [tex]C=75,F=167[/tex]
Now, plugging these values in the above equation and solving for 'm' and 'b', we have:
[tex]59=15m+b\\167=75m+b\\(-)\\---------- \\-108=-60m\\\\m=\frac{108}{60}=1.8[/tex]
Now, plugging 'm' value in first equation to get 'b' value, we have:
[tex]b=59-15\times 1.8=32[/tex]
Therefore, the equation expressed for 'F' in terms of 'C' is given as:
[tex]F=1.8C+32[/tex]
(b)
In order to solve for 'C', we isolate 'C' from the above equation.
Add -32 both sides. This gives,
[tex]F-32=1.8C[/tex]
Divide both sides by 1.8. This gives,
[tex]C=\frac{F-32}{1.8}[/tex]
Therefore, the equation solved for 'C' is [tex]C=\frac{F-32}{1.8}[/tex]
(c)
Let the temperature be 'x' when F = C.
Therefore, [tex]F = x, C = x[/tex]
[tex]x=\frac{x-32}{1.8}\\\\1.8x=x-32\\\\1.8x-x=-32\\\\0.8x=-32\\\\x=\frac{-32}{0.8}=-40[/tex]
Therefore, at -40 degree, the temperature in Fahrenheit equals that in Celsius.
