Answer:
(a) [tex]\therefore C=\frac59(F-32)[/tex]
(b)The boiling point of water in Celsius scale is 100°C.
(c)The setting in Celsius scale is 26.7°C.
Step-by-step explanation:
Given that,the formula is
[tex]F=\frac95 C+32[/tex]......(1)
(a)
Given that,
[tex]F=\frac95 C+32[/tex]
[tex]\Rightarrow F-32=\frac95 C+32-32[/tex] [ subtracting 32 from both sides]
[tex]\Rightarrow F-32=\frac95 C[/tex]
[tex]\Rightarrow \frac95 C=F-32[/tex]
[tex]\Rightarrow C=\frac59(F-32)[/tex] ......(2) [Multiplying [tex]\frac59[/tex] ]
[tex]\therefore C=\frac59(F-32)[/tex]
(b)
Given that, the boiling point of water is 212°F.
Putting F=212 in equation (2)
[tex]\therefore C=\frac59(212-32)[/tex]
[tex]\Rightarrow C=\frac59\times 180[/tex]
[tex]\Rightarrow C=5\times 20[/tex]
[tex]\Rightarrow C=100[/tex]
The boiling point of water is 100°C.
(c)
Given that, a house thermostat is set at 80 degree.
Putting F=80 in equation (2)
[tex]\therefore C=\frac59(80-32)[/tex]
[tex]\Rightarrow C=\frac59\times 48[/tex]
[tex]\Rightarrow C\approx26.7[/tex]
The setting in Celsius scale is 26.7°C.
