Answer:
A compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car is [tex]-40^\circ F<\frac{9C}{5}+32<284^\circ F[/tex]
Step-by-step explanation:
Given : The label on the car's antifreeze container claims to protect the car between -40°C and 140°C. To convert Celsius temperature to Fahrenheit temperature, the formula is [tex]C=\frac{5}{9} (F-32)[/tex].
To find : Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car ?
Solution :
First we convert formula in terms of Celsius and get formula of Fahrenheit,
[tex]C=\frac{5}{9} (F-32)[/tex]
[tex]\frac{9C}{5}=(F-32)[/tex]
[tex]\frac{9C}{5}+32=F[/tex]
Now, Converting Celsius into Fahrenheit,
-40°C into °F,
[tex]F=\frac{9(-40)}{5}+32[/tex]
[tex]F=-72+32[/tex]
[tex]F=-40^\circ F[/tex]
140°C into °F,
[tex]F=\frac{9(140)}{5}+32[/tex]
[tex]F=252+32[/tex]
[tex]F=284^\circ F[/tex]
As, [tex]-40^\circ C<\frac{5}{9} (F-32)<140^\circ C[/tex].
Similarly, [tex]-40^\circ F<\frac{9C}{5}+32<284^\circ F[/tex].
Therefore, A compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car is [tex]-40^\circ F<\frac{9C}{5}+32<284^\circ F[/tex]
