Question

The label on the car's antifreeze container claims to protect the car between −40°C and 140°C. To covert Celsius temperature to Fahrenheit temperature, the formula is C equals five ninths times the quantity F minus thirty two.. Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car.

Answer 1

Answer:

-40 < t < 284

Step-by-step explanation:

The antifreeze protects the car between −40°C and 140°C.

Using t for temperature, the compound inequality of the Celsius temperature range is:

-40 < t < 140

The conversion formula is given to find degrees C in given degrees F. We can solve the formula for F, so we get degrees F in terms of degrees C.

C = (5/9)(F - 32)     <------ conversion formula from deg F to deg C

Solve for F:

(9/5)C = F - 32

(9/5)C + 32 = F

F = (9/5)C + 32    <------ conversion formula from deg C to deg F

Now we convert -40 deg C to deg F using the formula we just derived.

F = (9/5)C + 32

F = (9/5)(-40) + 32

F = -72 + 32

F = -40

-40 deg C = -40 deg F

(This is not a mistake or a typo. -40 deg C really is the same as -40 deg F.)

Now we convert 140 deg C to deg F using the formula we just derived.

F = (9/5)C + 32

F = (9/5)(140) + 32

F = 252 + 32

F = 284

140 deg C = 284 deg F

Now we rewrite the compound inequality with Fahrenheit temperatures.

-40 < t < 284