MATH SOLVE

5 months ago

Q:
# Tell whether x and y are in a proportional relationship. If so, find the unit rate.Let y be the temperature x hours after midnight. The temperature is 60 degrees Fahrenheit at midnight and decreases 2 degrees Fahrenheit every 1/2 hour.

Accepted Solution

A:

Answer:y = 60 - 4x-4°F per hourStep-by-step explanation:We have x hours after midnight the temperature is y. Now, the temperature is 60°F at midnight and decreases 2°F every 1/2 hours.
So, the relation between x and y can be written as y = a - bx ....... (1)
Now, at x = 0, y = 60.
Hence, a =60. {From equation (1)} and y = 60 - bx ...... (2)
Again at x =0.5, y = 60-2 = 58.
Hence, from equation (2), 58 = 60 - b(0.5), ⇒ b = [tex]\frac{2}{0.5}[/tex] = 4
Therefore, the final relation between x and y is, y = 60 - 4x ...... (3)
So, we can conclude that the relation between x and y is not proportional but linear and the unit rate of change of temperature with respect to time is -4°F per hour. (Answer)