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Answer :
Final Answer:
The constant of proportionality is found by dividing the cooling capacity by the room area: 4320 BTUs / 270 square feet = 16 BTUs per square foot. If an air conditioner has a cooling capacity of 6400 BTUs, it can cool a room with an area of 400 square feet.
Explanation:
To determine the constant of proportionality, we use the given values for a room of 270 square feet requiring 4320 BTUs. The formula for proportionality is: constant = cooling capacity / room area. Substituting the values: constant = 4320 BTUs / 270 square feet = 16 BTUs per square foot.
Now, to find the area a 6400 BTU air conditioner can cool, we rearrange the formula: room area = cooling capacity / constant. Substituting the values: room area = 6400 BTUs / 16 BTUs per square foot = 400 square feet.
In summary, the constant of proportionality is 16 BTUs per square foot, and the air conditioner with a cooling capacity of 6400 BTUs can cool a room with an area of 400 square feet.
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