As a certain engine's rotation speed increases, its temperature increases at a constant rate.
The table compares the engine's rotation speed (in cycles per second) and its temperature (in degrees Celsius).
rotation speed (cycles per sec) temp (degrees celsius)
--------------------------------------------------------------------------------------------
9 22.2
12 24.6
15 27.0
What is the engine's temp at rest?
What is the engine's temperature at rest?
degrees Celsius
Answers
Given : As a certain engine's rotation speed increases, its temperature increases at a constant rate.
To find : What is the engine's temperature at rest
Solution:
Speed Temperature
9 22.2
12 24.6
15 27.0
Rate of increase of temperature wrt to speed = ( 24.6 - 22.2)/(12 - 9) = 2.4/3 = 0.8
or (27 - 24.6)/(15 - 12) = 2.4/3 = 0.8
Equation of line
y = 0.8x + c
y = Temperature (in degrees Celsius).
x = engine's rotation speed (in cycles per second)
27 = 0.8 * 15 + c
=> 27 = 12 + c
=> c = 15
y = 0.8x + 15
When engine is at rest => x = 0
=> y = 0.8 * 0 + 15
=> y = 15
engine's temp at rest = 15°C
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