#29. The speed of sound in air,s, in meters per second , is related to the temperature, t, in degrees Celsius, by the formula s= √401(273+ t). How much greater is the speed of sound on a day when the temperature is 30°C than on a day when the temperature is -20°C? Express you answer to the nearest meter per second.
First we have to find the speed of sound on a day when the temperature is 30°C.
To find the answer we have to use the formula s=√401(273+ t)
s= √401(273+ t)
s= √401(273+ 30)
To find the answer we have to use BEDMAS
273+30= 303
s= √401(303)
s= √121503
s=348.5728044
Then we have to find the speed of sound on a day when the temperature is -20°C
To find the answer we have to use the formula s= √401(273+ t)
s= √401(273+ t)
s= √401(273+ -20°C)
To find the answer we have to use BEDMAS
273+(-20)= 253
s= √401(253)
s= √101453
s= 318.5168755
Now that we have found the speed of sound for both temperatures, next we subtract.
348.5728044- 318.5168755= 30.0559289
Since the question says to round to the nearest meter we have to round
30.0559289= 30
The speed of sound is greater by 30m/s on a day that the temperature is 30°C than on a day that is -20°C.
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