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anzhelika [568]
3 years ago
10

The veloctiy of sound in air is given by the equation v=20 times the square root of 273+t where v is the velocity in meters per

second and t is the temperature in degrees Celcius. Find the temperature when the velocity of sound in air is 369 meters per second. Round to the nearest degree.
Mathematics
2 answers:
Nikitich [7]3 years ago
5 0
So we just need to plug in our values and solve
v = 20 \sqrt{273 + t}
we are given v is 369 so we have
369 = 20 \sqrt{273 + x}
now we solve for x.
divide both sides by 20
square both sides
subtract 273 from both sides
369 = 20 \sqrt{273 + x}  \\ 18.45 =  \sqrt{273 + x}  \\ 340.40 = 273 + x \\ x = 67.4
so a temp of about 67 degrees C
kkurt [141]3 years ago
3 0

Answer:

The velocity of sound in air is 369 meters per second at 67 degrees Celcius.

Step-by-step explanation:

The veloctiy of sound in air is given by the equation

v=20\sqrt{273+t}

where v is the velocity in meters per second and t is the temperature in degrees Celcius.

We need find the temperature when the velocity of sound in air is 369 meters per second.

Substitute v=369 in the give equation.

369=20\sqrt{273+t}

Divide both sides by 20.

\frac{369}{20}=\sqrt{273+t}

18.45=\sqrt{273+t}

Taking square both the sides.

(18.45)^2=273+t

340.4025=273+t

Subtract 273 from both the sides.

340.4025-273=t

67.4025=t

t\approx 67

Therefore the velocity of sound in air is 369 meters per second at 67 degrees Celcius.

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