Question

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.

Answer 1

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

Answer 2

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.