Question

Can I get one more help please? Thank you!

The velocity of sound in air is given by the equation `v=20sqrt(273+t)` , where `v` is the velocity in meters per second and `t` is the temperature in degrees Celsius. Find the temperature when the velocity is 329 meters per second by graphing the equation. Round the answer to the nearest degree. Show your work

Answer 1

Per given information the equation governing velocity `v` of sound at `t^@C` is

`v=20(273+t)^(1/2)`

Plotting the equation using inbuilt graphing tool `x`-axis representing temperature and `y`-axis representing velocity in `ms^-1` we get the following graph.

We are to find temperature at which `v=329ms^-1`.

Expanding the graph at the point of interest as below:

graph{y=20*(273+x)^(1/2) [-2.8, -2, 328, 330]}

We see that `v=329ms^-1` at `t=-2.4^@C`

`t=-2^@C`, rounded to nearest degree.