Question

At a temperature of t degrees​ Fahrenheit, sound travels s feet per​ second, where s equals 21.9 StartRoot 5 t plus 2457 EndRoot . During blasting for avalanche control in the​ mountains, sound traveled at a rate of 1121 ​ft/sec. What was the​ temperature?

Answer 1

The​ temperature when sound traveled at 1,121 ft/s was 32.63 degrees fahrenheit.

Explanation:

Hi, well, we need to solve for T the following equation.

`S(T)=21.9√(5T+2,457)`

And we need to substitute S(T) for 1,121. Let´s solve this.

`1,121=21.9√(5T+2457)`

`(1,121)/(21.9) =√(5T+2457)`

`((1,121)/(21.9) )^(2) =(√(5T+2457) )^(2)`

`2620.13=5T+2,457`

`163.13=5T`

`T=32.63`

So, if the speed of sound during the blasting was 1,121ft/s, the tempeture was 32.63 Fahrenheit

Answer 2

32.63 F

Explanation:

The function:

`s = 21.9 \; √( 5 t + 2457 )`

represents sound travels s at feet per​ second, where t is the temperature at Fahrenheit degrees​.

We know that sound traveled at a rate of 1121 ​ft/sec. To find the temperature we need to replace with s value and isolate t for the above function.

`1121 = 21.9 \; √( 5 t + 2457 )`

`(1121)/(21.9) = √( 5 t + 2457 )`

`51.19^2 = 5 t + 2457`

`2620.13 - 2457 = 5 t`

`(163.13)/(5) = t`

`32.63 \; F= t`