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

Answer:

32.63 F

Step-by-step explanation:

The function:

$s = 21.9 \; \sqrt{ 5 t + 2457 }$

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.

$1121 = 21.9 \; \sqrt{ 5 t + 2457 }$

$\frac{1121}{21.9} = \sqrt{ 5 t + 2457 }$

$51.19^2 = 5 t + 2457$

$2620.13 - 2457 = 5 t$

$\frac{163.13}{5} = t$

$32.63 \; F= t$

Answer 2

Answer:

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

Step-by-step explanation:

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

$S(T)=21.9\sqrt{5T+2,457}$

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

$1,121=21.9\sqrt{5T+2457}$

$\frac{1,121}{21.9} =\sqrt{5T+2457}$

$(\frac{1,121}{21.9} )^{2} =(\sqrt{5T+2457} )^{2}$

$2620.13=5T+2,457$

$163.13=5T$

$T=32.63$

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