Respuesta :
Answer:
32.63 F
Step-by-step explanation:
The function:
[tex]s = 21.9 \; \sqrt{ 5 t + 2457 }[/tex]
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.
[tex]1121 = 21.9 \; \sqrt{ 5 t + 2457 }[/tex]
[tex]\frac{1121}{21.9} = \sqrt{ 5 t + 2457 }[/tex]
[tex]51.19^2 = 5 t + 2457[/tex]
[tex]2620.13 - 2457 = 5 t[/tex]
[tex]\frac{163.13}{5} = t[/tex]
[tex]32.63 \; F= t[/tex]
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.
[tex]S(T)=21.9\sqrt{5T+2,457}[/tex]
And we need to substitute S(T) for 1,121. Let´s solve this.
[tex]1,121=21.9\sqrt{5T+2457}[/tex]
[tex]\frac{1,121}{21.9} =\sqrt{5T+2457}[/tex]
[tex](\frac{1,121}{21.9} )^{2} =(\sqrt{5T+2457} )^{2}[/tex]
[tex]2620.13=5T+2,457[/tex]
[tex]163.13=5T[/tex]
[tex]T=32.63[/tex]
So, if the speed of sound during the blasting was 1,121ft/s, the tempeture was 32.63 Fahrenheit
