For this case we have the following equation:
![l(dB) = 10log( \frac{l}{lo} )](https://tex.z-dn.net/?f=l%28dB%29%20%3D%2010log%28%20%5Cfrac%7Bl%7D%7Blo%7D%20%29)
We must replace the following value in the equation:
![l = 10^8lo](https://tex.z-dn.net/?f=l%20%3D%2010%5E8lo)
Substituting we have:
![l(dB) = 10log( \frac{10^8lo}{lo} )](https://tex.z-dn.net/?f=l%28dB%29%20%3D%2010log%28%20%5Cfrac%7B10%5E8lo%7D%7Blo%7D%20%29)
Simplifying the given expression we have:
![l(dB) = 10log(10^8)](https://tex.z-dn.net/?f=l%28dB%29%20%3D%2010log%2810%5E8%29)
Then, using logarithm properties in base 10, we can rewrite the expression:
![l(dB) = 10(8)](https://tex.z-dn.net/?f=l%28dB%29%20%3D%2010%288%29)
Finally, making the product, the result is:
Answer:
option 4
Answer:
-11.8
Step-by-step explanation:
hope this helps!!!:)
Answer: After 18.05 minutes, the temperature of steel becomes 100 degrees.
Step-by-step explanation:
Since we have given that
Initial temperature = 2500
At t = 0,
we get that
![f(t)=Ce^{-kt}+80\\\\2500=C+80\\\\2500-80=C\\\\2420=C](https://tex.z-dn.net/?f=f%28t%29%3DCe%5E%7B-kt%7D%2B80%5C%5C%5C%5C2500%3DC%2B80%5C%5C%5C%5C2500-80%3DC%5C%5C%5C%5C2420%3DC)
After 2 minutes, the temperature of the steel is 1500 degrees.
so, it becomes,
![1500=2420e^{-2k}+80\\\\1500-80=2420e^{-2k}\\\\\dfrac{1420}{2420}=e^{-2k}\\\\0.587=e^{-2k}\\\\\ln 0.587=-2k\\\\-0.533=-2k\\\\k=\dfrac{0.533}{2}\\\\k=0.266](https://tex.z-dn.net/?f=1500%3D2420e%5E%7B-2k%7D%2B80%5C%5C%5C%5C1500-80%3D2420e%5E%7B-2k%7D%5C%5C%5C%5C%5Cdfrac%7B1420%7D%7B2420%7D%3De%5E%7B-2k%7D%5C%5C%5C%5C0.587%3De%5E%7B-2k%7D%5C%5C%5C%5C%5Cln%200.587%3D-2k%5C%5C%5C%5C-0.533%3D-2k%5C%5C%5C%5Ck%3D%5Cdfrac%7B0.533%7D%7B2%7D%5C%5C%5C%5Ck%3D0.266)
So, We need to find the number of minutes when the temperature of steel would be 100 degrees.
So, it becomes,
![100=2420e^{-0.266t}+80\\\\100-80=2420e^{-0.266t}\\\\20=2420e^{-0.266t}\\\\\dfrac{20}{2420}=e^{-0.266t}\\\\\ln \dfrac{20}{2420}=-0.266t\\\\-4.8=-0.266t\\\\t=\dfrac{4.8}{0.266}\\\\t=18.05](https://tex.z-dn.net/?f=100%3D2420e%5E%7B-0.266t%7D%2B80%5C%5C%5C%5C100-80%3D2420e%5E%7B-0.266t%7D%5C%5C%5C%5C20%3D2420e%5E%7B-0.266t%7D%5C%5C%5C%5C%5Cdfrac%7B20%7D%7B2420%7D%3De%5E%7B-0.266t%7D%5C%5C%5C%5C%5Cln%20%5Cdfrac%7B20%7D%7B2420%7D%3D-0.266t%5C%5C%5C%5C-4.8%3D-0.266t%5C%5C%5C%5Ct%3D%5Cdfrac%7B4.8%7D%7B0.266%7D%5C%5C%5C%5Ct%3D18.05)
Hence, after 18.05 minutes, the temperature of steel becomes 100 degrees.
Answer: 125 000
Step-by-step explanation:
50^3 is equal to 50 * 50 * 50
or 50 times itself 3 times
which equals 50 * 50 * 50 = 125000