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:
D
Step-by-step explanation:
The formula for the circumference of a circle is 2
r. So if we know that C=60
then we can trace our steps back. We are given that pi remains constant so we are left with the 2r from the formula and a 60. 60/2 =30.
The radius is 30cm
Answer:
4=3/4(-8)+b
Step-by-step explanation:
You have to use the equation Y=mx+b
M is your slope so 3/4
x=-8
Y=4
Then u put it into the equation and get 4=3/4(-8)+b
Hope this helps:)
Answer:
A decimal in the wrong place can change the value of a number COMPLETELY!
Step-by-step explanation:
for example
0.4 can be converted to 40 cents or 2/5, but if you change the decimal 0.04 converts to 4% or 1/25.
hope this helps!