Answer:
This does not make sense.
Step-by-step explanation:
Just because you are a musician does not mean you play the guitar.
You can play the piano and a trumpet, but not be able to play a guitar!
Option D, 5^9 is the correct answer
A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.
![\frac{dT}{dt} = \alpha(T -52)](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdt%7D%20%3D%20%5Calpha%28T%20-52%29%20)
B) Find general solution by separating variables and integrating
![\int\frac{dT}{T-52} = \alpha \int dt \\ ln (T-52) = \alpha t + C \\ T = C e^{\alpha t} +52](https://tex.z-dn.net/?f=%5Cint%5Cfrac%7BdT%7D%7BT-52%7D%20%3D%20%5Calpha%20%5Cint%20dt%20%20%20%5C%5C%20%20ln%20%28T-52%29%20%3D%20%5Calpha%20t%20%2B%20C%20%20%5C%5C%20%20T%20%3D%20C%20e%5E%7B%5Calpha%20t%7D%20%2B52)
:
C) Initial condition is t=0, T = 87
![87 = C +52 \\ C = 35](https://tex.z-dn.net/?f=87%20%3D%20C%20%2B52%20%5C%5C%20%20C%20%3D%2035)
D) Total time elapsed is 10 minutes, new temperature is 84
![84 = 35 e^{10\alpha} +52](https://tex.z-dn.net/?f=84%20%3D%2035%20e%5E%7B10%5Calpha%7D%20%2B52)
solve for alpha
![e^{10\alpha} =\frac{32}{35} \\ \alpha = \frac{ln(32/35)}{10} \\ \alpha = -.00896](https://tex.z-dn.net/?f=%20e%5E%7B10%5Calpha%7D%20%3D%5Cfrac%7B32%7D%7B35%7D%20%20%5C%5C%20%20%5Calpha%20%3D%20%5Cfrac%7Bln%2832%2F35%29%7D%7B10%7D%20%5C%5C%20%20%5Calpha%20%3D%20-.00896)
E) Temperature function is:
![T = 35 e^{-.00896 t} +52](https://tex.z-dn.net/?f=T%20%3D%2035%20e%5E%7B-.00896%20t%7D%20%2B52)
solving for t
![t = \frac{ln (\frac{T-52}{35})}{-.00896}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bln%20%28%5Cfrac%7BT-52%7D%7B35%7D%29%7D%7B-.00896%7D)
Plug in T = 98.6
![t = -31.95](https://tex.z-dn.net/?f=t%20%3D%20-31.95)
This is approximately 32 minutes before he arrived or about 1:20 AM
Answer:P(2) = 2(2)³ - 2(2)²- 3
= 16 - 8 - 3
= 5
Remainder or value of P(2) = 5
Quotient = (2x³- 2x² - 3)/ x-2 = 2x² + 2x + 4
Step-by-step explanation:
Answer:
81
Step-by-step explanation:
just do it step by step adding them together.