Answer:
![\boxed{\sf B. \ All \ real \ numbers}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20B.%20%5C%20All%20%5C%20real%20%5C%20numbers%7D)
Step-by-step explanation:
The domain is all possible values for x.
![f(x)=(\frac{1}{4} )^x](https://tex.z-dn.net/?f=f%28x%29%3D%28%5Cfrac%7B1%7D%7B4%7D%20%29%5Ex)
There are no restrictions on x.
The domain is all real numbers.
Answer:11
Step-by-step explanation:8+5+2+3=18 5+2=7 18-7=11
Hey there!
The answer is D. 1/5
An explanation is in the attached image below.
Hope this helps!
Answer:
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Answer:
![I(t)=\frac{1}{3}(1-e^{-30t})](https://tex.z-dn.net/?f=I%28t%29%3D%5Cfrac%7B1%7D%7B3%7D%281-e%5E%7B-30t%7D%29)
Step-by-step explanation:
We are given that
![\frac{dI}{dt}+\frac{R}{L}I=\frac{V(t)}{L}](https://tex.z-dn.net/?f=%5Cfrac%7BdI%7D%7Bdt%7D%2B%5Cfrac%7BR%7D%7BL%7DI%3D%5Cfrac%7BV%28t%29%7D%7BL%7D)
R=150 ohm
L=5 H
V(t)=10 V
![P=\frac{R}{L}=\frac{150}{5}=30](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BR%7D%7BL%7D%3D%5Cfrac%7B150%7D%7B5%7D%3D30)
![I.F=e^{\int Pdt}=e^{\int 30 dt}=e^{30 t}](https://tex.z-dn.net/?f=I.F%3De%5E%7B%5Cint%20Pdt%7D%3De%5E%7B%5Cint%2030%20dt%7D%3De%5E%7B30%20t%7D)
![I(t)\times I.F=\int e^{30 t}\times 10 dt+C](https://tex.z-dn.net/?f=I%28t%29%5Ctimes%20I.F%3D%5Cint%20e%5E%7B30%20t%7D%5Ctimes%2010%20dt%2BC)
![I(t)\times e^{30 t}=\frac{10}{30}e^{30 t}+C](https://tex.z-dn.net/?f=I%28t%29%5Ctimes%20e%5E%7B30%20t%7D%3D%5Cfrac%7B10%7D%7B30%7De%5E%7B30%20t%7D%2BC)
![I(t)=\frac{1}{3}+Ce^{-30 t}](https://tex.z-dn.net/?f=I%28t%29%3D%5Cfrac%7B1%7D%7B3%7D%2BCe%5E%7B-30%20t%7D)
I(0)=0
Substitute t=0
![0=\frac{1}{3}+C](https://tex.z-dn.net/?f=0%3D%5Cfrac%7B1%7D%7B3%7D%2BC)
![C=-\frac{1}{3}](https://tex.z-dn.net/?f=C%3D-%5Cfrac%7B1%7D%7B3%7D)
Substitute the values
![I(t)=\frac{1}{3}-\frac{1}{3}e^{-30 t}](https://tex.z-dn.net/?f=I%28t%29%3D%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7De%5E%7B-30%20t%7D)
![I(t)=\frac{1}{3}(1-e^{-30t})](https://tex.z-dn.net/?f=I%28t%29%3D%5Cfrac%7B1%7D%7B3%7D%281-e%5E%7B-30t%7D%29)