Answer:
For any string, we use ![s = xyz](https://tex.z-dn.net/?f=s%20%3D%20xyz)
Explanation:
The pumping lemma says that for any string s in the language, with length greater than the pumping length p, we can write s = xyz with |xy| ≤ p, such that xyi z is also in the language for every i ≥ 0. For the given language, we can take p = 2.
Here are the cases:
- Consider any string a i b j c k in the language. If i = 1 or i > 2, we take
and y = a. If i = 1, we must have j = k and adding any number of a’s still preserves the membership in the language. For i > 2, all strings obtained by pumping y as defined above, have two or more a’s and hence are always in the language.
- For i = 2, we can take and y = aa. Since the strings obtained by pumping in this case always have an even number of a’s, they are all in the language.
- Finally, for the case i = 0, we take
, and y = b if j > 0 and y = c otherwise. Since strings of the form b j c k are always in the language, we satisfy the conditions of the pumping lemma in this case as well.
Answer:
K
Explanation:
For installations where the nonlinear load is huge, most consulting engineers will specify K-rated transformers.
Answer:
q=39.15 W/m²
Explanation:
We know that
Thermal resistance due to conductivity given as
R=L/KA
Thermal resistance due to heat transfer coefficient given as
R=1/hA
Total thermal resistance
![R_{th}=\dfrac{L_A}{AK_A}+\dfrac{L_B}{AK_B}+\dfrac{1}{Ah_1}+\dfrac{1}{Ah_2}+\dfrac{1}{Ah_3}](https://tex.z-dn.net/?f=R_%7Bth%7D%3D%5Cdfrac%7BL_A%7D%7BAK_A%7D%2B%5Cdfrac%7BL_B%7D%7BAK_B%7D%2B%5Cdfrac%7B1%7D%7BAh_1%7D%2B%5Cdfrac%7B1%7D%7BAh_2%7D%2B%5Cdfrac%7B1%7D%7BAh_3%7D)
Now by putting the values
![R_{th}=\dfrac{0.01}{0.1A}+\dfrac{0.02}{0.04A}+\dfrac{1}{10A}+\dfrac{1}{20A}+\dfrac{1}{0.3A}](https://tex.z-dn.net/?f=R_%7Bth%7D%3D%5Cdfrac%7B0.01%7D%7B0.1A%7D%2B%5Cdfrac%7B0.02%7D%7B0.04A%7D%2B%5Cdfrac%7B1%7D%7B10A%7D%2B%5Cdfrac%7B1%7D%7B20A%7D%2B%5Cdfrac%7B1%7D%7B0.3A%7D)
![R_{th}=4.083/A\ K/W](https://tex.z-dn.net/?f=R_%7Bth%7D%3D4.083%2FA%5C%20K%2FW)
We know that
Q=ΔT/R
![Q=\dfrac{\Delta T}{R_{th}}](https://tex.z-dn.net/?f=Q%3D%5Cdfrac%7B%5CDelta%20T%7D%7BR_%7Bth%7D%7D)
![Q=A\times \dfrac{200-40}{4.086}](https://tex.z-dn.net/?f=Q%3DA%5Ctimes%20%5Cdfrac%7B200-40%7D%7B4.086%7D)
So heat transfer per unit volume is 39.15 W/m²
q=39.15 W/m²
1 micro gram of Strontium-90 has an activity of
0.0000053 terabecquerels (TBq),
Explanation:
Given information denotes that .,one gram of Strontium-90 has an activity of 5.3 terabecquerels (TBq)
the activity of 1 micro gram is
1 gram = 1,000,000 micro gram has activities of 5.3 terabecquerels
therefore 1 micro gram has the activity of (5.3 ÷ 1,000,000 = 0.0000053 )
= ![(5.3 ÷ 1,000,000 = 0.0000053 )](https://tex.z-dn.net/?f=%285.3%20%C3%B7%20%201%2C000%2C000%20%3D%200.0000053%20%29)
Hence ., 1 micro gram of Strontium-90 has an activity of
0.0000053 terabecquerels (TBq),