Answer:
For any string, we use 
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:
Gravitational Potential =58.914 KJ
Explanation:
We know that
Given mass = 251 kg
Height= 24 m
g is acceleration due to gravity = 
Applying values in the equation we get
Answer:
Implements a reordering of the letters of the alphabet.
Explanation: GIVE ME 5 STARS AND a HEART!!! Those contacts are wired across the rotor so that each contact on the left connects to the contact on the right in some scrambled arrangement. Each rotor, therefore, implements a reordering of the letters of the alphabet, which mathematicians call a permutation.
Answer:
No, they need to be somewhat flexible so that forces such as turbulance don't shear the wing off.
Answer:
a) 
, b) 
Explanation:
a) The counterflow heat exchanger is presented in the attachment. Given that cold water is an uncompressible fluid, specific heat does not vary significantly with changes on temperature. Let assume that cold water has the following specific heat:
The effectiveness of the counterflow heat exchanger as a function of the capacity ratio and NTU is:
The capacity ratio is:
Heat exchangers with NTU greater than 3 have enormous heat transfer surfaces and are not justified economically. Let consider that 
. The efectiveness of the heat exchanger is:
The real heat transfer rate is:
The exit temperature of the hot fluid is:
The log mean temperature difference is determined herein:
The heat transfer surface area is:
Length of a single pass counter flow heat exchanger is:
b) Given that tube wall is very thin, inner and outer heat transfer areas are similar and, consequently, the cold side heat transfer coefficient is approximately equal to the hot side heat transfer coefficient.
