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:
Three ways that engineers explore possible solutions in their projects are;
1) Prototyping
2) Simulation
3) Calculations
Explanation:
1) Prototyping is the process of experimental testing of samples of design, or model of a product with the possibility of the inclusion of control of parameters in order to determine the workability of a solution.
2) Simulation is the process of creating an imitation of a situation, operation or process which can be used to determine if a particular solution will be able to work as required in the simulated environment of a problem.
3) Calculations are used to find preliminary results of particular situations, their cause and effects based on scientific laws, theories and hypothesis such that the factor of the problem is equated with the available ideas to find the best possible solution.
Answer:
Common Uses: Boxwood is well-suited for carving and turning, and the tree's diminutive size restricts it to smaller projects. Some common uses for Boxwood include: carvings, chess pieces, musical instruments (flutes, recorders, woodwinds, etc.), rulers, handles, turned objects, and other small specialty items.If you want a small, compact, low-growing shrub to form a hedge that serves as an accent or border along your walkway, fence line or planting beds, dwarf boxwood varieties are the best pick. The "Dwarf English" boxwood (Buxus sempervirens “Suffruticosa”) creates a border hedge approximately 1 to 2 feet in height.
Explanation:
When an object has the same number of positive and negative charges, its electrical charge will become neutral.
What is an electric charge?
When the matter is put in an electromagnetic field, it has an electric charge, which causes it to experience a force. A positive or negative electric charge can exist.
Now when the two equal magnitude charges with opposite natures come together they become neutral.
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