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Numerical Series Expansion
Mathematicians, scientists, and engineers often need solutions for difficult to unsolvable equations in order to progress in their work. Fortunately, through various methods of numerical and polynomial series expansions, some of the most problematic equations can be approximated to easily workable forms. Please post all questions regarding the various expansions and series, such as the Taylor and Maclaurin series expansions, the binomial expansion, and the geometric expansion, as well as the rules that govern them, into this category.
274 Questions
Why to use a converging and diverging nozzle in a steamturbine?
I tried to answer this question 4 times but WikiAnswers won't accept the code word to submit it, even though it is correct all 4 times. Converging / diverging nozzles are used with compressible fluids (gases, including steam) to increase their velocity. The converging section (cross-sectional area decreasing in the direction of flow) increases the velocity until it reaches the velocity of sound in the gas (sonic velocity - "Mach 1"). At that point, further reduction in area would slow the gas down, but increasing the cross-sectional area in the direction of further flow allows the gas to expand and increase its velocity to supersonic. If you only had a converging nozzle the maximum speed of the gas could only be subsonic or sonic. The diverging portion of the nozzle needs to be added to achieve supersonic speeds. The converging-diverging nozzle (also known as DeLaval nozzle) is used in steam turbines, most if not all rocket engines and all supersonic wind tunnels.
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Actually, gas flowing though a diverging nozzle LOSES velocity but gains pressure, and it is pressure in the impinging stream the turbine needs, not its velocity.
What is ungrouped data in statistics?
Ungrouped data in statistics refers to raw, individual data points that have not been sorted or organized into any specific groups or categories. This type of data is often presented in a list format and may require further analysis or manipulation to draw meaningful insights or conclusions.
Sample of a very short story-plot summary?
A young girl discovers a mysterious portal in her backyard that leads to a magical kingdom. She embarks on a journey to rescue the kingdom from an evil sorcerer, learning about courage and friendship along the way. In the end, she unlocks her true potential and saves the kingdom from destruction.
Why was there no 1994 World Series?
The 1994 World Series was canceled due to a players' strike that began on August 12, 1994, and led to the remainder of the season being canceled, including the World Series. This was the first time in 90 years that the World Series was not played.
What is the objective for numerical maths?
The objective is to provide approximate solutions for problems that don't have a traditional (exact) solution. For example, numerical integration can provide definite integrals in cases where you can't find an exact solution via an antiderivative. Note that in this example, you can get the answer as exact as you want - that is, you can make the error as small as you want (but not zero).
What is the pattern 1-5-1-15-45-1?
One possible answer is:
Un = (-3n5 + 38n4 - 159n3 + 250n2 - 90n - 30)/6
Why you use series expansion ie Taylor or maclaron or any other series during solving problems?
Some functions cannot be evaluated by normal means and you need an infinite series to get approximate answers.
What does an binomial expansion do?
Binomial Expansion makes it easier to solve an equation. It brings an equation of something raised to a power down to a solveable equation without parentheses.
How do you tell if a geometric series diverges or con verges?
If the absolute value of the common multiple is less than 1 then it converges and, if not, it diverges.
How do you get numbers 8 9 and 12 by using four 5's?
The answer depends on what mathematical operations are permitted.
One set of solutions is:
8 = 5!/(5+5+5)
9 = 5 + 5 - 5/5
12 = .5*5!/sqrt(5*5)
How many degress are there in one-sixth of a circle?
There are 360 degrees in a circle, therefore 1/6 of a circle is 60 degrees.
How do you find the sum of a series of numbers?
There is no simple answer. There are simple formulae for simple sequences such as arithmetic or geometric progressions; there are less simple solutions arising from Taylor or Maclaurin series. But for the majority of sequences there are no solutions.
The expression "acyclic number" is not recognised: additional context may help.
