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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
There is no next since numbers are infinitely dense. This means that there are infinitely many numbers between any two numbers. So, if you suggest that 84.1 is next, you are wrong, because there are infinitely many numbers between 84 and 84.1 and one of them has a better claim to be next. But then, there are infinitely many numbers between 84 and that number and one of these has an ever better claim to be next. And so on.
Therefore, there is no such thing as a next number.
When is a binomial distribution cumulative?
It is cumulative when you add together the probabilities of all events resulting in the given number or fewer successes.
What number when multiplied by 10 is 50 less than 650?
Let's call the number x.
When x is multiplied by 10, it is 50 less than 650. We can write this as:
10x+50 = 650
Now that we have an equation, let's solve it.
Firstly, subtract 50 from both sides
10x = 600
Then, divide both sides by 10
x = 60
The number 60 is 50 less than 650 when it is multiplied by 10.
Is this sequence 10 10.25 10.50625 10.76890625 arithmetic?
No, it is geometric, since each term is 1.025 times the previous.
An example of an arithmetic sequence would be 10, 10.25, 10.50, 10.75, 11.
Where can you find a site for selective school sample test papers?
In the UK, selective state schools use National Foundation for Educational Research (NFER) exams whereas independent selective schools exams are set by the Independent Schools Examinations Board (ISEB). Their web sites can offer some samples. More may be obtained from the sites for the individual schools.
What does the number 0408163245576318222527346277 mean?
It does not mean anything specifically. In a particular context it may have some meaning but you have chosen not to share that context with us.
What conditions must be met to use the normal distribution to approximate the binomial distribution?
What is converging and diverging?
Divergent and convergent are both boundaries that form different kinds of landmasses.
What is the proof of newton raphson iterative equation?
Suppose you have a differentiable function of x, f(x) and you are seeking the root of f(x): that is, a solution to f(x) = 0.Suppose x1 is the first approximation to the root, and suppose the exact root is at x = x1+h : that is f(x1+h) = 0.
Let f'(x) be the derivative of f(x) at x, then, by definition,
f'(x1) = limit, as h tends to 0, of {f(x1+h) - f(x1)}/h
then, since f(x1+h) = 0, f'(x1) = -f(x1)/h [approx] or h = -f'(x1)/f(x1) [approx]
and so a better estimate of the root is x2 = x1 + h = x1 - f'(x1)/f(x1).
What is the formula for exponential growth?
It can vary , but it is something along the lines of
G(t) = Ae^(xt)
Where
'G' is growth at time 't'
'A' is a constnt
'e' is the exponential 2.7818....
'x' is the variable factor
't' is the time.
e^(xt) is the exponential raised to the power of 'variable factor multiplied to time'.
What is the Frequency of a free falling object?
The frequency of a free falling object is determined by the rate at which it falls due to gravity. This rate is typically constant (9.8 m/s^2 on Earth) and results in a consistent frequency of oscillation for the object as it free falls.
What is meant by Cauchy's constants?
The refractive index of a substance can be expanded out with a Fourier transform into the Cauchy equation n = A + B/λ2 + C/λ4 where n is the refractive index and λ is the wavelength of the electromagnetic wave in question. The coefficients in this equation, A, B, and C, are called the Cauchy constants and can be figured out experimentally.
What is a example of convergence?
An example of convergence is when a group of friends with differing opinions gradually come to a consensus on where to go for dinner by considering everyone's preferences and finding a common choice that satisfies all parties.
The natural frequencies of an object are the frequencies at which the object tends to vibrate easily. Harmonics are frequencies that are integer multiples of the fundamental frequency. When an object is excited at its natural frequencies, it tends to resonate and produce harmonics of those frequencies.
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.
