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ad-work [718]
3 years ago
12

A formal power series over R is a formal infinite sum f = X[infinity] n=0 anxn, where the coefficients an ∈ R. We add power seri

es term-by-term, and two power series are the same if all their coefficients are the same. (We don’t plug numbers in for x, because we don’t want to worry about issues with convergence of the sum.) There is a vector space V whose elements are the formal power series over R. There is a derivative operator D ∈ L(V ) defined by taking the derivative term-by-term: D X[infinity] n=0 anxn ! = X[infinity] n=0 (n + 1)an+1xn What are the eigenvalues of D? For each eigenvalue λ, give a basis of the eigenspace E(D, λ). (Hint: construct eigenvectors by solving the equation Df = λf term-by-term.)

Mathematics
1 answer:
Ksivusya [100]3 years ago
5 0

Answer:

Check the explanation

Step-by-step explanation:

where the letter D is the diagonal matrix with diagonal entries λ1,…,λn. Now let's assume V is invertible, that is,  this particular given eigenvectors are linearly independent, you get M=VDV−1.

Kindly check the attached image below to see the step by step explanation to the question above.

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Answer:

The answer is below

Step-by-step explanation:

a) For a normal model the sample size has to be equal or greater than 30 so that it can be a normal distribution.

b) Given that:

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The z score determines how many standard deviations the raw score is above or below the mean. It is given by:

z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }

For x < 10 minutes

z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.8/\sqrt{45} }= -1.68

Therefore from the normal distribution table, P(x < 10) = P(z < -1.68) =  0.0465

7 0
3 years ago
What is the value represented by the letter B on the box plot of data?
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3 years ago
Read 2 more answers
Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min, and its coarseness is such that it forms a pile in the shap
pogonyaev

Answer:

Rate of increase in height =\frac{dh}{dt}=0.3156ft/min

Step-by-step explanation:

we know that volume of a cone is given by

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It is Given that diameter equals height thus we have

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\frac{dV}{dt}=\frac{1}{12}\pi \frac{dh^{3}}{dt}\\\\\frac{dV}{dt}=\frac{1}{12}\pi(3h^{2}\frac{dh}{dt})

Applying values and solving for \frac{dh}{dt} we get

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