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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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1. Over 3 years, how much more does $3000 in a savings account with an APR of 3.2% compounded
Sedbober [7]

Answer:

$1080

Step-by-step explanation:

((3000 \times 0.032) \times 2) \times 3 = 576

convert % to decimal by multiplying 3.2%x100=0.032

then multiply by initial amount 3000x0.032

then multiply by 2 because it's compounding semiannual

then multiply by 3 because it's over a 3 yr period

do the same for the quarterly compound but multiply by 4 because it's quarterly

((3000 \times 0.03) \times 2) \times3 = 1080

over a 3 yr period the quarterly compounded amount will earn:

1080 - 576 = 504

$504 more than the account compounded semiannual

5 0
3 years ago
Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small com
Rasek [7]

Answer:

a) The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

b)

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c) They are respected, as the upper bound of both intervals is below the new FAA recommendations.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve these questions.

Question a:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 100 - 1 = 99

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 1.9842

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.9842\frac{20}{\sqrt{100}} = 4

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 183 - 4 = 179 pounds.

The upper end of the interval is the sample mean added to M. So it is 183 + 4 = 187 pounds.

The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

Question b:

Critical value is the same(same sample size and confidence level).

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.9842\frac{23}{\sqrt{100}} = 4.6

The lower end of the interval is the sample mean subtracted by M. So it is 190 - 4.6 = 185.4 pounds.

The upper end of the interval is the sample mean added to M. So it is 190 + 4.6 = 194.6 pounds.

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c. The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).

They are respected, as the upper bound of both intervals is below the new FAA recommendations.

7 0
3 years ago
Write the expression 12-2 in simplest form.
Vesnalui [34]

well, if the expression is simply 12-2, then you would do simple subtraction and your answer would be 10. that would be simplest form. you cannot take it any simpler because there is nothing else left now. your answer would be 10.

3 0
3 years ago
The mean of this data set: (5, 8, 1, 7, 4, 3, 2, 2)= 5
Softa [21]

Step-by-step explanation:

4

Add all to get 32

Divide by the number of items which is 8

answer =4

4 0
2 years ago
Read 2 more answers
A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute.
Sphinxa [80]
In 1 minute, bison runs 3520 feet
In 60 minutes, the bison would run
3520*60 feet
211200 feet per hour.
These are equivalent to;
40 miles per hour since 1 mile is equivalent to 5280 feet.
The bison is faster by 10 miles per hour
6 0
3 years ago
Read 2 more answers
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