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KatRina [158]
3 years ago
9

Suppose f(x) is a function such that for some positive integer n, f has n linearly dependent derivatives. In other words, if f(x

),f′(x),…,f(n−1)(x),f(n)(x) are all linearly dependent functions, then f(x) is expressible in terms of a,xk,eax,sin(ax),cos⁡(ax), and any combination of such functions, where a is a constant and k is a positive integer. Prove this statement

Mathematics
1 answer:
Anon25 [30]3 years ago
6 0

Answer:

See explaination for the prove of the statement.

Step-by-step explanation:

To establish this prove, lets refer back to what we already know.

We know that "If the set of reactions {d1,d2,d3,......dn} in a vector space V over a field f be linearly dependent, then atleast one of the vectors of the set can be expressed as a linear combination of the remaining others.

Please kindly go to attachment for a detailed step by step explaination of the prove.

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A motel rents double rooms at $34 per day and single rooms at $26 per day. If 26 rooms were rented one day for a total of $804,
lubasha [3.4K]

Answer: 16 double rooms and 10 single rooms were rented.

Step-by-step explanation:

Let x represent the number of double rooms that were rented.

Let y represent the number of single rooms that were rented.

The total number of rooms rented in a day is 26. It means that

x + y = 26

A motel rents double rooms at $34 per day and single rooms at $26 per day. If all the rooms that were rented for one day cost a total of $804, it means that

34x + 26y = 804 - - - - - - - - - - -1

Substituting x = 26 - y into equation 1, it becomes

34(26 - y) + 26y = 804

884 - 34y + 26y = 804

- 34y + 26y = 804 - 884

- 8y = - 80

y = - 80/ - 8 = 10

x = 26 - y = 26 - 10

x = 16

5 0
3 years ago
L is the midpoint of line segment KM. If KL = 2x - 3 and LM = x + 7. find the value of x.
tatyana61 [14]

Answer:

x = 10

Step-by-step explanation:

Since L is the midpoint

KL = LM

2x-3 = x+7

Subtract x from each side

2x-3-x = x+7-x

x-3 = 7

Add 3 to each side

x-3+3 = 7+3

x = 10

4 0
3 years ago
Read 2 more answers
Use the graph below to list the x value(s) where the limits as x approaches from the left and right of those integer values(s) a
kirza4 [7]
<span>the limits as x approaches from the left and right of 1 is not equal.</span>
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3 years ago
Write an equation in point-slope form of the line that passes through (-4,1) and (4,3).
SVEN [57.7K]

Step-by-step explanation:

y-y₁=m(x-x₁) 

1-(-4)=m(4-3)

5=m

5 0
3 years ago
We are continuing to study the difference in average time for completion for the two matching schemes. However, this time we had
IgorLugansk [536]

Answer:

We are 95% confident that the time to completion for the same color method is between 4.617 <u>less</u> to 9.383 <u>less</u> than the different color method.

Step-by-step explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence for the difference in the completion time of treatment is<em> and </em>d<em> is,</em>

<em>CI</em><em> = </em>(-4.617, -9.383)

The parameter of the study is defined as:

treatment_<em>s - </em>treatment_<em>d </em>

Consider the 95% confidence interval, (-4.617, -9.383). The confidence interval consists of all negative values.

This implies that the difference between the completion time of treatment <em>s</em> and <em>d</em> is less than 0, i.e. the completion time of treatment <em>s</em> is less than that for treatment <em>d</em>.

Thus, the complete statement is:

"We are 95% confident that the time to completion for the same color method is between 4.617 <u>less</u> to 9.383 <u>less</u> than the different color method."

7 0
3 years ago
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