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3 years ago

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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

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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Tyler’s family is using a shipping trailer that is 5 feet tall, 4 feet wide, and 12 feet long to load boxes of apples in. Each b

kogti [31]

Hello.

To get the volume 5184 in3 you can use the dimension 18in x 24in x 12in.

First, you should draw a picture of your shipping container. It is a rectangular prism that is 5 by 12 by 4.

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Those boxes would be stack on the base without any left over space. Now, just figure out how many would go on the next rows. They would be able to stand up and down.

Have a nice day.

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3 years ago

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Which number expresses 6.72 as a fraction in simplest form?

Dimas [21]

The number that expresses 6.72 as a fraction is simplest form is...

6.72= 168/25

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3 years ago

A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normall

Vlad1618 [11]

Answer: (2.54,6.86)

Step-by-step explanation:

Given : A random sample of 10 parking meters in a beach community showed the following incomes for a day.

We assume the incomes are normally distributed.

Mean income : $\mu=\dfrac{\sum^{10}_{i=1}x_i}{n}=\dfrac{47}{10}=4.7$

Standard deviation : $\sigma=\sqrt{\dfrac{\sum^{10}_{i=1}{(x_i-\mu)^2}}{n}}$

$=\sqrt{\dfrac{(1.1)^2+(0.2)^2+(1.9)^2+(1.6)^2+(2.1)^2+(0.5)^2+(2.05)^2+(0.45)^2+(3.3)^2+(1.7)^2}{10}}$

$=\dfrac{30.265}{10}=3.0265$

The confidence interval for the population mean (for sample size <30) is given by :-

$\mu\ \pm t_{n-1, \alpha/2}\times\dfrac{\sigma}{\sqrt{n}}$

Given significance level : $\alpha=1-0.95=0.05$

Critical value : $t_{n-1,\alpha/2}=t_{9,0.025}=2.262$

We assume that the population is normally distributed.

Now, the 95% confidence interval for the true mean will be :-

$4.7\ \pm\ 2.262\times\dfrac{3.0265}{\sqrt{10}} \\\\\approx4.7\pm2.16=(4.7-2.16\ ,\ 4.7+2.16)=(2.54,\ 6.86)$

Hence, 95% confidence interval for the true mean= (2.54,6.86)

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3 years ago

Evaluate the exponent using the power to a power rule.<br><br> (2²a4b7)^3

slega [8]

The answer is 64a^12b^21

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2 years ago

2. Alicia is writing the program for a video game. For one part of the game she uses the rule to move points on the screen.

Gwar [14]

<em>Complete Question:</em>

<em>Alicia is writing the program for a video game. For one part of the game she uses the rule (x,y)->(x-3,y+4) to move points on the screen. </em>

<em>A) what output does the rule give when the input is (-6,0)? </em>

<em>B)What output does the rule give when the input is (3,-4)? </em>

<em>C) Is the rule a function? Explain why it is or why it is not </em>

Answer:

a. The output is (-9,4)

b. The output is (0,0)

c. See Explanation

Step-by-step explanation:

Given

Rule: (x,y)->(x - 3, y + 4)

Solving (a):

Inputs:

$x = -6$

$y = 0$

The outputs is as follows;

$x => x - 3$

$x => -6 - 3$

$x => -9$

$y=> y + 4$

$y=> 0 + 4$

$y=> 4$

Hence:

The output is (-9,4)

Solving (b):

Inputs:

$x = 3$

$y = -4$

The outputs is as follows;

$x => x - 3$

$x=>3-3$

$x = 0$

$y=> y + 4$

$y=>-4+4$

$y=>0$

Hence:

The output is (0,0)

Solving (c):

The function is a rule and the rule is that:

It shifts the graph left by 3 units and up by 4 units

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2 years ago