Without the aid of the Wronskian, determine whether the given set of functions is linearly independent or linearly dependent on the indicated interval.

a. f1(x) = ln x, f2(x) = ln x^5, (0, [infinity])
b. f1(x) = x^n, f2(x) = x^n + 2, n = 1, 2, \ldots, (−[infinity], [infinity])
c. f1(x) = x, f2(x) = x + 8, (−[infinity], [infinity])
d. f1(x) = cos(x + π), f2(x) = sin x, (−[infinity], [infinity])

Answers

Answer 1

Answer and Step-by-step explanation:

Solution:

(a) The function. f1(x) = ln x, f2(x) = ln x^5 is linearly independent or not.

According to “Linear independent theorem: if two functions f1and f2 are linearly dependent if one can be represent as the constant multiple of other.

f1 = n. f2

Consider given function:

f1(x) = lnx f2(x) = lnx5

(b) Set of function f1(x) = x^n, f2(x) = x^n + 2, is linearly independent or not on the interval [-∞, ∞].

According to “Linear independent theorem: if two functions f1and f2 are linearly dependent if one can be represent as the constant multiple of other.

f1 = n. f2

Consider the given function:

f1(x) = xn f2(x) = xn+2

(c) f1(x) = x, f2(x) = x + 8, (−[infinity], [infinity])

Function is not linearly independent.

Linear independent theorem states that two functions f1 and f2 are linearly dependent if one can represent as the constant multiple of other.

F1= n.f2

(d) f1(x) = cos(x + π), f2(x) = sin x. [-∞, ∞]

According to “Linear independent theorem: if two functions f1and f2 are linearly dependent if one can be represent as the constant multiple of other.

f1 = n. f2

The given function:

f1(x) = cos(x + π)f2(x)


Related Questions

3(4 + 5y)
Simplify the expression

Answers

Answer:

12 + 15y

Step-by-step explanation:

Multiply 3 by all the variables inside the ()

There are 454 grams in a pound. Convert 330 grams to ounces.

Answers

U have to Substract the numbers and then there your answer

11.6 ounces

330g x 1lb/454g x 16oz/1lb = 11.6 ounces

If the conversion factors are properly set up and all numbers are correct, the unwanted units cancel out leaving the units of the final answer.  (citing my source usa test prep but i worked it out.)

Please help ! :))
Find the equation of a line perpendicular to -3x + y=-5 that contains the point (1,4). Write the equation in slope.

Answers

Answer:

  y = -1/3x + 13/3

Step-by-step explanation:

-3x + y=-5

y = 3x -5

Slope of perpendicular line is the opposite inverse so 3 becomes -1/3.

y-intercept going through point (1, 4):

y = mx + b

4 = -1/3(1) + b

4 = -1/3 + b

b = 13/3

Perpendicular equation of a line:

y = mx + b

y = -1/3x + 13/3

Which relation represents a function? {(0, 3), (2, 4), (0, 6)} {( - 7, 5), ( - 7, 1) ( - 10, 3), ( - 4, 3)} {( 2,0), (6, 2), (2, -2)} {( - 6, 5), ( - 3, 2), (1, 2), (6, 5)}

Answers

Answer:

is it none of the above

Step-by-step explanation:

Please help this is due today!! Question: What is the relationship between the 6s in 660,472?​

Answers

Answer:

The first 6 is in the hundred thousands place.

The second 6 is in the ten thousands place.

Here are the info for the rest of the numbers:

6 = hundred thousands

6 = ten thousands

0 = thousands

,

4 = hundreds

7 = tens

2 = ones

Hope this helps you!

Best of luck!

Help me ASAP please

Answers

from what I remember from what my teacher taught me was that its nonlinear. I'm 98% sure its nonlinear

I'm am so sorry if I get it wrong. I'm apologizing ahead. if you want you can get the points back I dont mind because I feel bad when I get things wrong but I'm pretty sure its non linear

Two companies offer online gaming subscriptions. Company A charges $75 upfront and then $20 a month. Company B does not charge an upfront fee but charges $35 a month. After how many months will the two companies charge the same amount?

Answers

Answer:

After 5 months each company will charge the same amount

Step-by-step explanation:

Math Modeling

The situation raised in the question can be modeled as follows.

Company A charges $75 upfront (flat or fixed fee) plus $20 a month. Being x the number of months of subscription, the total charge Ca is:

Ca = 75 + 20x

Company B charges no upfront fees, and $35 a month. We model its charges Cb as:

Cb = 35x

We want to know the number of months needed to make both companies charge the same amount. We'll do that by equating Ca=Cb:

75 + 20x = 35x

Subtracting 20x:

75 = 35x - 20x

Swapping and simplifying:

15x = 75

Solving:

x=75 / 15

x=5

After 5 months each company will charge the same amount

A recipe says it produces the best summer drink. The recipe calls for cup of lemonade for every 1 cups of iced tea. If 16 cups of the summer drink are made, how many of those are cups of lemonade? Re-create the table to give your answer.

Answers

I think it’s 8 not 100% but I think

the quotient of 9 3/4 and 5/8​

Answers

Answer:

15.6

Step-by-step explanation:

The answer is 15.6 because if you divide 9 3/4 by 5/8, you get 78/5, or 15.6 in decimal form. Hope it helps!

15.6. If you convert 9 3/4 to a decimal, you get 9.75. 5/8 as a decimal would be .625. Divide those, and you get 15.6z

A rectangular room is 4 yards long and 5 yards wide . Lucas is covering the floor with tiles that are 1 square foot . How many tiles will he need ?

Answers

Answer:

I think like 21

Step-by-step explanation:

i think it correct but if it not it okay but alaest I try my best on it

whats the decimal of -3 13/20​

Answers

Step-by-step explanation:

-3 13/20

-3 65/100

-3 0.65

= -3.65

it is -1.95 ! put it on a calculator

Which number
not in scientific notation?
6x10^24
2.01x10^-2
1.3x10^-4
0.5x10^3

Answers

Answer:

It's 0.5x10^3

Step-by-step explanation: A number in scientific notation has to be between 1 an 10. It can't be less than one or 10.

I think the answer would be 0.5x10^3

Use partial quotients to divide. Show your work.
)
​___ group(s) of
​___ group(s) of
​___ group(s) of
0
Add the partial quotients.

Answers

I need more information on what I'm meant to be doing so I can help you because I don't understand the question after I re-read it over and over again.

Malcolm drew a circle with a diameter of d units, a radius of runits, a circumference of C units, and an area of A units. Which of the following could Malcolm use with his circle to define
PI?

HELP ME

Answers

Answer:

c because definition of circumference: the enclosing boundary of a curved geometric figure, especially a circle.

Answer:

C

Step-by-step explanation: water

7b-2/5=6b-7/5 nudfghnkdfbvugyteugdyvbbbvybhjedfs

Answers

Answer:

b=−1

Step-by-step explanation:

The number of suitcases lost by airlines.

Answers

Answer:

4.3 billion

Step-by-step explanation:

What is fo)?
12 only
2 and 3 only
-2, -1, 1, and 2 only
-2, -1, 1, 2 and 12

Answers

9514 1404 393

Answer:

  f(0) = 12 . . . only

Step-by-step explanation:

We don't know your intended meaning of "fo)". If it is supposed to be f(0), that is the value of the function at x=0, in other words, the y-intercept.

The graph of f(x) crosses the y-axis at y=12, so ...

  f(0) = 12

Answer: 4,12

Step-by-step explanation: Gimme points  I counted the lines where the f(x) is located at then found 4 same for y ( I started with X then Y)

Round four hundred seventy-six thousand three hundred twenty-one and fifty thousand eight hundred nine hundred-thousandths to the nearest dollar.

Answers

Answer:

476,321.50

476,322

Step-by-step explanation:

Solve the absolute value equation for n
1-8n +41 + 6 = 34

Answers

Answer:

n=1.85

Step-by-step explanation:

1-8n+41+6=36

-7n+47=36

shift 47 to the other side

-7n=36-47

-7n=-13

n=-13/-7

cancel the negative sign

n=13/7

n=1.85

please mark as brainliest!!!

The linear function f(x) = 0.3x + 76 represents the average test score in your history class, where x is the number of the tests taken. Determine the test average for your history class after completing test 3.
A.
76.9

B.
79.9

C.
76.3

D.
76

Answers

Answer:C

Step-by-step explanation:

The answer is C. 76.3

what equation equivalent to 4x - 6y = 12

Answers

Answer:

12+6y=4x

Step-by-step explanation:

Answer:

y=2/3x−2

Step-by-step explanation:

Find the measure of angle b

Answers

Answer:

I'd say 42 degrees, but I might be wrong.

Step-by-step explanation:

It looks the same as the other labeled angle, which is 42 degrees, so that would make angle b 42 degrees.

A train goes from Springfield, MA to Boston at a speed of 40 mph. On the return journey it moves at a speed of 80 mph. If the return journey takes an hour less than the outward journey, what is the average speed overall of the train?

Answers

Answer:

The answer is 53.3333333

Step-by-step explanation:

first you know that the speed on the way there is 40 mph and the back is 80

lets call the time x On the way there the time would just be X on the way back it would be x-1 because it took one less our

to calculate the distance you need to do speed times time therefor the distance on the way there would be 40x and the way back would be 80x-80

Then I made an equation 40x=80x-80 X=2

so the distance would be 80 miles but to find average speed you need to do total distance over total time so it would be 160 over 3 because the time is 2x-2 x=2 so thats 3

Hope this helps

 

3. Find the precise. or exact. sum of these two numbers. 123+358 = ​

Answers

Answer:

481

Step-by-step explanation:

Dionne Washington wants to sell natural fruit flavored water at her neighborhood block party. She wrote the amount of money she spent as a function of the number of bottles sold. Which set of numbers would be an appropriate domain for Dionne's function?

Answers

Complete question is;

Dionne Washington wants to sell natural fruit flavored water at her neighborhood block party. She wrote the amount of money she spent as a function of the number of bottles sold. Which set of numbers would be an appropriate domain for Dionne’s function?

A) 0, 1, 2, 3, 4, …

B) …, −4, −3, −2, −1, 0

C) …, −3, −2, −1, 0, 1, 2, 3, …

D) …, −3.5, −2.5, −1.5, 0, 1.5, 2.5, 3.5, …

Answer:

Option A: {0,1, 2, 3, 4,....}

Step-by-step explanation:

Domain is simply a set of input while the range is a set of output values.

For example, if we have a function named f(x) = x², the domain will be all possible values of x being inputed while the range will be the value of f(x) for all possible values of x inputed.

Now, from the question, we are told that she wrote the amount of money she spent as a function of the number of bottles sold.

If the number of bottles sold is denoted by "x", it means the function is; f(x).

Now, number of bottles has to be a non-negative whole number or simply a non-negative integer. Thus, the possible values of x are all non-negative whole numbers like, 0,1, 2, 3, 4, 5....

Thus,domain is {0,1, 2, 3, 4,....}

Answer:

A. 0,1,2,3,4,.....

Step-by-step explanation:

Logan is solving this problem:

The cheetah ran 0.05 hours at a rate of 70 mph. How far did the cheetah run?

Logan solves the problem by writing:

d = r t. d = 70.05 miles.

What is wrong with Logan’s work?

A.) Logan used the wrong formula. He should have used A = bh.
B.) Logan did not use parentheses when substituting, and he did not multiply the numbers.
C.) Logan's work is correct.
D.) Logan labeled his answer incorrectly. The correct label is feet.

Answers

Answer:

Logan did not use parentheses when substituting, and he did not multiply the numbers.

Step-by-step explanation:

took the assignment, it was correct.

Answer:

B

Step-by-step explanation:

F(x)=2x+2 solve the inverse when x=4

Answers

The answer is f= 5/2

The value of the x-intercept for the graph of 4x - 5y = 40 is

Answers

Answer: The x intercept is 10   or (10,0)

Step-by-step explanation:

4x - 5y = 40   The x-intercept of a line is when its y coordinate is equal to zero. Input zero into the equation for y and solve for x to find the x intercept.

4x-5(0) = 40

4x + 0  = 40

  4x = 40    

 x=  10

The x intercept is 10   or (10,0)

Divide. Round your answer to the nearest whole number.
5,481 - 0.605

Answers

Answer:

Step-by-step explanation:

It matters what the order is when you do the rounding.

5481 = 5500

0.605 = 1

The rounded answer is 5500 / 1 = 5500

However if you do the question and then round you get a much closer answer.

5481 ÷ 0.605 = 10712

guys help me 3(x−4)≥−2x+3

Answers

Answer:

sensya na bobo den ako e✌

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