Two linearly independent solutions of the differential equation y" - 4y' + 4y = 0 are (Select the correct answer). ii) Write the general solution. a. y, re", y = * Ob. y =eº, y = xenºn | d. y = "", y = xe ey, = e. Yn = xe**

Answers

Answer 1

The given differential equation is y'' - 4y' + 4y = 0. To get two linearly independent solutions, we can use the characteristic equation method.

The characteristic equation for this differential equation is: r^2 - 4r + 4 = 0
This can be factored as (r - 2)^2 = 0. So, the root is r = 2 with multiplicity 2. Since the root has multiplicity 2, the two linearly independent solutions are: y1 = e^(2x) and y2 = x * e^(2x). So, the correct answer is d. y = e^(2x), y = x * e^(2x). To write the general solution of the differential equation, we can combine the linearly independent solutions with arbitrary constants C1 and C2: y(x) = C1 * e^(2x) + C2 * x * e^(2x)

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Related Questions

v divided by 2 + 15 = -4

Answers

Answer:

v = -38

Step-by-step explanation:

v/2 + 15 = -4

Subtract 15 from each side

v/2 + 15-15 = -4-15

v/2 = -19

Multiply by 2

v/2 *2 = -19*2

v = -38

Answer:

v = -38

Step-by-step explanation:

v/2 + 15 = -4

Isolate the variable -->

15-15 --> -4-15 --> 0, -19

v/2  = -19

Multiply both sides by 2 to get rid of the /2

-19 x 2 = -38 =>

v = -38

Hope this helps!

CAN SOMEONE HELP!!!!

CAN SOMEONE HELP!!!!

Answers

Answer:

x int is where the line crosses the x axis. direct variation is proportional, straight line that goes through the origin. slope is the rate of change. y int is where the line crosses the y axis


PLS SOMEONE ANSWER THIS ITS EASY (MCQ)!!!

PLS SOMEONE ANSWER THIS ITS EASY (MCQ)!!!

Answers

Answer:

i think itss B but im not 100 percent sure

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Fill blank boxes with the right answer.

Mrs. Favre sees that the Chicken Joint is having a sale. A small bucket of chicken usually cost $12.00 but today they are giving 30% off the small bucket.

How much will Mrs. Favre save on one small bucket of chicken? $______

What is the discount cost of one small bucket of chicken? $________

What is the discount cost of 5 small buckets? $______

Answers

Answer:

1. $3.60

2. $8.40

3. $42

Step-by-step explanation:

Hope this helps.

Find the values of a, b and c.

Find the values of a, b and c.

Answers

Answer:

∠a= 65°, ∠b= 115°, ∠c= 25°

Step-by-step explanation:

The sum of the angles in a triangle is 180°. This is abbreviated to '∠ sum of ∆'.

∠c +55° +60° +40°= 180° (∠ sum of ∆PQR)

∠c +155°= 180°

∠c= 180° -155°

∠c= 25°

∠a +60° +55°= 180° (∠ sum of ∆PQS)

∠a +115°= 180°

∠a= 180° -115°

∠a= 65°

The sum of the angles on a straight line is 180°. It's abbreviation is 'adj. ∠s on a str. line'.

∠b +∠a= 180° (adj. ∠s on a str. line)

∠b +65°= 180°

∠b= 180° -65°

∠b= 115°

By multiplying 5/3^4 by _________, we get 5^4

Answers

The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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NEED ASAP DUE IN 1 HOUR

NEED ASAP DUE IN 1 HOUR

Answers

10. As 8x = 2x + 60. So x =10
Answer: 10

Explanation:
As 8x=2x+60
x=10

solve for x, 2^2=128

Answers

Answer:

x=32

Step-by-step explanation:

The function F gives the number of copies a book has sold W weeks after that it was published the equation FW equals 500×2 to the W power defines this function 


Select all domains for which the average rate of change could be a good measure for the number of books sold

The function F gives the number of copies a book has sold W weeks after that it was published the equation

Answers

Good models are expected to reflect the number of books sold between zero and w numbers of weeks where w is defined.

What is a domain?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Here, we have

Given: The function f gives the number of copies a book has sold w weeks after it was published. The equation f(w) = 500 * 2^w defines this function.

The following are all domains for which the average rate of change could be a good measure of the number of books sold:

0 ≤ w ≤ 2

0 ≤ w ≤ 7

0 ≤ w ≤ 10

Hence, good models are expected to reflect the number of books sold between zero and w numbers of weeks where w is defined.

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Mai made $95 for 5 hours of work.
At the same rate, how many hours would she have to work to make $133?

Answers

To find the number of hours Mai would have to work at the same rate to make $133, we need to divide $133 by Mai's hourly rate, which is $95/5 hours or $19/hour:


$133 / $19 = number of hours
number of hours * $19 = $133
number of hours = $133 / $19

Solving for number of hours we get:


number of hours = 7.00 hours

So Mai would need to work 7.00 hours at the same rate to make $133.

rewrite 7x 49 using a common factor. 7(x 7) 7(x 49) 7x(x 7) 7x(x 49)

Answers

The correct option is 7(x 7) by highest common factor.

The given expression is 7x49. We have to rewrite the given expression using a common factor.

To rewrite 7x 49 using a common factor, we can factor out 7.

7x49 can be written as 7 × x × 7 × 7.7x49 = 7 × x × 7 × 7

Therefore, the correct option is 7(x 7).

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*
#17) Michelle has 8 pints of milk. How many quarts of milk does she have?

Answers

Answer:

4 quarts

Step-by-step explanation:

1 quart = 2 pints

2 quart = 4 pints

3 quart = 6 pints

4 quarts = 8 pints,

therefore Michelle has 4 quarts of milk

hope i helped you!

PLEASE HELP!! I NEED IT DONE ASAP!!
Write the sentence as an equation:
367 equals the quotient of n and 204

Answers

367= n/204 ????? maybe

367=204n is the correct answer

Is x(x-6)=20 a quadratic equation

Answers

Answer: Yes, it is a quadratic equation

We can distribute the outer x to each term inside

x(x-6) = x^2-6x

So the original equation turns into

x^2-6x = 20

Then you could subtract 20 from both sides to get everything to the same side

x^2-6x-20 = 20-20

x^2-6x-20 = 0

This quadratic equation is in the form ax^2+bx+c = 0 with a = 1, b = -6, c = -20.

The presence of the x^2 term, and having it be the largest exponent, is what makes this a quadratic.

What is the percent decrease when the balance in a bank account goes from $300 to $60?
The percent decrease is 20%.
The percent decrease is 25%.
The percent decrease is 80%.

Answers

80% because its a huge amount the bank account goes to

Answer:

The percent decrease is 80%. or C.

Step-by-step explanation:

Hope this helps! (:

At the museum, 10% of the visitors were senior citizens. If there were 150 senior citizens , what was the total number of visitors?

Answers

Answer:

1500 visitors

Step-by-step explanation:

150=10%

10%*10=100%

So: 150*10=1500 visitors

Answer:

1,500

Step-by-step explanation:

10% of 1,500 is 150 basically

Jean bought 7 packages of sandwich meat.
Each package weighs 23 pound.

Answers

Answer:

Total is 23 times 7 which is 161 pounds

Step-by-step explanation:

you do 7 × 23 and u get 161

and thats how you figure it out

What is the slope below?

What is the slope below?

Answers

Answer :
Positive

(Unless there is any information or problem on there)

Kaylee deposits $500 into a savings account with a 3% intrest rate what will her balance be in 3 years

Answers

Answer: $576.99 in 3 years

Step-by-step explanation:

Answer:

546.36

Step-by-step explanation:

Interest rate calculator

-3x-11= -17 helppppppppppppppppppppp

Answers

Answer: X= -2

Step-by-step explanation: -3x -11 = -17

 add 11 to both sides

 which gives you -6 then you divide by negative 3x which gives you -2

Answer:

Step-by-step explanation:

3x - 11 = -17

3x - 11 + 11 = -17 +11

Simplify:

add the numbers
3x = -6

Divide both sides by the same factor:

\(\frac{3x}{3} = \frac{-6}{3}\)

Simplify (ANSWER):

x= -2

Math school please need help

Math school please need help

Answers

Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

You have an equally likely chance of choosing any integer from 1 through 50. Find the probability of the given event. A perfect square is chosen.

Answers

Answer:

The answer is 0.02

Step-by-step explanation:

1/50=0.02

Austin recorded the weights in pounds, of nine fish in an aquarium. The data is shown in the list.


8.7.5, 7.6, 3, 74, 7.9, 81,2,7.7


Move words to the blanks to describe the best measure of variability for this data.


The best measure of variability for the data is the


because the distribution is

Answers

The best measure of variability for the data is the range because the distribution is scattered.What is the range?The range of data is defined as the difference between the maximum value and the minimum value

. The list of weights is given below:8.7.5, 7.6, 3, 74, 7.9, 81,2,7.7The minimum value in the list is 3, and the maximum value in the list is 81. So, the drange is calculate as follows:Range = Maximum value – Minimum value= 81 – 3= 78The distribution is scattered because the range is relatively large.    

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I don’t get how to divide with big numbers please help

I dont get how to divide with big numbers please help

Answers

Answer:

Step-by-step explanation:

Just think how many times each two number goes into the first two numbers

Your answer would be fourteen

What numbers do i put in the blanks

What numbers do i put in the blanks

Answers

The solutions of the system are y = -8 and x = 9.

What is the system of equations?

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

A system of equations,

5x + 6y = -3   {Equation 1}

8x + 8y = 8     {Equation 2}.

Multiply 8 into equation 1 and multiply by 5 into equation 2,

and subtract the equation,

we get,

40x + 48y - 40x - 40y = -24 - 40

8y = -64

y = -8 and x = 9

Therefore, the solutions are y = -8 and x = 9.

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The asymptote of f(x) = 5(2^x)
*
(Type an equation.)

Answers

Answer:

y=0

Step-by-step explanation:

Remark that exponential functions have horizontal asymptotes .

Graph attached

The asymptote of f(x) = 5(2^x)*(Type an equation.)

Figure B is a scaled copy of Figure A

What is the scale factor from Figure A to Figure B?

Figure B is a scaled copy of Figure AWhat is the scale factor from Figure A to Figure B?

Answers

Answer:

\(1/2\)

Step-by-step explanation:

Because they are scaled copies, the ratios of the sides are equal.

Figure A has a base of 6 units by inspection.

Figure B has a base 3 units by inspection.

So, the scale factor from Figure A to Figure B is \(3/6=\boxed{1/2}\) and we're done!

The scale factor from Figure A to Figure B is 1/2

What is the scale factor from Figure A to Figure B?

Figure A:

Base = 6 units

Height = 4 units

Figure B:

Base = 3 units

Heights = 2 units

Using Base of the shape:

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape

= 3 units / 6 units

= 1/2

Using Height of the shape:

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape

= 2 units / 4 units

= 1/2

Hence, 1/2 is the scale factor from Figure A to Figure B.

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Solve the following inequality. 8.2 – 1 < 15​

Solve the following inequality. 8.2 1 &lt; 15

Answers

Answer:

x < 2

Step-by-step explanation:

Solve this the way you would solve an equation:

\(8x - 1 < 15\\ 8x < 16\\x < 2\)

Answer:

x<2

Step-by-step explanation:

I need the answers noww plz​
all of them plzzz

I need the answers noww plzall of them plzzz

Answers

Answer:

1.

a. 70

b.40

c.130

d.130

e.95

f.115

2.

a.102

b.40

c.80

Hope it helps .

plz mark me brainest and follow me to get the answer faster.

Step-by-step explanation:

1.

a. Isosceles right triangle

a° = 180 - (90 + 20)

a° = 180 - 110 = 70

b. Isosceles acute triangle

a° = 180 - (70+70)

a° = 180 - 140 = 40

c. The three angles inside a triangle always add up to 180°

∠A = 180 - (70 + 60)

∠A = 180 - 130

∠A = 50

so a° = 180 - 50 = 130

d. Isosceles acute triangle

∠A = 180 - (65 + 65)

∠A = 180 - 130

∠A = 50

so a° = 180 - 50 = 130

e. The angles of a rectangle add up to 360°

a° = 360 - (100 + 95 + 70)

a° = 360 - 265

a° = 95

f. The angles of a rectangle add up to 360°

2a° = 360 - (70 + 60)

2a° = 360 - 130

2a° = 230

a° = 115

2.

a. Straight angle is 180°

180 - 141 = 39

so x° = 180 - (39 + 39)

x° = 180 - 78

x° = 102

b. The three angles inside a triangle always add up to 180°

180 - (40 + 60)

180 - 100 = 80

opposite angle

x° = 180 - (80 + 35)

x° = 180 - 115 = 65

c. The angles of a rectangle add up to 360°

(x + 20)° + x° = 360 - (90 + 90)

(x + 20)° + x° = 360 - 180

(x + 20)° + x° = 180

x° = 80

please give me a brainliest answer

What is the square root of -1?

Answers

Answer:

\( \sqrt{i} \)

Step-by-step explanation:

i = -1

This is a complex number

in here we take -1 = i

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