Please find the power series for the given solution and the
radius of convergence.
2y’ + y = 0

Answer:

16404.2 feet

Step-by-step explanation:

1 in = 2.54 cm

1 km = 100000 cm

5 km = 100000*5 = 500000

1 feet = 12 in

500000 cm = 500000/2.54 = 196850.39 in  

196850.39 in = 196850.36 / 12 = 16404.2 feet

97 decibel sound is 2.5 times more intense than a 93 decibel sound

Correct option is C.

Sound intensity also known as acoustic intensity, is defined as the power transmitted by a sound wave per unit area in a direction perpendicular to that area. Sound intensity is the sound power in watts divided by the area (in square meters) covered by the sound. Sound loudness relates the intensity of a particular sound to its strength at the threshold of hearing, measured in decibels (dB).

Given expression for loudness

L = 10 log(I/I₀)

Loudness of two different sounds are

L₁ = 97 decibel and L₂ = 93 decibel.

Let the intensity for the loudness L₁ and L₂ are I₁ and I₂

Then,

L₁ = 10log(I₁/I₀) = 97

⇒ log(I₁/I₀) = 9.7

taking antilog

I₁/I₀ = antilog (9.7)

I₁/I₀ = 5011872336.27271

L₂ = 10log(I₂/I₀) = 93

⇒ log(I₂/I₀) = 9.3

taking antilog

I₂/I₀ = antilog (9.3)

I₂/I₀ = 1995262314.96888

Then,

(I₁/I₀)/(I₂/I₀) = 5011872336.27271/1995262314.96888

I₁/I₂ = 2.51188643 ≈ 2.5

Hence, 2.5 times more intense is 97 decibel sound than 93 decibel sound.

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The total amount in the account at the end of 8 years, if no deposits or withdrawals were made, at 3.5 percent simple interest is $384

The simple interest on an amount is; I  = P × R × T

Where;

I = The simple interest on the amount

P = The principal amount saved

R = The interest rate.

The amount or principal deposited in the account, P = $300

The interest rate on the account, R = 6.5% simple interest

The number of years, which is the time duration of the deposit, or savings, T = 8 years

The interest earned on the account after 8 years is therefore;

Interest, I = $300 × (3.5/100)/year × 8 years = $84

The amount in the account after 8 years, A = P + I

Therefore;

The total amount in the account, A = $300 + $84 = $384

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The measure of angle <3 is 105 degrees

The diagram that completes the question is added as an attachment

The angle is given as

<6 = 75

From the diagram, we have

<3 + <6 = 180 degrees

The above is true by the sum of internal angles between parallel lines

So, we have

<3 + 75 = 180

Subtract 75 from both sides of the equation

So, we have

<3 + 75 - 75 = 180 - 75

Evaluate the like terms

So, we have

<3 = 105

Hence, the measure of angle <3 is 105 degrees

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The area of this circle is equal to 49π square meters.

Mathematically, the circumference of a circle can be calculated by using this formula:

C = 2πr

Where:

Next, we would determine the radius of this circle as follows:

Radius, r = C/2π

Substituting the given parameters into the formula, we have;

Radius, r = 14π/2π

Radius, r = 7 meters.

Mathematically, the area of a circle can be calculated by using this formula:

Area = πr²

Area = π × 7²

Area = π × 49

Area = 49π square meters.

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Answer:

2 numbers

Step-by-step explanation:

4/5 and -4/5

Answer: 20/25 , 8/10 ,24/30 ,40/50 and so on.

Step-by-step explanation ---> not requested.

Answer: x=2,-7

Step-by-step explanation:

= im not good at explaining but yea that's the answer

Answer:

x= 4/3

Step-by-step explanation:

Subtract 3/7 from both sides

-x= 2x-28/7

simplify

-x=2x-4

Subtract 2x from both sides

-3x=4

divide both sides by -3

x= 4/3

The maximum value of the objective function Z = 40x₁ + 5x₂, subject to the constraints x₁ + x₂ ≤ 5 and 6x₁ + x₂ ≤ 20, where x₁, x₂ are integers between 0 and 25, can be found using the branch and bound method.

To solve this problem, we start with an initial solution by considering the constraints and finding the feasible region. Then, we compute the objective function for this initial solution. Next, we branch the problem into subproblems by considering different combinations of x₁ and x₂. We calculate the lower bounds for each subproblem to determine the potential for improvement. We continue branching and bounding until we find the optimal solution with the maximum value of Z.

The branch and bound method systematically explores the solution space, optimizing the objective function by considering different feasible regions. It provides a structured approach to find the optimal solution for linear programming problems.

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(a) The velocity when the particle reaches B is 8 m/s.

(b) The distance between point A and B is 5.33 m.

(c) The value of t when the particle reaches C is 1.63 seconds.

(d) The distance AC​ is 8.7 m.

The velocity when the particle reaches B is calculated as follows;

v = ∫a. dt

where;

v =  ∫(4t . dt)

v = 4t²/2

v = 2t²

v(2) = 2(2)²

v(2) = 8 m/s

Thus, the velocity when the particle reaches B is 8 m/s.

x = ∫v

where;

x = ∫2t². dx

x = ²/₃t³

x(2) = ²/₃(2)³

x(2) = 5.33 m

Thus, the distance between point A and B is 5.33 m.

when the particle reaches point C, final velocity, vf = 0

vf = v + at

where;

0 = 8 - 3t(t)

0 = 8 - 3t²

3t² = 8

t² = 8/3

t² = 2.67

t = √(2.67)

t = 1.63 seconds

x = ∫vf

x = ∫(8 - 3t²)

x = 8t  - t³

x(1.63) = 8(1.63) - (1.63)³

x(1.63) = 8.7 m

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The cost of one daylily is $2.

The cost of one geranium is $1.

Let x be the cost of one daylily and y be the cost of one geranium. We can set up the following system of equations:

```

x + 3y = 12

10x + y = 33

```

We can solve this system of equations by multiplying the first equation by -10 and adding it to the second equation. This gives us:

```

9x = 21

x = 2

```

Substituting this value into either of the original equations, we can solve for y:

```

2 + 3y = 12

3y = 10

y = 3.33

```

Therefore, the cost of one daylily is $2 and the cost of one geranium is $1.

Here is a table showing the steps involved in solving the system of equations:

| Equation | Step | Result |

|---|---|---|

| x + 3y = 12 | Multiply by -10 | -10x - 30y = -120 |

| 10x + y = 33 | Add the two equations | -29y = -87 |

| y = -87 / -29 | Divide both sides by -29 | y = 3 |

| x + 3(3) = 12 | Substitute y = 3 into the first equation | x + 9 = 12 |

| x = 2 | Subtract 9 from both sides | x = 2 |

As you can see, the solution to the system of equations is x = 2 and y = 3. This means that the cost of one daylily is $2 and the cost of one geranium is $1.

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The Dimension Index is 0.322.

The Dimension Index is calculated using the formula:

\[ \text{Dimension Index} = \frac{\text{Actual Value} - \text{Minimum Value}}{\text{Maximum Value} - \text{Minimum Value}} \]

Given that the Actual Value is 8.5, the Minimum Value is 4.0, and the Maximum Value is 19.3, we can plug these values into the formula:

\[ \text{Dimension Index} = \frac{8.5 - 4.0}{19.3 - 4.0} = \frac{4.5}{15.3} \approx 0.294 \]

So, the Dimension Index is approximately 0.294.

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Answer:

p=1/4 or 0.25

Step-by-step explanation:

2p+3=5-6p Subtract 2p from both sides.

-2p       -2p

3=5-8p        Subtract 5 on both sides.

-5 -5

-2=-8p         Divide by -8 on both sides.

/-8  /-8

1/4=p or (as a decimal) 0.25=p

Hope this helps you out!! Have a great day c:

The indefinite integral of \(\int\limits(ln(x))^2\frac{1}{x}dx\) = \(\frac{ln^2(x)}{2}+C\), where C is the constant of integration.

What is the indefinite integral?

The indefinite integral is a fundamental concept in calculus that represents the antiderivative of a function. Given a function f(x), the indefinite integral of f(x) with respect to x is denoted as ∫f(x) dx.

To find the indefinite integral of the expression\(\int\limits(ln(x))^2\frac{1}{x}dx\), we can use integration by parts. Let's proceed with the solution:

Let u=ln(x) and \(dv=\frac{1}{x}dx.\)

Differentiating u with respect to x, we get:

\(du=\frac{1}{x}dx.\)

Integrating dv, we get:

v=ln(x).

Now, we can apply the integration by parts formula:

\(\int\limits u dv=uv-\int\limits v du\)

Substituting the values, we have:

\(\int\limits (ln(x))^2\frac{1}{x}dx=ln(x)ln(x)-\int\limits ln(x)\frac{1}{x}dx\)

Now, let's evaluate the remaining integral on the right side:

\(\int\limits(ln(x))\frac{1}{x}dx\)

Again, applying integration by parts with u=ln(x) and \(dv=\frac{1}{x}dx:\)

\(du=\frac{1}{x}dx\) and v=ln(x)

Using the integration by parts formula:

\(\int\limits u dv=uv-\int\limits v du\)

\(\int\limits (ln(x))\frac{1}{x}dx=ln(x)ln(x)-\int\limits ln(x)\frac{1}{x}dx\)

Notice that we have the same integral on both sides. We can simplify the equation as follows:

\(2\int\limits (ln(x))^2\frac{1}{x}dx=ln(x)ln(x)\)

Now, we solve for

\(\int\limits (ln(x))\frac{1}{x}dx:\\\\\int\limits (ln(x))\frac{1}{x}dx=\frac{ln^2(x)}{2}+C\)

Therefore, the indefinite integral of \(\int\limits(ln(x))^2\frac{1}{x}dx\) is \(\frac{ln^2(x)}{2}+C\), where C is the constant of integration.

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Answer:

5.6ft squared

Step-by-step explanation:

4x7 = 28 divided by 5 which is 5.6

Answer:

X = -14

All you have to do is type in 2(x+5)=(x-4) in to a algebra calculator and you will get -14

Answer:

03.97655 that will be there for answers

An alternative that best describes the language represented by the following regular expression is (A) strings do not have 2 consecutive 0s.

Therefore, an alternative that best describes the language represented by the following regular expression is (A) strings do not have 2 consecutive 0s.

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The complete question is given below:

What alternative best describes the language represented by the following regular expression?

(0∪ε)(1∪10)

Group of answer choices

(A) Strings do not have 2 consecutive 0s.

(B) Strings that only start with 1.

(C) Strings do not have 2 consecutive 1s.

(D) Strings that consist of alternating 0s and 1s.

Answer:

-3.4 or -17/5

Step-by-step explanation:

3 and 2/5= 17/5 or 3.4

-7 and 1/5 = -34/5 or -6.8

Answer:

4r-7

Step-by-step explanation:

-14+7-9r+13r

combine like terms

4r-14+7

combine like terms

4r-7

hope this helped :)

Answer:

-7 + 4r

Step-by-step explanation:

You need to combine like terms for this problem. All the basic numbers(without the r) are added together. -14 + 7 = -7. Then the numbers with the r's are added together. -9r + 13r = 4r. This comes out to -7 + 4r

Answer:

The team scored 7 points a game

Step-by-step explanation:

Answer:

an= a1 +(n-1)*4

Step-by-step explanation:

a1 = 1, a2 =5, a3 = 9, a4= 13,... an= ?

we see that each term is getting bigger so usually that will happen because of addition or multiplication-in our case add 4 to previous term

a1 = 1,

a2 = a1+(2-1) 4 = 1+4 = 5,

a3 = a1 + (3-1)*4 = a1+8 = 1 + 8 = 9,

a4= a1 + (4-1)*4 = a1 + 12 = 1+12= 13,

...

an= a1 +(n-1)*4

The ratio of pens Meredith has to ratio of pens Brody has is 2 : 1

The of pencils Meredith has to ratio of pencils Brody has is 1 : 2

Ratio refers to the number representing a comparison between two named quantities.

Comparison of their ratios of pens to pencils:

Ratio of pens Meredith has to ratio of pens Brody has = 8 pens : 4 pens

= 8 / 4

= 2 / 1

= 2 : 1

Ratio of pencils Meredith has to ratio of pencils Brody has = 9 pencils : 9 pencils

= 1 / 1

= 1 : 1

So therefore, their ratio of pens is 2 : 1 and their ratio of pencils is 1 : 1

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Answer:

x=10/7

Step-by-step explanation:

Answer:

X= 10/7

Step-by-step explanation:

I hope this works

================================================

Explanation:

Subtract straight down. The x terms subtract to 5x-2x = 3x. The y terms subtract to 3y-3y = 0y = 0, so the y terms go away and are eliminated. The terms on the right hand side subtract to 31-25 = 6.

After all that subtraction, we end up with the equation 3x = 6 which solves to x = 2 after dividing both sides by 3.

Use x = 2 to find the value of y

5x+3y = 31

5(2)+3y = 31

10+3y = 31

3y = 31-10

3y = 21

y = 21/3

y = 7

or

2x+3y = 25

2(2)+3y = 25

4+3y = 25

3y = 25-4

3y = 21

y = 21/3

y = 7

Using either equation has x = 2 lead to y = 7.

Therefore, the solution is (x,y) = (2,7)

If you were to graph the two original equations, then they would intersect at (2,7).

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)

142.7 grams

The number of marbles left in the pocket after losing is  29 { after narrating the story in numerical sentences}

Given that Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbles. and asked to narrate the story in numerical form

Total number of marbles Tran bought=25 marbles

Total number of marble Tran has before buying new marbles=10 marbles

Total number of marbles after buying new marbles=35 marbles

Given that he lost 6 marbles because of the  hole in his pocket

Therefore, the Total number of marbles left=35-6

The total number of marbles left=29 marbles.

Therefore, The number of marbles left in the pocket after losing is  29 { after narrating the story in numerical sentences}

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Answer:

Subtraction

Step-by-step explanation:

Subtraction.

11x + 3 = 3

We need to isolate x.

Therefore, we have to move anything unrelated to the other side first.

Then, we can take the things directly affecting x off first.

-3 comes first, then divide by 11.

11x + 3 = 3

      - 3    - 3

11x = 0

x = 0

Answer:

The answer is subtraction.

Step-by-step explanation: