find the solution of the initial value problem. Discuss the interval of existence and provide a sketch of your solution. xy' + 2 y = sin x, y(pi/2) = 0

Answer:

-6 and -3 for the dots

Step-by-step explanation:

hope this is correct im bad at math

Answer:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. The range is the set of all valid y values.

Step-by-step explanation:

The company's upgrade in production machinery, which allows for real-time transmission of data about the fit tolerance for assembled parts of each unit produced, represents an increase in the timeliness and efficiency of data transmission.

Prior to the upgrade, data about the fit tolerance for assembled parts was transmitted at the end of a production run.

This means that the information regarding the quality and precision of the assembled parts was collected and transmitted after the entire production process was completed.

However, with the upgrade in production machinery, the company now has the capability to transmit this data in real-time as the measures are taken during the production process.

The upgrade represents an increase in the timeliness and efficiency of data transmission.

By transmitting the data in real-time, the company can immediately identify any deviations or issues in the fit tolerance of the assembled parts.

This allows for timely interventions and adjustments to be made during the production process, reducing the likelihood of producing defective or substandard units.

Real-time data transmission also enables the company to have a more accurate and up-to-date understanding of the quality of each unit produced. This information can be used for immediate feedback, quality control purposes, and process improvements.

Overall, the upgrade in production machinery enhances the company's ability to monitor and control the fit tolerance of assembled parts, leading to improved production efficiency and product quality.

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Answer:

325

Step-by-step explanation:

40/100=130/x

Cross multiply to find x

40x=13000

/4            /4

x=325

Answer:15 should be on the x and add all together with the 69

Step-by-step explanation:

Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

\(\frac{3}{4}\) ÷ \(\frac{1}{2}\)

Since we are dividing by a fraction, we switch \(\frac{1}{2}\) to it's reciprocal.

Doing that would make it \(\frac{3}{4}\) x \(\frac{2}{1}\). In other words, that is \(\frac{3}{4}\) x \(2\).

We can use cross multiplying to simplify/solve for it.

(Look at the image to see the cross multiplying).

Therefore, the answer is \(\frac{3}{2}\).

Answer:

\(135\)

Step-by-step explanation:

\(3y = 3 \times 45 = 135\)

Hope this helps ;) ❤❤❤

Answer:

answer is 41

Step-by-step explanation:

subscribe to itzz sneaky

:the anser is

41

i just did it

To find the x-coordinate of the endpoint B on the curve y = (2/3)^(x^3/2), we need to determine the value of x when the curve's length from point A to B is 78 units.

The length of a curve can be calculated using the arc length formula:

L = ∫[a, b] sqrt(1 + (dy/dx)^2) dx,

where a and b are the x-coordinates of the starting and ending points, respectively.

In this case, the starting point A has an x-coordinate of 3, so we can set a = 3. Let's denote the x-coordinate of the endpoint B as x_B.

To find x_B, we need to solve the following integral equation:

78 = ∫[3, x_B] sqrt(1 + (dy/dx)^2) dx.

First, let's find the derivative dy/dx:

dy/dx = d/dx ((2/3)^(x^3/2))

      = (2/3)^(x^3/2) * d/dx (x^3/2)

      = (2/3)^(x^3/2) * (3/2) * x^(1/2)

      = (3/2) * (2/3)^(x^3/2) * x^(1/2).

Now, let's compute the integral:

78 = ∫[3, x_B] sqrt(1 + ((3/2) * (2/3)^(x^3/2) * x^(1/2))^2) dx.

Unfortunately, this integral does not have an elementary closed-form solution. We would need to use numerical methods or approximation techniques to solve it.

One common method is to use numerical integration techniques like the trapezoidal rule or Simpson's rule. These methods approximate the integral by dividing the interval [3, x_B] into smaller subintervals and approximating the function within each subinterval. By summing up these approximations, we can estimate the integral and solve for x_B.

Alternatively, if you have access to mathematical software or calculators that can perform symbolic integration, you can input the integral equation directly and solve for x_B.

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Answer: 272/3 OR 90.67

Step-by-step explanation:

First, turn the mixed fraction into an improper fraction. Using the times-addition method, you take the whole number (2) and multiply it by the denomitor (3). You get 6, and then add the numerator (2) to 6, getting 8, so th improper fraction of the first term is 8/3.

Then, you multiply 8/3 by 34. To do this, you do 8 times 34 divided by 3. 34 times 8 is 272, and then you divide it by 3. You don't get a whole number, so the answer could be written as 272/3 or 90.67

Answer:

71%

Step-by-step explanation:

The original price is 200. The dress was sold for 142.

Take the price of the dress divide the original price (142/200) then times 100.

Answer:

27% off

Step-by-step explanation:

If there are 450 grams of element and half life is 8 minutes, then it will take 28.83 minutes the element to decay to 37 grams

Half life of radio active element = 8 minutes

Initial quantity of radio active element = 450 gram

Final quantity of radio active element = 37 grams

y = a(0.5)^(t/h)

Substitute the values in the equation

37 = 450 (0.5)^(t/8)

Move 37 to left hand side of the equation

37 / 450 = 0.5^(t/8)

Convert the terms to logarithm

t/8 = \(log_{0.5}\frac{37}{450}\)

t/8 = 3.60

t = 8 × 3.60

Multiply the numbers

t = 28.83 minutes
Therefore, the it will take 28.83 minutes to decay to 37 grams

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Given

Equation

x tea chart __, 0, 2, __

y tea chart 0,__, __, 3

Procedure

y = 0

12x = 16

x = 16/12

x = 4/3

x = 0

-8y = 16

y = 16/-8

y = -2

x = 2

12(2) - 8y = 16

24 - 8y = 16

-8y = 16-24

-8y = -8

y = 1

y = 3

12x - 8(3) = 16

12x - 24 = 16

12x = 16+24

12x = 40

x = 40/12

x = 20/6

x tea chart 4/3, 0, 2, 20/6

y tea chart 0, -2, 1, 3

Answer:

bc

Step-by-step explanation:

2:9 is equivalent to

18: 81 because is 2*9 : 9*9

12:54 because is 2*6 : 9* 6

The range of exponential functions is y > 0. An exponential function's graph may be found to be strictly increasing or strictly decreasing graph.

The graph of an exponential function is found to be asymptotic to the x-axis in nature as x approaches negative infinity or as it approaches positive infinity.

An exponential function is a mathematical function which has the formula f (x) = axe, where "x" is a variable and "a" is a constant also known as the base of the function and it should be greater than zero.

The number e, which is approximately equal to 2.71828, is the most often used exponential function base.

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Answer

Find out the  m∠p .

To prove

As in ΔDAB is a right triangle

Apply pythagorean theorem

Hypotenuse ² = Perpendicular ² + Base²

DB² = AB² + AD²

AB = 5 units

AD = 6 units

Put in the above formula

DB² = 5² + 6²

     = 25 + 36

    = 61

          = 7.8 units (approx)

Now in  ΔDCB is a right triangle .

By using the trignometric identity .

As DC = 4 units

DB = 7.8 units  (approx)

Put all the values in the trignometric identity .

∠p = 59.15 ° (approx)

The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

        -----------------------------------------

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

The optimal number of square feet of space to be added is approximately 101 square feet.

We have,

To determine the optimal number of square feet of space to maximize the restaurant's profit, we need to analyze the relationship between the additional square footage, the number of new customers, and the resulting profit.

Let's start by defining some variables:

Let "x" represent the number of additional square feet of space to be added beyond the initial 100 square feet.

Let "C(x)" represent the cost in dollars to add x square feet of space. In this case, C(x) = $100 * x.

Let "N(x)" represent the number of new customers attracted per month when x square feet of space is added.

Let "P(x)" represent the profit generated per month when x square feet of space is added. In this case, P(x) = $50 * N(x).

Given the information provided, we know that each additional square foot of space attracts 2 new customers per month.

So, N(x) = 2x.

However, the number of new customers per month is expected to decrease by 1% for every 10 square feet of additional space beyond the initial 100 square feet.

To incorporate this, we can modify our equation for N(x) as follows:

N(x) = 2x * (1 - 0.01 * (x - 100) / 10)

Now, we can express the profit function P(x) in terms of x:

P(x) = $50 * N(x)

= $50 * [2x * (1 - 0.01 * (x - 100) / 10)]

= $100x * (1 - 0.01 * (x - 100) / 10)

To find the optimal number of square feet of space that maximizes profit, we need to find the value of x that maximizes P(x).

We can do this by taking the derivative of P(x) with respect to x, setting it equal to zero, and solving for x.

dP(x)/dx = $100 * (1 - 0.01 * (x - 100) / 10) + $100x * (-0.01 / 10)

= $100 - $1 * (x - 100) + $100x * (-0.01 / 10)

= $100 - $1x + $100 * (-0.01 / 10) - $1x

= $100 - $2x - $0.01x + $10x

= $100 + $7x - $0.01x

Setting dP(x)/dx equal to zero:

$100 + $7x - $0.01x = 0

$7x - $0.01x = -$100

0.99x = $100

x ≈ $100 / 0.99

x ≈ 101.01

Since we're dealing with square footage, we can round the result to the nearest whole number.

Therefore,

The optimal number of square feet of space to be added is approximately 101 square feet.

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The complete question:

The manager of a restaurant is considering expanding the seating area. She wants to determine how many additional square feet of space should be added to maximize the restaurant's profit. The cost to add new space is $100 per square foot, and the profit generated per square foot is estimated to be $50 per month. The manager expects that each additional square foot of space will attract 2 new customers per month. However, the number of new customers per month is expected to decrease by 1% for every 10 square feet of additional space beyond the initial 100 square feet.

What is the optimal number of square feet of space that should be added to maximize the restaurant's profit?

Answer:

−5m/5 does not equal m.

Step-by-step explanation:

Answer: 207

I hope you get it right

Answer:

seventeen out of twenty

Step-by-step explanation:

The phrase that describes this probability would be

seventeen out of twenty

This is because the bag has a total of 20 candies ( 3 strawberry chews and 17 cherry chews). If he randomly chooses one from the bag, he has a 17/20 chance of getting a cherry chew because there are 17 total cherry chews in the bag. If we were to change this fraction into a phrase it would be the phrase above in bold.

Answer: 60 %

Step-by-step explanation:

To find what percent 144 is of 240, we can use the following proportion:

part/whole = percent/100

Let x be the percentage we are trying to find, then we can write:

144/240 = x/100

To solve for x, we can cross-multiply:

14400 = 240x

Dividing both sides by 240, we get:

x = 14400/240 = 60

Therefore, 144 is 60% of 240.

Answer:

60%

Step-by-step explanation:

Percent proportion:

240 - 100%

144 - x%

Cross-multiply to find x:

\( \frac{144 \times 100\%}{240} = \frac{14400}{240} = 60\%\)

So, 144 is 60% of 240

\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

Since the culture is observed to double every 6 hours, we know that the growth rate is constant at r = ln(2)/6 per hour.

To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value. The most frequent time intervals for growth rates are annually, quarterly, monthly, and weekly.

We can use the formula for exponential growth to model the number of bacteria in the culture after t hours:

n(t) = n0e^(rt)where n0 is the initial number of bacteria.

Substituting in the values given in the problem, we get:

n(t) = 25e^[(ln(2)/6)t]Simplifying this expression using the properties of logarithms, we can rewrite it in the form:

n(t) = 25(2)^(t/6)This is the exponential model for the number of bacteria in the culture after t hours.

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The exponential model for population of bacteria, \(n(t) = n_0{2}^{\frac{t}{a} }\) can be written \(n(t) = 25 \times {2}^{\frac{t}{6} }\) for the number of bacteria in the culture after t hours. The estimate number of bacteria after 13 hours is equals to the 112. In 92 hours, the bacteria count will reach to 1 million.

We have a certain culture of the bacterium Rhodobacter.

Initial population, n₀ = 25

The population become doubles in every 6 months. The exponential model

\(n(t) = n_0{2}^{\frac{t}{a} }\) for the number of bacteria in the culture after t hours. Now, the population become double in 6 hours, so a = 6 , then exponential equation is \(n(t) = 25 \times {2}^{\frac{t}{6} }\).

We have to estimate the number of bacteria after 13 hours. That is t = 13 hours, \(n( t) = 25( 2)^{\frac{t}{6}}\)

Substitute t = 13 hours

\( = 25( 2)^{\frac{13}{6}}\)

\(= 25( 2)^{2.16}\)

= 111.728713807 ~ 112

So, n(13) = 112

We have to determine the value of t in hours for n(t) = 1 million = 1000000, using the above equation, \(1000000 = 25( 2)^{\frac{t}{6}}\)

\(40000 = ( 2)^{\frac{t}{6}}\)

Taking natural logarithm both sides

=>\( ln( 40000) = ln(( 2)^{\frac{t}{6}})\)

=> \(ln(40000) = \frac{t}{6} ln(2)\)

=> \(t = \frac{6 ln( 40000)}{ ln(2)}\)

= 91.7262742773 ~ 92

Hence, required value is 92 hours..

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Pipelining is a technique that breaks down a complex task into smaller, simpler tasks that can be performed in parallel. This allows the computer to complete the task more quickly than if it were to perform the task sequentially.

Pipelining is a common technique used in computer architecture. It is a way of breaking down a complex task into smaller, simpler tasks that can be performed in parallel. This allows the computer to complete the task more quickly than if it were to perform the task sequentially. For example, consider the task of adding two numbers. This task can be broken down into the following smaller tasks:

Fetch the first number from memory.

Fetch the second number from memory.

Add the two numbers together.

Store the result in memory.

If these tasks were performed sequentially, the computer would have to wait for each task to complete before it could start the next task. This would take a long time. However, if these tasks were performed in parallel, the computer could start working on the next task as soon as the previous task was finished. This would allow the computer to complete the task much more quickly.

The theoretical speedup in a system that uses pipelining is equal to the number of stages in the pipeline. The theoretical speedup in a system that uses pipelining is equal to the number of stages in the pipeline. This is because each stage in the pipeline can be working on a different task at the same time. For example, consider a system with a pipeline that has four stages. The first stage could be fetching the first number from memory, the second stage could be fetching the second number from memory, the third stage could be adding the two numbers together, and the fourth stage could be storing the result in memory.

If all four stages were working at the same time, the system could complete the task of adding two numbers in one-fourth of the time it would take if the task were performed sequentially. In practice, the actual speedup in a system that uses pipelining is less than the theoretical speedup. This is because there are some overheads associated with pipelining, such as the time it takes to switch from one stage to the next. However, pipelining is still a very effective way to improve the performance of a computer system.

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The angular velocity of the circle is approximately 19 m/s.

In order to find the missing quantity, we can use the relationship between linear velocity and angular velocity in a circle. The linear velocity of a point on the edge of a circle is the product of the radius and the angular velocity. This can be expressed as:

v = r * w

where v is the linear velocity, r is the radius, and w is the angular velocity.

To find the value of w, we can rearrange this equation to solve for w:

w = v / r

Substituting the given values of v and r, we get:

w = 1235 m/min / 65 m

w = 19 m/s

It's important to note that units must be consistent when using formulas to solve problems. In this case, we converted the given linear velocity from m/min to m/s before plugging it into the formula. Also, we rounded the answer to the nearest tenth, as instructed, since the given values were rounded to the nearest unit.

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Answers:

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

Explanation:

Answer:

$250.00

Step-by-step explanation:

twenty $1 bills- 20 x 1 = 20

six $5 bills- 6 x 5 = 30

four $10 bills- 4 x 10 = 40

five $20 bills- 5 x 20 = 100

thirty $1 bills- 30 x 1 = 30

four $5 bills- 4 x 5 = 20

five $10 bills- 5 x 10 = 50

one $20 bill- 1 x 20 = 20

Add the bold totals together and get the final answer of $250.00