7) Compute the derivative of the function m(x) = -5xğ · V(x2 – 9)3. =

Integrate the absolute value of the velocity function over each subinterval, and sum up the results to find the distance traveled.

Remember, displacement is the net change in position, while distance traveled is the total length of the path the particle moves along.

Hi! To find the displacement and distance traveled during the time interval [-2, 5], we need to integrate the velocity function v(t) = -t^2 + 5t - 4 over the given interval.

First, let's find the antiderivative of v(t) which gives us the position function s(t):
s(t) = ∫(-t^2 + 5t - 4) dt = (-1/3)t^3 + (5/2)t^2 - 4t + C

For displacement, we simply need to find the difference in the position function at the endpoints of the interval:
displacement = s(5) - s(-2)

For distance traveled, we need to consider both the positive and negative parts of the velocity function. Find the time when v(t) = 0 to determine when the particle changes direction:
-t^2 + 5t - 4 = 0

Solve this quadratic equation for t. Next, divide the interval [-2, 5] into subintervals based on the values of t where the particle changes direction. Integrate the absolute value of the velocity function over each subinterval, and sum up the results to find the distance traveled.

Remember, displacement is the net change in position, while distance traveled is the total length of the path the particle moves along.

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To find the work done by the force, we need to integrate the product of the force and the distance over the range of x.

Given that the force is F(x) = x^2 * 9.24 N and the distance is x, we have:

Work = ∫ F(x) * dx
     = ∫ (x^2 * 9.24) * dx
     = 9.24 ∫ x^2 dx
     = 9.24 * [x^3 / 3]

Evaluating the integral between the limits of 0 and 6 (since the distance is given as x), we get:

Work = 9.24 * [(6^3 / 3) - (0^3 / 3)]
    = 9.24 * (72)
    = 665.28 Joules

Therefore, the work done by the force is 665.28 Joules.

To find the work done by the force, we need to calculate the integral of the force function with respect to distance. Given the force function F(x) = 6x, and the distance x ∈ [0, 2.9], we can set up the integral as follows:

Work = ∫(6x dx) from 0 to 2.9

To find the integral, we'll apply the power rule for integration:

∫(6x dx) = 3x^2 + C

Now, we need to evaluate the definite integral from 0 to 2.9:

Work = (3 * (2.9)^2) - (3 * (0)^2) = 3 * (8.41) = 25.23 N·m

So, the work done by the force is approximately 25.23 N·m.

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The value of the test statistic is approximately -2.49

To find the value of the test statistic for the marketing executive's claim that the percentage of laptop owners is different from the reported 30%, we will use the following formula for a proportion hypothesis test:

[tex]Test Statistic (Z) =\frac{ (Sample Proportion - Hypothesized Proportion)}{Standard Error}[/tex]

Here are the given values:
- Hypothesized proportion (p) = 0.30
- Sample size (n) = 130
- Sample proportion (p-hat) = 0.20

First, we need to calculate the standard error (SE) using this formula:
[tex]SE+\frac{\sqrt{p(1-p)} }{n}[/tex]
[tex]SE+\frac{\sqrt{0.30(1-0.30)} }{130}[/tex]
[tex]SE=\sqrt{\frac{0.21}{130} }[/tex]
[tex]SE=\sqrt{0.0016153846}[/tex]
[tex]SE = 0.04019[/tex]

Now, we can calculate the test statistic (Z) using the given formula:
[tex]Z=\frac{ (0.20 - 0.30)}{0.04019}[/tex]
[tex]Z=\frac{-0.10}{ 0.04019}[/tex]
[tex]Z = -2.49[/tex]

So, the value of the test statistic is approximately -2.49, rounded to two decimal places.

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Answer:

Step-by-step explanation:

V=4

3πr 3=4

3·π·83≈2144.66058

The given equation, 3πr3=4, suggests that the volume of some object is 4, which can be solved to find the radius.

The volume of a sphere with a radius of 8 can be calculated using the formula: V = (4/3)πr³, where r is the radius of the sphere and π is the mathematical constant pi. Substituting the value of the radius into the formula,

we get V = (4/3)π(8³) = 2144π or approximately 26808.47 cubic units. Therefore, the volume of the sphere is approximately 26808.47 cubic units.

It will take 6 years for the enrollment at both schools to be equal.

To solve this problem, we need to set up an equation to represent the enrollment at both schools over time.

From the problem it can be deduced that

For Central Middle School:

Nichols Middle School

set these two equations equal to each other and solve for x:

800 + 75x = 890 + 60x

Simplifying the equation

15x = 90

Dividing both sides by 15, we get:

x = 6

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Step-by-step explanation:

f(x)  =  2x^2 -12x + 16       to get to vertex form you will need to complete the square for 'x'....to do THAT you will need the x^2 coefficient to be '1'

Start like this:

2 (x^2 - 6x)    + 16        now complete the square

2 (x^2 - 6x +9)  - 18    + 16

f(x) =  2 (x-3)^2  - 2        Done.

When 7 gallons an hour is converted to cups per minute it would be = 1.9 cups /min.

To convert gallons per hour to cups per minute the following is carried out.

The constitution of a gallon when measured in cups = 16 cups.

Therefore if 1 gallon = 16 cups

7 gallons = X cups

Make X the subject of formula;

X = 16×7

= 112 cups

This means that , 112 cups = 1 hour(60 mins)

y cups = 1 min

make y the subject of formula;

y = 112/60

= 1.9 cups /min

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The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is: 39,600

(a) The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is given by:

number of arrangements with a in first position + number of arrangements with b in last position - number of arrangements with both a in first position and b in last position

= (7!) + (7!) - (6!)

Number of ways with a in first position = 7! (arrange b, c, d, e, f, g, h in the remaining 7 positions)

Number of ways with b in last position = 7! (arrange a, c, d, e, f, g, h in the first 7 positions)

Number of ways with both a in first position and b in last position = 6! (arrange c, d, e, f, g, h in the remaining 6 positions)

Therefore, the total number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is:

7! + 7! - 6! = 10,080

(b) To find the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b, we can use complementary counting.

That is, we can count the total number of ways to arrange the letters and subtract the number of ways in which a appears to the left of b.

Total number of ways to arrange 8 letters = 8! = 40,320

To count the number of ways in which a appears to the left of b, we can fix the positions of a and b as the first two letters, and then arrange the remaining 6 letters in the remaining positions.

There are 6! ways to do this.

Therefore, the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is:

8! - 6! = 40,320 - 720 = 39,600

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To predict how many students might enjoy swimming during the summer break, we will use the information from Mrs. Baker's survey. According to her survey, 21 out of 30 students preferred to go swimming during the summer break.

Step 1: Find the fraction representing the proportion of students who preferred swimming:
21 students preferred swimming / 30 total students = 21/30

Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3:
[tex](21 ÷ 3) / (30 ÷ 3) = 7/10[/tex]

Step 3: Use the simplified fraction to predict the number of students who might enjoy swimming in a school with 1200 students:
[tex]7/10 * 1200 = (7 * 1200) / 10[/tex]

Step 4: Perform the calculations:
[tex]7 * 1200 = 8400[/tex]
8400 / 10 = 840

Your answer: Based on Mrs. Baker's survey, we predict that approximately 840 students out of the total 1200 students might enjoy swimming during the summer break.

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If the photo’s current height is 314 inches, the enlarged height should be approximately 547.6 inches (rounded to one decimal place), which is 80.0% larger than the current height.

To calculate the enlarged height, you need to find out the percentage increase in height from the current height to the desired height.

The desired height is 234 inches, which is 234/314 = 0.744 or 74.4% of the current height.

To find the actual enlarged height, you need to increase the current height by 74.4%.

Enlarged height = current height + (current height x percentage increase)
Enlarged height = 314 + (314 x 0.744)
Enlarged height = 314 + 233.616
Enlarged height = 547.616

Therefore, the enlarged height should be approximately 547.6 inches (rounded to one decimal place), which is 80.0% larger than the current height.

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The potential function f(x, y, z) evaluated at the endpoints of C gives the same result:

f(1, 1, 1) - f(0, 0, 0) = (1 + 5 + 5 + 1/2 + 1/2) - 0 = 12

This confirms that f is indeed the potential function for F.

To confirm that F is conservative, we need to check if its curl is zero. The curl of F is given by:

Substituting F(x, y, z) = (1z + 5y) i + (1z + 5x)j + (1y + 1x)k into the above equation, we get:

curl(F) = 0i + 0j + 0k

The potential function f for F, we need to integrate F along any path from (0,0,0) to (1,1,1). Let C be the path given by the line segment connecting (0,0,0) and (1,1,1).

The parametric equations of C are:

where 0 ≤ t ≤ 1.

We need to evaluate the line integral ∫CF.dr, where r(t) = ti + tj + tk is the position vector of C at time t. The potential function f is defined as the line integral of F from (0,0,0) to (x,y,z), so we need to find an antiderivative of F to evaluate this integral.

The antiderivative of F is:

where C is a constant of integration. We want f to have a constant term of 0, so we choose C = 0.

Now we can evaluate the line integral ∫CF.dr by substituting the parametric equations of C into F and taking the dot product with the differential of r(t):

Integrating from t=0 to t=1, we get:

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If the school district surveyed 500 families to see if they were satisfied or not satisfied with the new district website. the maximum number of families who are satisfied with the new district website is approximately 130,771.

First, we need to calculate the confidence level, which is 1 minus the margin of error:

Confidence level = 1 - margin of error

Confidence level = 1 - 0.027

Confidence level = 0.973

Next, we can use the proportion of satisfied families in the sample to estimate the proportion in the population:

Proportion satisfied in population = Proportion satisfied in sample

Proportion satisfied in population = 480/500

Proportion satisfied in population = 0.96

Now we can use this proportion and the confidence level to calculate the maximum number of satisfied families in the population:

Maximum number of satisfied families = Proportion satisfied in population x Total number of families x Confidence level

Maximum number of satisfied families = 0.96 x 140,000 x 0.973

Maximum number of satisfied families ≈ 130,771

Therefore, the maximum number of families who are satisfied with the new district website is approximately 130,771.

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Quadrilateral ABCD is not necessarily congruent to quadrilateral KLMN. If both conditions are met, then quadrilateral ABCD is congruent to quadrilateral KLMN.

Determine if quadrilateral ABCD is congruent to quadrilateral KLMN, we'll need to follow these steps:
Identify the corresponding sides and angles in both quadrilaterals.
Check if all corresponding sides are equal in length (AB = KL, BC = LM, CD = MN, and DA = NK).
Check if all corresponding angles are equal in measure (angle A = angle K, angle B = angle L, angle C = angle M, and angle D = angle N).
If both conditions are met, then quadrilateral ABCD is congruent to quadrilateral KLMN.

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For the function f(x, y) = 1 - xy + y²= -y = -1, fy(-2,1) = 2y - x = 3.

When y is stationary, the rate of change of f with respect to x is determined by the partial derivative fx. Meanwhile, fy measures the rate of change of f in relation to y while holding x constant.

At the point (-2,1), the fx partial derivative symbolizes the incline of the level curve tangent line that follows the x-direction in relation to f. Its counterpart fy denotes the incline of the level curve tangent line that follows the y-direction regarding f at (-2,1).

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Complete answer - Let f(x, y) = 1 - xy + y² Compute fx(-2, 1) and fy(-2,1), and interpret these partial derivatives geometrically."

The next of the sequence 1, 2, 6, 22 is equal to 86.

First term of the sequence is equal to 1

Second term of the sequence is 2

Which can be written as

1 + 2⁰ = 2

Third term is 6

which can be written as

2 + 2² = 2 + 4

          = 6

Fourth term is 22

which can be written as

6 + 2⁴ = 6 + 16

          = 22

Next term using the above pattern is equal to

Pattern is add the previous term with increment of the even square of 2.

22 + 2⁶ = 22 + 64

            = 86

Therefore, the next term of the given sequence is equal to 86.

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The given question is incomplete, I answer the question in general according to my knowledge:

What comes next in the sequence: 1, 2, 6, 22, ____ ?

The example describes learned behavior in a living thing is give by Most humans begin to speak when they are one or two years old, option B.

Living creatures include bacteria, fungus, algae, protozoans, plants, and animals. Organisms are another word for living things. Because living things behave differently from nonliving things, scientists can distinguish between the two. On Earth, there are around 1.5 million different species of living organisms, according to scientists.

With the use of their own energy, all living things can move. Plants remain stationary, yet they move their leaves to catch the sunshine. Additionally sensitive or perceptive are living things. Simplest living forms just have a feeling of warmth and cold or can only feel when they are touched.

Chemicals are ingested and expelled by living beings. Carbon dioxide is exhaled and oxygen is inhaled by animals. Through their leaves, green plants absorb carbon dioxide and exhale oxygen. All living things require the vitamins and energy that food provides. Green plants use sunlight to produce their own sustenance. For energy, animals consume both vegetation and other creatures. Waste is also released by organisms.

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Most humans begin to speak when they are one or two years old. This example describes learned behavior in a living thing, as humans learn to speak by observing and imitating the speech of others around them.

Babies first begin to discriminate between distinct sounds, such as vowels and consonants, by listening to the speech of those around them.

The sounds they have heard are then repeated by them. They gradually begin to blend the sounds to create words.

Eventually, when babies hear more spoken language, they start to comprehend the meanings of the words and can utilise them appropriately.

As their vocabulary and linguistic knowledge increase, they become more fluent speakers and are able to communicate effectively. Language acquisition is a difficult process that takes many years of exposure and practise to master.

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The number of units that must be produced and sold in order to break even = 120

Consider equation C = 15x +300

This equation represents the​ cost, in​ dollars, of x units of a product

and equation R = 17.5x represents the​ revenue, in​ dollars, from the sale of x units.

In order to find the number of units that must be produced and sold in order to break even, consider C = R

i.e., 15x + 300 = 17.5x

We solve this equation for x.

17.5x - 15x = 300

(17.5 - 15)x = 300

2.5x = 300

x = 300/(2.5)

x = 120

This is the required number of units.

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If Mr Louis gets a 6. 5% discount on the price of the oil, Mr. Louis gets a discount of £65.41 on this purchase.

First, let's find out how many litres of oil Mr. Louis needs to fill his tank:

Maximum capacity of the tank: 1,400 litres
Current oil in the tank: 150 litres
Litres needed to top up: 1,400 - 150 = 1,250 litres

Next, we'll calculate the original price of the oil without the discount:

Price per litre: £0.805
Cost of oil needed: 1,250 litres * £0.805 = £1,006.25

Now, let's calculate the discount amount:

Discount percentage: 6.5%
Discount amount: £1,006.25 * 0.065 = £65.41

So, Mr. Louis gets a discount of £65.41 on this purchase.

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Two events are independent if the occurrence of one event does not affect the occurrence of the other event. In other words, the probability of one event happening is not affected by whether or not the other event happens.

A simple example would be flipping a coin and rolling a die. The outcome of the coin flip does not affect the outcome of the die roll, so these events are independent.

On the other hand, two events are mutually exclusive if they cannot happen at the same time. If one event happens, the other event cannot happen. For instance, when rolling a die, the events of getting a 1 or a 2 are mutually exclusive because it is impossible to roll both numbers at the same time.

To summarize, two events are independent if the probability of one event happening is not affected by the occurrence of the other event, while two events are mutually exclusive if they cannot happen at the same time.

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Ajay's profit on each orange is Rs. 25, and the profit percentage is 125%.

Ajay makes a profit of Rs. 25 on each orange he sells, which is the difference between the selling price and the cost price. The profit percentage is calculated by dividing the profit by the cost price and then multiplying it by 100.

In this case, the cost price of each orange is Rs. 20 and the profit on each orange is Rs. 25. So, the profit percentage is (25/20) x 100 = 125%.

This means that Ajay is making a profit of 125% on each orange he sells, which is a significant profit margin. It also shows that buying in bulk at a lower price and selling at a higher price can be a profitable business strategy.

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The error caused an understatement of the gross profit for the year, as the cost of goods sold was overstated by $14,750.

The error in inventory caused an understatement of the inventory value on the balance sheet, which in turn caused an overstatement of the cost of goods sold. This is because the cost of goods sold is calculated by subtracting the cost of the ending inventory from the cost of goods available for sale.

Therefore, an understatement of the ending inventory leads to an overstatement of the cost of goods sold, which ultimately results in an understatement of the gross profit. None of the other items on the balance sheet are directly affected by the error in inventory.

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Answer:

A

Step-by-step explanation:

Simple interest gains interest only on the principal sum and so each year has the same interest. So, this example is not simple interest. Compound interest is calculated on the principal and the accumulated interest of the previous years. So, this is compound interest.

      Interest is 4%.

      [tex]A = P*(1 + R \%)^n[/tex]

Here A is the amount we receive after n years, P is the principal and R is the rate of interest.

        A = $1300 , R = 4%

            [tex]1300 = P * (1+0.04})\\\\1300 = P * 1.04\\\\\dfrac{1300}{1.04}=P\\\\\\\dfrac{130000}{104}=P[/tex]

            P = $ 1250

Answer: 81

Step-by-step explanation: this would be 81 because [tex]3^{3}[/tex] is basically 3 x 3 x 3 and 3 x 3 x 3=27 then multiply 27 by 3, and you get 81

Answer:

3^4. my answer needs to be 20+character sooooooooo

The basketball coach can order approximately 34 shooting shirts for $300.

To determine the number of shooting shirts the basketball coach can order for $300, we need to solve the equation C = 0.2x^2 + 1.6x + 15, where C represents the cost and x represents the number of shooting shirts.

The equation is given as C = 0.2x^2 + 1.6x + 15.

To find the number of shooting shirts for $300, we set the cost C equal to 300 and solve for x:

0.2x^2 + 1.6x + 15 = 300

0.2x^2 + 1.6x + 15 - 300 = 0

0.2x^2 + 1.6x - 285 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For this equation, a = 0.2, b = 1.6, and c = -285. Plugging in these values into the quadratic formula:

x = (-1.6 ± sqrt(1.6^2 - 4 * 0.2 * -285)) / (2 * 0.2)

Simplifying the equation further:

x = (-1.6 ± sqrt(2.56 + 228)) / 0.4

x = (-1.6 ± sqrt(230.56)) / 0.4

x = (-1.6 ± 15.18) / 0.4

Now we have two solutions:

x1 = (-1.6 + 15.18) / 0.4 = 33.95

x2 = (-1.6 - 15.18) / 0.4 = -44.95

Since the number of shooting shirts cannot be negative, we discard the negative solution.

Therefore, the basketball coach can order approximately 34 shooting shirts for $300.

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By using completing the square, the equation can be rewritten as (x + (-11/4))² = 9/16.

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

2x² - 11x + 14 = 0

By dividing all through by 2, we have:

x² - 11x/2 + 7 = 0

x² - 11x/2 = -7

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 11x/2 + (-11/4)² = -7 + (-11/4)²

x² - 11x/2 - 121/16 = 9/16

(x - 11/4)² = 9/16.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Each car cost $0.81, you would need to do 0.81 times 25 and you would get $20.25

Step-by-step explanation:

The expression that represents the side length of the square pool is 2x² + 36x - 1120 = 0. The side length of the square pool is x = 16.31 feet.

Let's denote the side length of the square pool as x.

The walkway on two opposite sides of the pool is 8 feet, which means that the overall length of the pool and walkway on those sides is x + 8 + 8 = x + 16.

Similarly, x + 10 + 10 = x + 20.

The total area covered by the pool and walkway is given as 1,440 square feet.

Total Area = Pool Area + Walkway Area

The area of the square pool is x², and the area of the walkway is the difference between the total area and the pool area:

Walkway Area = Total Area - Pool Area

Substituting the values, we have:

1440 = x² + (x + 16)(x + 20)

1440 = x² + (x² + 36x + 320)

Combining like terms:

1440 = 2x² + 36x + 320

2x² + 36x + 320 - 1440 = 0

2x² + 36x - 1120 = 0

After solving, we get:

[tex]x=-9+\sqrt{641},\:x=-9-\sqrt{641}[/tex]

Take positive value:

[tex]x=-9+\sqrt{641},\\x = -9+25.31\\x = 16.31[/tex]

So, the side length of the square pool is 16.31 feet.

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The cost of one movie ticket, including sales tax, is $13.02

The cost of the movie ticket is $12.00, and the sales tax rate is 8.5%. To find the amount of sales tax on the ticket, we can multiply the ticket price by the tax rate:

Sales tax = 12.00 * 0.085

= 1.02

So the sales tax on the ticket is $1.02.

To find the total cost of the ticket, we add the ticket price to the sales tax:

Total cost = 12.00 + 1.02

= 13.02

Therefore, the cost of one movie ticket, including sales tax, is $13.02.

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The probability of getting strawberry is 11/60. The correct option is d.

To determine the probability of getting strawberry, we need to consider the probabilities of all the possible flavors and calculate the probability of strawberry using the information given.

Given probabilities:

Probability of getting cherry = 1/5

Probability of getting orange = 1/4

Probability of getting lemon = 1/3

Since there are only four flavors in total, we can calculate the probability of getting strawberry by subtracting the sum of the probabilities of cherry, orange, and lemon from 1.

Probability of getting strawberry = 1 - (1/5 + 1/4 + 1/3)

To simplify the calculation, we find a common denominator for 5, 4, and 3, which is 60.

Probability of getting strawberry = 1 - (12/60 + 15/60 + 20/60)

                                 = 1 - 47/60

                                 = 13/60

Therefore, the probability of getting strawberry is indeed 13/60, which corresponds to option d) 11/60 in the given list of options.

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Now we need to apply the given boundary conditions to obtain the specific solution for u(x, y):

Boundary conditions in x-direction:
X(2) = X(27) = 0

Boundary conditions in y-direction:
Y(0) = Y(2m) = 0

1. Identify the Poisson equation and boundary conditions.
2. Use the method of separation of variables to solve the equation.
3. Apply the boundary conditions to obtain the specific solution.

Step 1: Identify the Poisson equation and boundary conditions
The given Poisson equation is:
Δu + 2g = 27 - 1,
where Δu is the Laplacian of the potential function u(x, y).

The provided boundary conditions are:
u(2, 0) = u(2, 2m) = 0,
u(0, y) = u(27, y) = 0.

Step 2: Use the method of separation of variables
We assume that the solution u(x, y) can be written as a product of two functions, one depending on x and the other depending on y, i.e., u(x, y) = X(x)Y(y).

Now, let's substitute this into the Poisson equation:
Δu + 2g = 27 - 1,
which becomes
(X''(x)/X(x) + Y''(y)/Y(y)) + 2g = 26.

Separate the variables:
X''(x)/X(x) = -Y''(y)/Y(y) - 2g = λ,
where λ is the separation constant.

This gives us two ordinary differential equations:
X''(x) = λX(x),
Y''(y) = -(λ + 2g)Y(y).

Step 3: Apply the boundary conditions
Now we need to apply the given boundary conditions to obtain the specific solution for u(x, y):

Boundary conditions in x-direction:
X(2) = X(27) = 0

Boundary conditions in y-direction:
Y(0) = Y(2m) = 0

Solving these equations with their respective boundary conditions will give us a specific solution for the potential function u(x, y). However, it is important to note that solving these equations involves solving eigenvalue problems and possibly infinite series expansions. The full solution process is quite involved and goes beyond the scope of this answer.

Nevertheless, I hope this outline of the solution method helps you understand the process of solving the Poisson equation with given boundary conditions.

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