For what value of x is sin(x) = cos(32°), where 0°< x < 90°?
A.
64°
B.
58°
C.
32°
D.
13°

Answer:

c

Step-by-step explanation:

x=1 g(x)=-10

x=2 g(x)=-12

x=3 g(x)=-14

f(x)=x+4

=＞ g(x)=-2·(x+4)

The organization that offers coverage on properties in areas of Florida deemed especially susceptible to windstorm damage is the Florida Windstorm Underwriting Association (FWUA), also known as Citizens Property Insurance Corporation.

The Florida Windstorm Underwriting Association (FWUA) is an organization established by the state of Florida to provide property insurance coverage for individuals in high-risk areas specifically prone to windstorm damage. The FWUA operates under the name Citizens Property Insurance Corporation.

1. Recognizing the need for coverage: Given the susceptibility of certain areas in Florida to windstorm damage, there is a need for specialized insurance coverage to protect property owners in those regions.

2. Creation of the Florida Windstorm Underwriting Association (FWUA): The state of Florida established the FWUA as an organization dedicated to providing insurance coverage for properties located in these high-risk areas.

3. Role of Citizens Property Insurance Corporation: The FWUA operates under the name Citizens Property Insurance Corporation, which offers coverage on properties in these vulnerable regions.

By offering coverage specifically tailored to windstorm damage, the FWUA (Citizens Property Insurance Corporation) helps protect property owners in areas of Florida prone to such risks, providing them with the necessary insurance coverage for their properties.

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Answer:

The 1990s basketball player did better than the current basketball player because his z-score is higher.

Step-by-step explanation:

i just took the test

The expression is simplified to give 2(9x + 2√3x - 5)

First, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms

From the information given, we have that;

(2√3x - 2)(3√3x + 5)

expand the bracket, we get;

6√9x² + 5(2√3x) - 6√3x - 10

Find the square root factor

6(3x)  + 10√3x - 6√3x - 10

collect the like terms, we have;

18x + 4√3x - 10

Factorize the expression, we have;

2(9x + 2√3x - 5)

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1. Objective Function and Constraints:

Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

2. Using Excel Solver, find the optimal allocation of funds.

3. The maximum value of the objective function is reported by Excel Solver.

We have,

Objective Function and Constraints:

Let:

x1 = amount spent on food

x2 = amount spent on shelter

x3 = amount spent on entertainment

Objective Function:

Maximize: 2x1 + 3x2 + 5x3 (since each dollar spent on food has a satisfaction value of 2, each dollar spent on shelter has a satisfaction value of 3, and each dollar spent on entertainment has a satisfaction value of 5)

Constraints:

Subject to:

x1 + x2 + x3 ≤ $1,500 (maximum disposable income)

x1 + x2 ≤ $1,100 (amount spent on food and shelter combined must not exceed $1,100)

x2 ≤ $800 (amount spent on shelter alone must not exceed $800)

x3 ≤ $400 (entertainment cannot exceed $400)

Using Excel Solver:

In Excel, set up a spreadsheet with the following columns:

Column A: Variable names (x1, x2, x3)

Column B: Objective function coefficients (2, 3, 5)

Column C: Constraints coefficients (1, 1, 1) for the first constraint (maximum disposable income)

Column D: Constraints coefficients (1, 1, 0) for the second constraint (amount spent on food and shelter combined)

Column E: Constraints coefficients (0, 1, 0) for the third constraint (amount spent on shelter alone)

Column F: Constraints coefficients (0, 0, 1) for the fourth constraint (entertainment limit)

Column G: Right-hand side values ($1,500, $1,100, $800, $400)

Apply the Excel Solver tool with the objective function and constraints to find the optimal allocation of funds.

Once the Excel Solver completes, it will report the maximum value of the objective function, which represents the optimal satisfaction value achieved within the given budget constraints.

Thus,

Objective Function and Constraints: Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

Using Excel Solver, find the optimal allocation of funds.

The maximum value of the objective function is reported by Excel Solver.

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The formula for calculating the population variance is given by the following expression: σ² = Σ(x - µ)² / N Where, σ² is the variance, Σ is the sum, x is the value of the observation, µ is the mean and N is the total number of observations. Using the above formula to calculate the population variance for the following numbers: 83, 94, 13, 72, -2Population Variance: Let's calculate the population variance for the given numbers.

μ = (83 + 94 + 13 + 72 - 2) / 5

= 252 / 5

= 50.4 The mean of the given numbers is 50.4 Now,

σ² = [ (83 - 50.4)² + (94 - 50.4)² + (13 - 50.4)² + (72 - 50.4)² + (-2 - 50.4)² ] / 5σ²

= [ (32.6)² + (43.6)² + (-37.4)² + (21.6)² + (-52.4)² ] / 5σ²

= (1062.76 + 1902.96 + 1400.36 + 466.56 + 2743.76) / 5σ²

= 957.88 Variance = 957.88 So, the population variance for the given numbers is 957.88.

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Line segment XY begins at (-6,4) and ends at (-2,4); XY is reflected over the x-axis and translated left 3 units to form line segment X'Y' which has a length of 4 units.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Line segment XY begins at (-6,4) and ends at (-2,4). Hence:

\(XY = \sqrt{(4-4)^2 + (-2 +6)^2} \\\\XY = \sqrt{0+16} \\\\XY = \sqrt{16} \\\\XY = 4\)

XY is reflected over the x-axis and translated left 3 units to form line segment X'Y'. Hence:

XY = X'Y' = 4 units

Line segment XY begins at (-6,4) and ends at (-2,4); XY is reflected over the x-axis and translated left 3 units to form line segment X'Y' which has a length of 4 units.

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Answer:

Points R(4,1) S(7,3) T(6,4) after translation

R(4-3, 1) S(7-3, 3) T(6-3, 4)

R'(1, 1) S'(4, 3) T'(3, 4)

Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection

R''(1, -3) S''(4, -5) T''(3, -6)

Step-by-step explanation:

Answer:Step-by-step explanation:Points R(4,1) S(7,3) T(6,4) after translation R(4-3, 1) S(7-3, 3) T(6-3, 4) R'(1, 1) S'(4, 3) T'(3, 4) Points R'(1, 1) ...

15.25-7.14=8.11

3.4x2.1=7.14

In finance, interest is the cost of borrowing money or the compensation paid to an individual or organization for lending money. It is usually expressed as a percentage of the amount borrowed and is calculated over a specific period of time.

1. To calculate the total interest payment for the first year, follow these steps in Excel:

Step 1: Enter the given values in separate cells.
Loan amount: $250 million in A1
Monthly installment: $5 million in A2
Number of installments: 60 in A3

Step 2: Calculate the monthly interest rate (i) using the RATE function.
In cell A4, type the formula: =RATE(A3, -A2, A1)

Step 3: Calculate the annual interest rate (I) by multiplying the monthly interest rate by 12.
In cell A5, type the formula: =A4*12

Step 4: Calculate the total interest for the first year by multiplying the annual interest rate by the loan amount.
In cell A6, type the formula: =A1*A5
The total interest payment for the first year is approximately $17 million.

2. To calculate the effective interest rate (j12) of the loan, use the following formula in Excel:

In cell A7, type the formula: =(1+A4)^12-1
The effective interest rate (j12) is approximately 7.4% p.a.

3. To calculate the principal repayment during the first year, follow these steps:

Step 1: Calculate the total amount paid in the first year by multiplying the monthly installment by 12.
In cell A8, type the formula: =A2*12

Step 2: Subtract the total interest payment for the first year (calculated in Step 1) from the total amount paid in the first year.
In cell A9, type the formula: =A8-A6
The principal repayment during the first year is approximately $43 million.

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Answer:

6 m

.006 km  

6,000 mm

Step-by-step explanation:

Let's look at some conversions real quick:

1 cm --> 10 mm (multiply cm by 10)

1 cm --> 0.00001 km (divide cm by 100000)

1cm --> 0.01 m (divide cm by 100)

Now that this is laid out, lets do these conversions for 600 cm.

Meters (m) = 600/100 = 6 meters

Kilometers (km) = 600/100000 = .006km

Millimeters (mm) = 600 * 10 = 6,000 mm

I hope this helps!!

- Kay :)

The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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Answer:

a) \(P(148<X<175)=P(\frac{148-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{175-\mu}{\sigma})=P(\frac{148-160}{8}<Z<\frac{175-160}{8})=P(-1.5<z<1.875)\)

\(P(-1.5<z<1.875)=P(z<1.875)-P(z<-1.5)= 0.970-0.0668= 0.9032\)

b) \(P(X>164)=P(\frac{X-\mu}{\sigma}>\frac{164-\mu}{\sigma})=P(Z>\frac{164-160}{8})=P(z>0.5)\)

\(P(z>0.5)=1-P(z<0.5)= 1-0.691= 0.309\)

c) \(P(X<179)=P(\frac{X-\mu}{\sigma}<\frac{179-\mu}{\sigma})=P(Z<\frac{179-160}{8})=P(z<2.375)\)

\(P(z<2.375)= 0.991\)

Step-by-step explanation:

Let X the random variable that represent the heights of Guinean travels , and for this case we know the distribution for X is given by:

\(X \sim N(160,8)\)  

Where \(\mu=160\) and \(\sigma=8\)

Part a

We are interested on this probability

\(P(148<X<175)\)

We can ue the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

Using this formula we got:

\(P(148<X<175)=P(\frac{148-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{175-\mu}{\sigma})=P(\frac{148-160}{8}<Z<\frac{175-160}{8})=P(-1.5<z<1.875)\)

And we can find this probability with this difference using the normal standard distribution or excel:

\(P(-1.5<z<1.875)=P(z<1.875)-P(z<-1.5)= 0.970-0.0668= 0.9032\)

Part b

\(P(X>164)=P(\frac{X-\mu}{\sigma}>\frac{164-\mu}{\sigma})=P(Z>\frac{164-160}{8})=P(z>0.5)\)

And we can find this probability with this difference using the normal standard distribution or excel:

\(P(z>0.5)=1-P(z<0.5)= 1-0.691= 0.309\)

Part c

\(P(X<179)=P(\frac{X-\mu}{\sigma}<\frac{179-\mu}{\sigma})=P(Z<\frac{179-160}{8})=P(z<2.375)\)

And we can find this probability with this difference using the normal standard distribution or excel:

\(P(z<2.375)= 0.991\)

Answer: 0

Step-by-step explanation:

Answer:

1. Distribute

2. Combine like terms

3. Get all variable on one side and everything else on the other (Inverse operations: Add / subtract)

4. Solve for one of your variables (inverse operation: Multiple / Division

5. Simplify

Answer:

ASA

Step-by-step explanation:

SAS, it must go in order and SAS covers it up, Side, Angle, Side

Answer:

The slower plane is flying at 175 miles per hour and complete the trip in 10 hours

The faster plane is flying at 250 Miles per hour and complete the trip in 7 hours

Step-by-step explanation:

Let s= speed of the slower plane s+75= speed of the faster plane

The time it takes the slower plane to make the flight = 1750/s

The time it takes the faster plane to make the flight is=1750/(s+75)

The difference in these two times is 3 hours

1750/s - 1750/(s+7)=3

{(s+75) / (s+75) * (1750/s)} - {(s/s) * (1750/s+75)} =3

(1750s+131250 / s^2+75s) - (1750s/s^2+75s) =3

1750s+131,250-1750s / s^2+75d =3

131,250 / s^2+75s = 3

Cross product

131,250=3(s^2+75s)

131,250=3s^2+225s

43,750=s^2+75s

s^2+75s-43,750=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a=1

b=75

c= -43750

x= -b +or- √b^2-4ac / 2a

= -75 +or- √(75)^2 - (4)(1)(-43750) / (2)(1)

= -75 +or- √(5625) - (-175,000) / 2

= -75 +or- √180625) / 2

= -75 +or- 425 / 2

x= -75 + 425/2 OR -75- 425/2

=350/2 OR -500/2

x=175 OR -250

We will ignore the negative sign because the planes are not flying Backward

The slower plane is flying at 175 miles per hour and complete the trip in 1750/175= 10 hours

The faster plane is flying at 250 Miles per hour and complete the trip in 1750/250= 7 hours

Answer:

$60378

Step-by-step explanation:

$58,000 represents 100% of the original cost

100 + 4.1= 104.1% = 104.1/100 = 1.041

Multiplying by 1.041 gives the cost after the increase

price = 53000 x 1.041  = $60378

Answer:

124.6

Step-by-step explanation:

27/x = 13/60, 13x = 1620, x = 124.6

Answer:

3,590.16 Honduran Lempira.

Answer:

True

Step-by-step explanation:

Microsoft Excel is a great tool and has saved me on countless occasions in graphs and tables. I agree with the earlier answer by Hedland.

Answer:

Geometric.

Step-by-step explanation:

It is Geometric because there is a common ratio between the terms.

50p/100p = 1/2

25p/50p = 1/2

The common ratio is 1/2.

Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.

Answer: The answer is the one in the bottom right.

Step-by-step explanation:

The probability that exactly 18 of the 25 smartphones selected are purchased with warranty is:  The probability that exactly 8 of the 25 smartphones selected are not purchased with warranty is: The probability that all 25 smartphones selected are purchased with warranty is:  

The probability that at most 15 of the 25 smartphones selected are purchased with warranty is: The probability that at least 14 of the 25 smartphones selected are purchased with warranty is: f) The probability that more than half (i.e. > 12) of the 25 smartphones selected are purchased with warranty is: 9) The probability that at least 14 but no more than 23 of the 25 smartphones selected are purchased with warranty is:

h) The probability that less than 12 or more than 19 of the 25 smartphones selected are purchased with warranty is: Part 2Mean = Standard Deviation =  Part 3To find the minimum sample size required to expect to find exactly 72 smartphones that are purchased with warranty, we use the following formula: N = [(Z * σ) / E]^2 where Z is the z-score corresponding to the desired level of confidence, σ is the standard deviation, and E is the maximum error of estimation. Using a 95% level of confidence, Z = 1.96.Using the calculated standard deviation of 2.91 and expecting to find exactly 72 smartphones, the maximum error of estimation is 0.5.N = [(1.96 * 2.91) / 0.5]^2N

= 337.11

Therefore, the minimum sample size required to expect to find exactly 72 smartphones that are purchased with warranty is 338.

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To test Acme's claim that 30% of the production run are rookies, 60% are veterans, and 10% are all-stars, you would use a hypothesis test. The null hypothesis would be that the claimed proportions are true (pR = 0.3, pV = 0.6, pA = 0.1) and the alternative hypothesis would be that at least one of the claimed proportions is incorrect.

You could use a goodness-of-fit chi-square test to compare the observed frequencies of each group of players in the package to the expected frequencies based on the claimed proportions. If the chi-square test statistic is large enough to reject the null hypothesis, then there is evidence that the claimed proportions are not accurate. The significance level would need to be chosen and the appropriate critical value for the chi-square distribution with 2 degrees of freedom would need to be calculated or looked up.

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The system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

Carlos graphed the system of equations that can be used to solve the equation x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

To graph this system of equations, we need to set the equation equal to zero. So, the equation becomes:

x^3 - 2x^2 + 5x - 6 + 4x^2 - 14x - 12 = 0

Combining like terms, we get:

x^3 + 2x^2 - 9x - 18 = 0

To graph this equation, you can use a graphing calculator or plot points manually. Here are the steps to manually plot the graph:

1. Choose a range for x, for example, from -5 to 5.
2. Pick a few values for x within the chosen range and substitute them into the equation to find the corresponding y-values.
3. Plot the points (x, y) on a coordinate plane.
4. Connect the plotted points to create a smooth curve.

By following these steps, you can graph the system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

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a) If the confidence level had been 90% instead of 98%, the new confidence interval would be (0.325, 0.475).

b) If the sample size had been 255 instead of 170, the new confidence interval would be (0.292, 0.508).

c) If the confidence level had been 99% instead of 98%, the new confidence interval would be (0.304, 0.496).

a) First, we find the mean of the original confidence interval:

Mean = (Lower Limit + Upper Limit) / 2 = (0.313 + 0.487) / 2 = 0.4

Margin of Error = (Upper Limit - Mean) = (0.487 - 0.4) / 2 = 0.0435

New Margin of Error = Margin of Error * \((Z_{90} / Z_{98})\)

where \(Z_{90}\) is the critical value for a 90% confidence level, and \(Z_{98}\) is the critical value for a 98% confidence level.

From the standard normal distribution table, we find:

\(Z_{90}\) ≈ 1.645

\(Z_{98}\) ≈ 2.326

New Margin of Error = 0.0435 * (1.645 / 2.326) ≈ 0.0306

Finally, we construct the new confidence interval using the adjusted margin of error:

New Confidence Interval = (Mean - New Margin of Error, Mean + New Margin of Error)

                     = (0.4 - 0.0306, 0.4 + 0.0306)

                     ≈ (0.3694, 0.4306)

Therefore, the new confidence interval at a 90% confidence level would be approximately (0.369, 0.431) when rounded to three decimal places.

b) Standard Error = \(\sqrt{(p_{hat} * (1 - p_{hat})) / n}\)

where \(p_{hat}\) is the sample proportion and n is the sample size.

Given that the sample size increases to 255 while the sample proportion remains the same, the new sample proportion is:

\(p_{hat}\) = 68 / 255 ≈ 0.267

Standard Error = sqrt((0.267 * (1 - 0.267)) / 255) ≈ 0.028

For a 98% confidence level, the critical value is \(Z_{98}\) ≈ 2.326.

New Margin of Error = \(Z_{98}\) * Standard Error = 2.326 * 0.028 ≈ 0.065

New Confidence Interval = (\(p_{hat}\) - New Margin of Error, \(p_{hat}\) + New Margin of Error)

                     = (0.267 - 0.065, 0.267 + 0.065)

                     ≈ (0.202, 0.332)

Therefore, the new confidence interval with a sample size of 255 would be approximately (0.202, 0.332) when rounded to three decimal places.

c) From the standard normal distribution table, we find:

\(Z_{99}\) ≈ 2.576

New Margin of Error = Margin of Error * (\(Z_{99}\) / \(Z_{98}\)) = 0.0435 * (2.576 / 2.326) ≈ 0.0482

New Confidence Interval = (Mean - New Margin of Error, Mean + New Margin of Error)

                     = (0.4 - 0.0482, 0.4 + 0.0482)

                     ≈ (0.3518, 0.4482)

Therefore, the new confidence interval at a 99% confidence level would be approximately (0.352, 0.448) when rounded to three decimal places.

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Answer:

y = 30

Step-by-step explanation:

the 2 marked sides are congruent, thus the triangle is isosceles with the 2 base angles being congruent, both (y + 24)°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

(4y - 12)° is an exterior angle of the triangle , then

4y - 12 = y + 24 + y + 24

4y - 12 = 2y + 48 ( subtract 2y from both sides )

2y - 12 = 48 ( add 12 to both sides )

2y = 60 ( divide both sides by 2 )

y = 30

Minimum cost in terms of material used:\(C = 4cπ(r^2 + rh) = 4c.\)

We can solve this problem using the method of optimization. Let's first identify the variables and constraints:

Variables:

r: the radius of the barrel

h: the height of the barrel

Constraints:

Volume constraint: \(πr^2h = 32π\)

Non-negative constraints: r ≥ 0, h ≥ 0

We want to minimize the cost of the material used, which consists of the cost for the side of the barrel and the cost for the top and bottom of the barrel. Let's denote these costs by Cs and Ctb, respectively.

To express Cs and Ctb in terms of r and h, we need to find the surface area of the side of the barrel and the surface area of the top and bottom of the barrel, respectively.

Surface area of the side of the barrel:

lateral area = 2πrh

Surface area of the top and bottom of the barrel:

top area = bottom area =\(πr^2\)

Therefore, the total surface area of the barrel is:

A = lateral area + 2(top area) =\(2πrh + 4πr^2\)

The cost of the material for the side of the barrel is half that of the cost for the top and bottom. Let's denote the cost per square foot of the top and bottom as Ct, then the cost per square foot of the side is Cs = 0.5Ct.

The total cost of the material used can now be expressed in terms of r and h as follows:

C = Cs(lateral area) + Ct(2 top area) = \(0.5Ct(2πrh) + Ct(4πr^2) = Ct(2πrh + 4πr^2)\)

Now, we need to express Ct in terms of Cs. Let's assume that the cost per square foot of the side is Cs = c, then the cost per square foot of the top and bottom is Ct = 2c.

Therefore, the total cost of the material used can be expressed as:

\(C(r, h) = 2c(2πrh + 4πr^2) = 4cπ(r^2 + rh)\)

Now, we can formulate the optimization problem as follows:

minimize \(C(r, h) = 4cπ(r^2 + rh)\)

subject to πr^2h = 32π

r ≥ 0, h ≥ 0

To solve this problem, we can use the method of Lagrange multipliers. The Lagrangian function is:

\(L(r, h, λ) = 4cπ(r^2 + rh) - λ(πr^2h - 32π)\)

Taking partial derivatives with respect to r, h, and λ, we get:

\(dL/dr = 8cπr + λπh = 0\)

\(dL/dh = 4cπr + λπr^2 = 0\)

\(dL/dλ = πr^2h - 32π = 0\)

Solving these equations simultaneously, we get:

\(r = (4/π)^(1/3)\)

h = 4r

\(λ = (2/π)^(2/3)/2\)

Therefore, the dimensions of the barrel that can be constructed at a minimum cost in terms of material used are:

\(r = (4/π)^(1/3)\)

\(h = 4r = 4(4/π)^(1/3)\)

To find the minimum cost, we need to substitute these values of r and h into the cost function:

\(C = 4cπ(r^2 + rh) = 4c\)

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