Find the lateral area and surface area of the solid. Round to the nearest tenth, if necessary. the numbers are 15, 3, and 8 all for cm

The function f(x,y) = 4x + 5y, at the point (5,1) in the direction θ = -π/6, we get the directional derivative D_θ f(5,1) = (20/√3).

The directional derivative of a function f(x,y) at a point (a,b) in the direction of a unit vector u = <cosθ, sinθ> is defined as the rate of change of f along that direction. It is given by the dot product of the gradient vector ∇f(a,b) and the unit vector u:

D_u f(a,b) = ∇f(a,b) · u

In this case, the direction is specified by the angle θ = -π/6, which corresponds to the unit vector u_θ = <cos(-π/6), sin(-π/6)> = <√3/2, -1/2>.

The gradient vector ∇f(x,y) of f(x,y) = 4x + 5y is given by:

∇f(x,y) = <∂f/∂x, ∂f/∂y> = <4, 5>

So, at the point (5,1), we have:

∇f(5,1) = <4,5>

Now, we need to compute the dot product of ∇f(5,1) and the unit vector u_θ:

D_θ f(5,1) = ∇f(5,1) · u_θ = <4,5> · <√3/2, -1/2> = 4(√3/2) - 5(1/2) = 20/√3

Therefore, the directional derivative of f(x,y) = 4x + 5y at the point (5,1) in the direction of the angle θ = -π/6 is (20/√3).

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The acute angle that the ladder makes with the ground is 70.94°.

To work out the size of the acute angle that the ladder makes with the ground, we need to use trigonometry. Let's call the angle we're trying to find "theta" (θ). We know that the ladder is the hypotenuse of a right-angled triangle, with the wall being one side and the ground being the other. Using the Pythagorean theorem, we can work out the length of the ladder's side of the triangle:
a² + b² = c²
where a = 1.8m (the distance from the wall to the base of the ladder), b =? (the distance from the base of the ladder to the ground), and c = 5.1m (the length of the ladder).
Rearranging this formula, we get:
b² = c² - a²
b² = (5.1)² - (1.8)²
b² = 24.21
b = √24.21
b = 4.92m (to 2 decimal places)
Now that we know the lengths of the sides of the triangle, we can use trigonometry to find the angle θ. Specifically, we can use the tangent function:
tan(θ) = opposite/adjacent
where opposite = b (the distance from the base of the ladder to the ground) and adjacent = a (the distance from the wall to the base of the ladder).
tan(θ) = 4.92/1.8
tan(θ) = 2.7333 (to 4 decimal places)
Now we need to find the inverse tangent (or arctan) of this value to get the angle θ:
θ = arctan(2.7333)
θ = 70.94° (to 1 decimal place)
Therefore, the acute angle that the ladder makes with the ground is 70.94°.

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Answer:

252

Step-by-step explanation:

Formula for find the area of a parellogram is B*H

B=14

H=18

14*18=252

Answer:

Step-by-step explanation:

the space inside a parallelogram is the area

Area = b × h  (where b is the base and h the height)

Area = 14 × 18

Area = 252 units²

We would employ the technique of comparing proportions from dependent samples to draw conclusions about whether the proportion of students who have known a cancer survivor is representative of all students at the university.

The presented scenario compares the proportion of university students who have knowledge about cancer survivors to the percentage of all university students. The proper procedure for drawing conclusions would be to compare proportions from dependent samples because the same set of students is being polled (dependent samples).

In order to do this research, the study would gather information from a random sample of students and calculate the percentage of those students who knew a cancer survivor. This percentage would be contrasted with the anticipated percentage of all university students who had known a cancer survivor. We may draw conclusions about the total student body at the university by using statistical tests, such as the McNemar's test, to see if the observed proportion in the sample differs significantly from the expected proportion.

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Complete Question: A University of Florida study asks a random sample of students if they have ever known someone that was a cancer survivor. We want to extend the results to all students at the university. In this problem, we want to make inferences about:

a. comparing proportions from dependent samples

b. comparing proportions from 2 independent samples

c. comparing means from 2 independent samples

d. one mean

e. comparing means from dependent samples

f. one proportion

Answer:

Step-by-step explanation:

Answer:

3.8%

Step-by-step explanation:

To find the maximal area of the enclosure, we need to determine the dimensions of the rectangle that will maximize the area.

Let x be the length of the side of the rectangle perpendicular to the stream and y be the length of the side of the rectangle parallel to the stream. Then we have 2x + y = 100 (since the perimeter of the rectangle is equal to the amount of fencing available) and the area of the rectangle is A = xy. Solving for y in terms of x using the equation 2x + y = 100, we get y = 100 - 2x. Substituting this expression for y into the area equation, we get A = x(100 - 2x) = 100x - 2x^2.

To find the value of x that maximizes the area, we can take the derivative of A with respect to x, set it equal to 0, and solve for x. Doing so yields x = 25, which corresponds to a width of y = 50. Therefore, the maximal area of the enclosure is A = xy = 25(50) = 1250 square feet.

In summary, to find the maximal area of the enclosure, we used the fact that the perimeter of the rectangle is equal to the amount of fencing available and the area of the rectangle is A = xy.

We then solved for y in terms of x using the equation 2x + y = 100, substituted this expression for y into the area equation, and found the value of x that maximizes the area by taking the derivative of A with respect to x, setting it equal to 0, and solving for x. The maximal area of the enclosure was found to be 1250 square feet.

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Use composites to approximate the shape of the curved sides of the pool

From the question, we have the following statement that can be used in our computation:

Shape of swimming pool = composite figure

Curved side = Not a semicircle.

To do this, we simply break the composite figures into smaller figures whose areas can be calculated

After then, we add the areas of the individual shapes

This method of calculation is referred to as the areas by composite figures i.e. approximation method

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The odds of an event happening are the ratio of the probability of the event happening to the probability of the event not happening. In this case, the odds of rain tomorrow are 0.25 or 1 in 4, meaning we expect rain on 1 out of 4 days with similar weather conditions.

The odds of an event happening are the ratio of the probability of the event happening to the probability of the event not happening. In this case, the probability of rain tomorrow is 0.2, and the probability of no rain is 1 - 0.2 = 0.8. So the odds of rain are 0.2 / 0.8 = 0.25, or 1 in 4. This means that for every 4 days with similar weather conditions, we expect rain on 1 of those days.

Odds are often used in gambling and betting, where they represent the ratio of the payout to the amount staked. For example, if the odds of a horse winning a race are 4 to 1, this means that for every dollar staked, the payout is 4 dollars if the horse wins.

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In the given circle, the measure of arc SM is 106°

From the question, we are to determine the measure of arc SM.

First, we will determine the measure of angle QSM

m ∠QSM = 37° (Angles in the same segment)

Now,

Let the center of the circle be O

Thus,

OS and OM are radii

Therefore,

m ∠OSM = m ∠OMS

m ∠OSM = 37°

But,

Measure of arc SM = m ∠SOM

Now, we will determine the measure of angle SOM

m ∠SOM = 180° - 37° - 37°

m ∠SOM = 106°

Hence, measure of arc SM is 106°

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The correct graph of amounts of water plot the measurements on a line plot is shown in image.

We have to given that;

The amounts of water plot the measurements on a line plot are,

1/8 oz, 1/8 oz, 1/4 oz, 1./4 oz, 1/4 oz, 1/2 oz, 1/2 oz , 1/2 oz, 3/4 oz, 1 oz

Now, We have;

1/8 oz is repeats two times.

1/4 oz is repeats three times.

1/2 oz is repeats two times.

3/4 oz is only one times

And, 1 oz is repeats one time.

Thus, The correct graph of amounts of water plot the measurements on a line plot is shown in image.

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Under the periodic inventory system, Crowder Corporation would record the return of $200 of goods originally sold on credit to Discount Industries by crediting the accounts receivable account for $200 and debiting the sales returns and allowances account for $200.

If Crowder Corporation recorded the return of $200 of goods originally sold on credit to Discount Industries using the periodic inventory system, the transaction would be recorded as follows:

1. The accounts receivable account would be credited for $200 to reflect the fact that the company's outstanding balance owed by Discount Industries has been reduced.
2. The sales returns and allowances account would be debited for $200 to reflect the decrease in sales due to the return of goods.
3. The inventory account would be credited for the cost of the goods returned. Assuming that the goods were originally sold for their cost, the cost of the returned goods would also be $200. This credit would reduce the inventory account balance to reflect the fact that the company has fewer goods on hand.

The journal entry to record the return of goods under the periodic inventory system would be:

Accounts Receivable        200
Sales Returns and Allowances   200
  (To record the return of goods sold on credit)

Inventory                      200
Cost of Goods Sold          200
  (To record the cost of goods returned)

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Complete question:- Crowder Corporation recorded the return of $200 of goods originally sold on credit to Discount Industries. Using the periodic inventory approach, Crowder would record this transaction as ?

Therefore, the function f(x) = ax + b is one-to-one, and its inverse function is given by: f1(y) = (y - b)/a.

To determine if the function f(x) = ax + b is one-to-one, we need to show that it passes the horizontal line test. That is, for any horizontal line y = k, the function intersects the line at most once.
To do this, suppose that f(x1) = f(x2), where x1 and x2 are two distinct values in the domain. Then we have:
a x₁ + b = a x2 + b
Subtracting b from both sides gives:
a x₁ = a x₂
Since a ≠ 0, we can divide both sides by a to get:
x₁ = x₂
Therefore, the function f(x) = ax + b is one-to-one, and its inverse function is given by:
f1(y) = (y - b)/a

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The required measure of interior angles 1 and 2 are 116° and 62°.

Here,
According to the property of the triangle sum of the remote interior angle is equal to the remote interior triangle.
∠1 + 21 = 137
∠1 = 137 - 21
∠1 = 116

Similarly,
∠1 = ∠2 + 54
116 = ∠2 + 54
∠2 = 116 - 54
∠2 = 62°

Thus, the required measure of interior angles 1 and 2 are 116° and 62°.

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If twice a certain number plus 4 is at the same number plus 10. Then the number is 6.

Let x = the number

According to the given statement, "Twice a certain number plus 4 is at the same number plus 10," we can form an equation:

2x + 4 = x + 10

Solve this equation to find the value of x.

2x - x + 4 = x - x + 10

x + 4 = 10

Next, subtracting 4 from both sides of the equation:

x + 4 - 4 = 10 - 4

Simplifying:

x = 6

Therefore, the number is 6.

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R satisfies all three properties (reflexivity, symmetry, and transitivity), it is an equivalence relation on A.

To prove that the relation R is an equivalence relation on A, we need to show that R satisfies three properties: reflexivity, symmetry, and transitivity.

1. Reflexivity: For any element a in A, there exists the identity element e in G such that e(a) = a. Therefore, a R a, and R is reflexive.

2. Symmetry: If a R b, then there exists g in G such that g(a) = b. Since G is a permutation group, g^(-1) is also in G, and we have g^(-1)(b) = a. Thus, b R a, and R is symmetric.

3. Transitivity: If a R b and b R c, then there exist g and h in G such that g(a) = b and h(b) = c. The composition of two elements in G is also in G, so we have h(g(a)) = c. Therefore, (hg)(a) = c, and a R c. R is transitive.

Since R satisfies all three properties (reflexivity, symmetry, and transitivity), it is an equivalence relation on A.

The equivalence classes resulting from this equivalence relation R are called the orbits of A under G. Each orbit consists of elements that are related to each other by some element in G, meaning they can be transformed into each other by elements of G.

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No, there would not be a collision if the x-coordinate of the second particle is given by x2 = 3 cos(t) instead of x2 = -3 + cos(t).

This is because the x-coordinate of the first particle, x1, has a maximum value of 3 and a minimum value of -3. The x-coordinate of the second particle, x2, also has a maximum value of 3 and a minimum value of -4.

Since the maximum value of x2 is now 3 instead of -3, the two particles can no longer collide.

To confirm this, we can set the x-coordinates of the two particles equal to each other and solve for t. If the resulting values of t are within the interval 0 ≤ t ≤ 2π, then a collision occurs.

However, when we set 3sin(t) = 3cos(t), we get tan(t) = 1, which gives t = π/4 or 5π/4. These values of t are not within the interval 0 ≤ t ≤ 2π, so there is no collision.

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Therefore, the length of the curve for t ∈ [0, 4] is 4√13.

To find the length of the curve defined by x(t) = 2t and y(t) = 3t - 1 for t ∈ [0, 4], we can use the arc length formula:

L = ∫[a,b] √[x'(t)^2 + y'(t)^2] dt

where x'(t) and y'(t) are the derivatives of x(t) and y(t) with respect to t.

Let's calculate the derivatives first:

x'(t) = d/dt (2t) = 2

y'(t) = d/dt (3t - 1) = 3

Now, we can calculate the integrand:

√[x'(t)^2 + y'(t)^2] = √[(2)^2 + (3)^2] = √[4 + 9] = √13

Substituting the integrand into the arc length formula and integrating with respect to t from 0 to 4:

L = ∫[0,4] √13 dt

= √13 ∫[0,4] dt

= √13 [t] from 0 to 4

= √13 (4 - 0)

= 4√13

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As the size of the house increases, the monthly cost to heat the house with natural gas also increases.Positive, meaning as the size of the house increases, the heating cost also increases.

Based on the data provided, it appears that there is a positive correlation between house size (x) and heating cost (y). As the size of the house increases, the monthly cost to heat the house with natural gas also increases.

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To find the equation of the line passing through the points (-4, -3) and (-4, 6),

we note that the x-coordinate of both points is the same, which means the line is vertical and parallel to the y-axis. In this case, the equation of the line can be written as x = a, where 'a' is the x-coordinate of any point on the line.

Since both points have an x-coordinate of -4, the equation of the line passing through them is x = -4.

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Answer:

x=-4

Step-by-step explanation:

The general equation is y=mx+b where m is the slope and b is the y intercept.

Notice that there are 2 different y coordinates (-3 and 6) for the same x (-4) coordinate!

Slope = rise/run = (y2-y1)/(x2-x1) = (-3-6)/(-4--4) = -9/0 = there's NO slope, you cannot divide by zero!

So the equation is just x=-4.

See attached screenshot.

Answer:

10.5

Step-by-step explanation:

you times 8+12+2 then x 2 and divide by 4 so

Thus, the total cost of the first 64 units is approximately $2730.67.

To find the total cost of the first 64 units, we need to integrate the marginal cost function over the range of production from x=0 to x=64.

The marginal cost function is given by C'(x) = 8√x.

Integrating this function with respect to x, we get:
C(x) = ∫(8√x dx) = 8 * (2/3)x^(3/2) + C

To find the total cost for the first 64 units, we need to evaluate C(x) at x=64 and x=0 and subtract the results:
C(64) - C(0) = (8 * (2/3) * 64^(3/2) + C) - (8 * (2/3) * 0^(3/2) + C)

Simplifying the equation, we get:
C(64) - C(0) = 8 * (2/3) * 64^(3/2)

Now, compute the value:
C(64) - C(0) = 8 * (2/3) * 512 = (16/3) * 512 ≈ 2730.67

So, the total cost of the first 64 units is approximately $2730.67.

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True. Correlation measures the strength of the relationship between variables. A correlation closer to 1 or -1 suggests a stronger relationship and supports the claim that x determines y.

Correlation measures the degree of association between two variables, typically denoted as x and y. A correlation coefficient ranges from -1 to 1, where a value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates a weak or no correlation.

When the correlation coefficient is close to 1 or -1, it suggests a strong relationship between the variables. If the correlation is positive and close to 1, it indicates that as the level of x increases, the level of y tends to increase as well. Similarly, if the correlation is negative and close to -1, it implies that as the level of x increases, the level of y tends to decrease.

Therefore, a correlation closer to 1 or -1 provides greater evidence that the level of x determines the level of y, supporting the claim of a strong relationship between the two variables.



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Answer: The graph of f(x) = x^2 should be shifted upward by 1 unit to produce the graph of g(x) = x^2 + 1.

Explanation: The function g(x) = x^2 + 1 is obtained by adding 1 to the function f(x) = x^2. This means that for any value of x, the value of g(x) is 1 unit greater than the value of f(x). Graphically, this corresponds to shifting the entire graph of f(x) upward by 1 unit. As a result, the graph of g(x) will be identical to the graph of f(x), but shifted upward by 1 unit.

You have an SRS of six observations from a Normally distributed population, the correct answer is (c) 2.015

To obtain an 80% confidence interval for the mean µ of a Normally distributed population with a small sample size (n<30), we need to use a t-distribution with n-1 degrees of freedom. In this case, since we have an SRS of six observations, our degrees of freedom are 6-1=5. To determine the critical value for an 80% confidence interval using a t-distribution with 5 degrees of freedom, we can use a t-table or a calculator. Using a t-table, we would find the row corresponding to 5 degrees of freedom and the column for a two-tailed test with an area of 0.10 (80% divided by 2). The intersection of this row and column gives us a critical value of 2.015. Therefore, the correct answer is (c) 2.015. Alternatively, we could use a calculator that has a t-distribution function. In this case, we would enter a confidence level of 0.80, a degree of freedom of 5, and ask the calculator to output the critical value. This would also give us a critical value of 2.015.

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We can use the error bound formula for the midpoint rule to find the smallest value of N for which the error is less than 10^-9:

Error ≤ K(b-a)^3/(12N^2) where K is the maximum value of the absolute value of the second derivative of f on the interval [a,b]. In this case, we have f(x) = x^(4/3) and we need to integrate from 1 to 2.

First, we find the second derivative of f:

f''(x) = (4/3)(1/3)x^(-2/3)

To find the maximum value of the absolute value of the second derivative on [1,2], we evaluate it at the endpoints and at critical points in the interval. Since the second derivative is decreasing on the interval, its maximum value occurs at the left endpoint, x=1:

|f''(1)| = (4/3)(1/3)(1)^(-2/3) = 1.5874

Next, we need to choose N such that the error bound is less than 10^-9:

K(b-a)^3/(12N^2) ≤ 10^-9

Plugging in the values we have:

(1.5874)(2-1)^3/(12N^2) ≤ 10^-9

Solving for N:

N^2 ≥ (1.5874)(2-1)^3/(12(10^-9))

N^2 ≥ 1.3245×10^9

N ≥ √(1.3245×10^9)

N ≥ 36413.89Since N must be an integer, we round up to get:N = 36414

Therefore the smallest value of N for which Error(SN) 10^-9 is 36414.

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We can use the error bound formula for the midpoint rule to find the smallest value of N for which the error is less than 10^-9:

Error ≤ K(b-a)^3/(12N^2) where K is the maximum value of the absolute value of the second derivative of f on the interval [a,b]. In this case, we have f(x) = x^(4/3) and we need to integrate from 1 to 2.

First, we find the second derivative of f:

f''(x) = (4/3)(1/3)x^(-2/3)

To find the maximum value of the absolute value of the second derivative on [1,2], we evaluate it at the endpoints and at critical points in the interval. Since the second derivative is decreasing on the interval, its maximum value occurs at the left endpoint, x=1:

|f''(1)| = (4/3)(1/3)(1)^(-2/3) = 1.5874

Next, we need to choose N such that the error bound is less than 10^-9:

K(b-a)^3/(12N^2) ≤ 10^-9

Plugging in the values we have:

(1.5874)(2-1)^3/(12N^2) ≤ 10^-9

Solving for N:

N^2 ≥ (1.5874)(2-1)^3/(12(10^-9))

N^2 ≥ 1.3245×10^9

N ≥ √(1.3245×10^9)

N ≥ 36413.89Since N must be an integer, we round up to get:N = 36414

Therefore the smallest value of N for which Error(SN) 10^-9 is 36414.

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Answer: The area is 83.6

Step-by-step explanation:

7.6 x 11 = 83.6

The domain of the set of ordered pairs include the following: {1, 2, 3, 4}.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the set of ordered pairs above, we can reasonably and logically deduce the following domain and range:

Domain = {1, 2, 3, 4}.

Range = {3, 4, 5}.

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The exact length of  curve y = (x^4/16) + (1/2)x^2 is obtained by integrating the arc length formula.

How we find the exact length of the curve defined by the equation y = (x[tex]^4[/tex]/16) + (1/2)x[tex]^2[/tex].

To find the exact length of the curve defined by the equation y = (x[tex]^4[/tex]/16) + (1/2)x[tex]^2[/tex], we can use the arc length formula. This formula calculates the length of a curve over a given interval by integrating the square root of the sum of the squares of the derivatives of x and y with respect to a parameter.

In this case, we need to find the derivative of y with respect to x, which is given by (4x[tex]^3[/tex]/16) + x.

Using this derivative, we substitute it into the arc length formula, which becomes an integral of √(1 + ((4x[tex]^3/16[/tex]) + x)[tex]^2[/tex]) dx over the desired interval.

By evaluating this integral, we can obtain the exact length of the curve. The result will be a numerical value that represents the length of the curve in the given interval.

It is important to note that the specific interval over which we calculate the length will affect the final result.

The arc length formula allows us to find the precise length of the curve, taking into account its shape and path.

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The theory behind Euler's equation and the boundary conditions for a column with one fixed end and the other end free. Therefore, the answer to the question is d) 1/2, as x = π/2L = (2(1) - 1)π/2L = (2n - 1)π/2L when n = 1/2.

Euler's equation is derived from the Euler-Bernoulli beam theory, which states that a slender column under axial compression will buckle when the compressive stress exceeds a certain critical value. The buckling load is given by the equation P= xt^2π^2Et, where P is the buckling load, x is a dimensionless factor called the slenderness ratio (the ratio of the column length to its cross-sectional dimensions), t is the thickness of the column wall, E is the modulus of elasticity of the column material, and π is the mathematical constant pi.

For a column with both ends pinned, the value of x is given by x = nπ/L, where n is an integer and L is the length of the column. For a column with one end fixed and the other end free, the value of x is given by x = (2n - 1)π/2L, where n is an integer.  In this case, we have a column with one fixed end and the other end free, so we need to use the equation x = (2n - 1)π/2L to find the value of x. Since n can be any integer, we can choose n = 1 to simplify the equation and get x = π/2L.

Substituting this value of x into Euler's equation, we get P = (π/2L)²π²Et = π²Et/4L². This means that the buckling load for a column with one fixed end and the other end free is proportional to the modulus of elasticity and inversely proportional to the square of the length of the column.

Therefore, the answer to the question is d) 1/2, as x = π/2L = (2(1) - 1)π/2L = (2n - 1)π/2L when n = 1/2

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