Numerical Analysis 2 -Use linear interpolation () to find the (6) for the data set {(3, 4), (8, 3)} a) O 21/5 b) O 17/5 c) O 13/5 d) O 4/5 e) O 16/5 O Leave blank

Divide and Conquer model. The largest numbers from each segment can be compared to determine the overall largest number.

The divide and conquer model involves breaking down the problem into smaller subproblems, solving them independently, and then combining their results to form the final solution. In the case of finding the largest number in a list, the list can be divided into smaller segments, and the largest number in each segment can be found concurrently. Finally, the largest numbers from each segment can be compared to determine the overall largest number.

Using the divide and conquer model in a MIMD parallel computing environment, the list of numbers can be distributed among multiple processors. Each processor can then independently execute the task of finding the largest number in its assigned segment. Once each processor has completed its task, the results can be communicated back and combined to determine the largest number in the entire list. This approach significantly reduces the time taken to find the largest number by taking advantage of parallelism and the computational power of multiple processors.

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The value of u in the equation tan( 34° ) = 9/u is approximately 13.34.

Given the equation in the question:

tangent( 34° ) = 9/u

To solve for u, rewrite the equation as 9/u = tangent( 34° ).

9/u = tan( 34° )

Cross multiply:

u × tangent( 34° )  = 9

Divide both sides by tangent( 34° )

u = 9 / tan( 34° )

Next, evaluate tangent( 34° ), tan( 34° ) = 0.67450851

Hence:

u = 9 / 0.67450851

Divide 9 by 0.67450851

u = 13.343

Therefore, u is measure approximately 13.34 units.

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The discriminant is negative, the conic section is an ellipse.

The given equation of the conic section is:

x^2 + y^2 - 8x + 14y + 61 = 0

To determine the type of conic section represented by this equation, we can analyze its coefficients. The general form of a conic section equation is:

Ax^2 + By^2 + Cx + Dy + E = 0

Comparing the given equation with the general form, we have:

A = 1, B = 1, C = -8, D = 14, E = 61

To further determine the conic section type, we can calculate the discriminant:

Discriminant = B^2 - 4AC

Plugging in the values, we get:

Discriminant = (1)^2 - 4(1)(1) = 1 - 4 = -3

Since the discriminant is negative, the conic section is an ellipse.

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Therefore, The covariance for X and Y is 0.1667 and the correlation coefficient (rho) is 0.643.

To compute the covariance for X and Y in Exercise 22, we need to use the formula Cov(X,Y) = E(XY) - E(X)E(Y). Plugging in the values from the joint pmf table, we get Cov(X,Y) = (0*1/12 + 1*1/6 + 2*1/4 + 3*1/6 + 4*1/12) - (1*1/3 + 2*1/2 + 3*1/6)(1*1/3 + 2*1/2 + 3*1/6) = 0.1667.
To compute rho for X and Y in the same exercise, we first need to find the standard deviations of X and Y. Using the formulas for variance and standard deviation, we get SD(X) = 0.82 and SD(Y) = 0.82. Then, using the formula rho = Cov(X, Y) / (SD(X)SD(Y)), we get rho = 0.643.

Therefore, The covariance for X and Y is 0.1667 and the correlation coefficient (rho) is 0.643.

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The value of Σ (X – μ ) for the population is 0. Therefore, the correct option is D.

The formula for Σ (X – μ ) is the sum of deviations from the mean, which should always equal zero for the entire population. Hence, to find the value of Σ(X - μ) for the population, you should know that Σ(X - μ) equals 0 for any population.

This is because when you sum up all the deviations from the mean, the positive and negative differences cancel each other out. Therefore, regardless of the value of SS and σ2, the sum of deviations from the mean for the entire population will always be equal to zero.

Hence, the correct answer is option D: 0.

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Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:

a) Adjacency lists:

In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.

Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.

b) Adjacency matrix:

In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.

c) Incidence matrix:

In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.

Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.

In summary:

a) Adjacency lists: O(n + m)

b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs

c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs

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the area of the surface obtained by rotating the curve y = sin(4x) or y = sin(2x), the specific interval or region of rotation needs to be specified. The process involves using the formula for surface area obtained by rotating a curve around the x-axis or y-axis.

To determine the surface area of the curve y = sin(4x) or y = sin(2x) when rotated, we need to specify the interval or region of rotation. Let's consider rotating the curve around the x-axis as an example.

The formula for the surface area obtained by rotating a curve y = f(x) around the x-axis over an interval [a, b] is given by the integral:

Surface Area = 2π ∫[a to b] f(x) × sqrt(1 + ([tex]f'(x))^2[/tex]) dx.

Applying this formula to the curve y = sin(4x) or y = sin(2x), we need to determine the interval [a, b] over which the curve is rotated. Additionally, we would need to calculate the derivative f'(x) of the given function.

Once the interval and derivative are determined, we can evaluate the integral using appropriate techniques, such as integration by substitution or integration by parts, to find the surface area of the rotated curve.

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The circumference of a circle with radius r in the taxicab metric and square metric is 8r.

In the taxicab metric, the distance between two points P(x₁, y₁) and Q(x₂, y₂) is defined as |x₂ - x₁| + |y₂ - y₁|. Therefore, the taxicab circumference can be calculated by finding the perimeter of a square with side length 2r, which is 4 * (2r) = 8r.

Similarly, in the square metric, the distance between two points P(x₁, y₁) and Q(x₂, y₂) is defined as max(|x₂ - x₁|, |y₂ - y₁|). The square circumference can be determined by finding the perimeter of a square with side length 2r, which is 4 * (2r) = 8r.

In both metrics, the circumference of a circle with radius r is 8r. This result holds because the taxicab and square metrics measure distances along the edges of a square, rather than along a curved path.

Therefore, the circumference of a circle with radius r in the taxicab metric and square metric is equal to 8 times the radius.

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The factored form of the quadratic equation is ( x + 9 ) ( x - 4 ) = 0

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 5x - 36 = 0

On factorizing , we get

x² - 4x + 9x - 36 = 0

Taking the common factors of the equation , we get

x ( x - 4 ) + 9 ( x - 4 ) = 0

( x + 9 ) ( x - 4 ) = 0

So , the solution to the equation is

x = -9

And , x = 4

Therefore , the values of x are x = -9 or x = 4

Hence , the equation is solved and x = -9 or x = 4

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Answer:

Step-by-step explanation:

a) The population for this study would be all of the crops that the farmer grows on his farm, which includes corn, beans, tomatoes, and peppers.

b) The sample for this study is the 10 plants of each crop that the farmer chose to test the different pesticides on.

c) The sampling technique used in this study is convenience sampling, as the farmer selected the plants that were most easily accessible to him for the experiment.

However, this may not necessarily represent the entire population accurately, as other factors such as soil quality and weather conditions may also influence crop growth.

It would be ideal to use a randomized sampling technique to ensure that the results are representative of the entire population.

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Answer: [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

    Since we are given two clear coordinate points on the graph, we can use the "rise over run" method. Starting at (0, 0), we will count 2 units up and 3 units right to (3, 2). This gives us a slope of 2 over 3 ("rise over run).

The correct expression in the expanded form of [tex]log6(4(2^9^x))[/tex] is log6(9x).

The given expression log6(4([tex]2^9^x[/tex])) represents the logarithm of the product of 4 and 2 raised to the power of 9x, all with base 6. To simplify this expression, we can apply the property of logarithms that states log(ab) = log(a) + log(b).

By using this property, we can separate the expression into two logarithms: log6(4) + log6([tex]2^9^x[/tex]). The first term, log6(4), remains unchanged.

However, the second term, log6([tex]2^9^x[/tex]), simplifies to 9x * log6(2) since the logarithm of an exponential expression with the same base results in the exponent multiplied by the logarithm of the base. Combining these terms, we obtain the expanded form expression of log6(4([tex]2^9^x[/tex])) as log6(4) + 9x * log6(2).

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The factors of the given quadratic equation are x = -3 or x = -8

Finding two binomials whose product is equal to zero is necessary to factor the quadratic equation x² + 11x + 24 = 0 in order to solve it.

This is how the equation can be factored:

(x + 3)(x + 8) = 0

If we set each element to zero, we get:

x + 3 = 0 or x + 8 = 0

When we solve these equations, we discover:

x = -3 or x = -8

Therefore, x = -3 and x = -8 are the answers to the quadratic equation x² + 11x + 24 = 0.

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The measure of the angle outside the circle is x = 25°

Given data ,

Let the circle be represented as T

where the measure of the angles subtended by the arcs are

The measure of arc of circle CAH = 205°

And , the measure of arc CH = 155°

The angle outside the circle is given by the relation:

x = ( mCAH - mCH ) / 2

On simplifying , we get

x = ( 205 - 155 ) / 2

x = 25°

Hence , the angle is x = 25°

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a)

i) The original cube has a side length of 4 cm. The volume of a cube is calculated by cubing the length of one side. So, the volume of the original cube is 4 cm x 4 cm x 4 cm = 64 cm³.

ii) The enlarged cube has a ratio of 3:1 compared to the original cube. This means that each side length of the enlarged cube is three times the length of the original cube. Therefore, the side length of the enlarged cube is 4 cm x 3 = 12 cm. The volume of the enlarged cube is calculated by cubing the length of one side: 12 cm x 12 cm x 12 cm = 1,728 cm³.

b) To find the ratio by which the volume has been increased, we can compare the volumes of the enlarged and original cubes. The ratio of the enlarged cube's volume to the original cube's volume is 1,728 cm³ : 64 cm³, which simplifies to 27 : 1.

This means that the volume of the enlarged cube is 27 times greater than the volume of the original cube. Therefore, the volume has been increased by a ratio of 27:1.

The functions that include a reflection of the parent function across the y-axis are g(x) = (-1/2x)², k(x) = (-5x)², p(x) = (-x)²

from the question, we have the following parameters that can be used in our computation:

The list of optons

The function of reflection of the parent function across the y-axis can be represented as

g(x) = -f(x)

This means that the x value is negated

using the above as a guide, we have the following:

The functions are g(x) = (-1/2x)², k(x) = (-5x)², p(x) = (-x)²

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θ = (2n + 1)π/2, where n is an integer.

To find the solutions to the equation 3sinθ + 5 = -2sinθ, we can start by simplifying the equation:

3sinθ + 5 = -2sinθ

5 = -2sinθ - 3sinθ

5 = -5sinθ

Next, we isolate the sine term by dividing both sides of the equation by -5:

5 / -5 = -5sinθ / -5

-1 = sinθ

Now, we need to find the values of θ that satisfy sinθ = -1. The solutions for this equation occur at angles where the sine function equals -1. In the unit circle, this occurs at the angle π/2 (or 90 degrees) and its multiples.

Therefore, the general formula for all the solutions to the equation is:

θ = (2n + 1)π/2

where n is an integer. This formula represents all the angles in radians that satisfy the equation 3sinθ + 5 = -2sinθ.

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Therefore, the inverse of the given isomorphism T is T^(-1)(c, d) = (d + c/8)x + (c/8).

Let's find the inverse of the given isomorphism T.
The given isomorphism T: P1 → R2 is defined as T(ax + b) = (8b, a - b). To find the inverse T^(-1)(c, d), we need to express a and b in terms of c and d. From the given transformation, we have:
1. 8b = c
2. a - b = d
From equation 1, we can express b as b = c/8. Now substitute this value into equation 2:
a - (c/8) = d => a = d + c/8
Now, we can express the inverse transformation T^(-1)(c, d) using a and b:
T^(-1)(c, d) = (d + c/8)x + (c/8)

Therefore, the inverse of the given isomorphism T is T^(-1)(c, d) = (d + c/8)x + (c/8).

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Answer: Yes

Step-by-step explanation:

To determine whether the rock will hit the water in 2 seconds, let's first analyze the motion of the falling object using the given information.

The equation for the displacement of an object in free fall is given by:

s = 16t^2

Where s represents the vertical displacement and t represents time.

In this case, the rock is dropped from a height of 64 feet above the water, so the equation becomes:

s = 64 - 16t^2

Here, s represents the displacement relative to the starting point, which is the height of the bridge.

To determine if the rock will hit the water in 2 seconds, we need to calculate the displacement of the rock at that time. Let's substitute t = 2 into the equation:

s = 64 - 16(2)^2

s = 64 - 16(4)

s = 64 - 64

s = 0

The result shows that at t = 2 seconds, the displacement of the rock is 0. This means that the rock has fallen exactly to the height of the water. Therefore, the rock will indeed hit the water in 2 seconds.

The required base of the given triangle = 2/3 ft

Given that,

Area of triangle  = 2/5 square ft

And height of the triangle = 6/5 ft

We we know that,

In a two-dimensional plane, the area of a triangle is the region enclosed by it. A triangle, as we all know, is a closed shape with three sides and three vertices.

Thus, the area of a triangle is the total space filled by the triangle's three sides. The general formula for calculating the area of a triangle is half of the product of its base and height.

Then,

Area = (1/2)xbxh

Where,

b is base of triangle

h is height of triangle

Here, we have h = 6/5

Now substitute the values in this formula of are of triangle we get

⇒ 2/5 = (1/2)x(6/5)xb

⇒ 2/5 = (3/5)xb

⇒     b = 2/3 ft

Hence,

⇒ Base = 2/3 ft

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The probability that Brandon will earn a free homework pass is approximately 0.026.

To calculate the probability that Brandon will earn a free homework pass, we need to determine the probability of him answering at least five questions correctly through guessing.

Since each question has five answer choices and Brandon is guessing, the probability of him answering any particular question correctly by chance is 1/5.

To find the probability of answering exactly five questions correctly, we can use the binomial probability formula.

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

where n is the number of trials (number of questions in this case), k is the number of successful outcomes (number of questions answered correctly), p is the probability of success (probability of answering a question correctly), and (nCk) represents the number of combinations.

Plugging in the values, we have:

P(X = 5) = (10C5) * (1/5)^5 * (4/5)^(10-5)

Calculating this expression, we find:

P(X = 5) ≈ 0.026

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Answer: Hello, I can help!

The probability that Jerry will have to wait for the bus for more than five minutes is 0.3. Therefore, the probability that he will not have to wait for more than five minutes is 0.7 (since the sum of the probabilities of all possible outcomes is 1).

The probability that Jerry does not wait for more than five minutes on any one day is 0.7. The probability that he does not wait for more than five minutes on all 5 days is:

0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807

Therefore, the probability that Jerry does not wait for more than five minutes all 5 days this week is 0.16807 or about 16.81%.

Step-by-step explanation: rest easy my friend:)

Answer:

To answer this question, we need to use the binomial probability formula:

P(X = k) = nCk * p^k * (1 - p)^(n - k)

where n is the number of trials, k is the number of successes, p is the probability of success, and nCk is the number of combinations of k elements out of n.

In this case, n = 5 (the number of days in a week), k = 5 (the number of days that Jerry does not wait for more than five minutes), and p = 0.7 (the probability that Jerry does not wait for more than five minutes on any given day).

Plugging these values into the formula, we get:

P(X = 5) = 5C5 * 0.7^5 * (1 - 0.7)^(5 - 5)

P(X = 5) = 1 * 0.16807 * 1

P(X = 5) = 0.16807

Therefore, the probability that Jerry does not wait for more than five minutes all 5 days this week is about 16.8%.

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Therefore, Finally, we factor out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)), which simplifies to 1/cos(t) or sec(t).

To simplify 1 + sec(t) / 1 + cos(t), we need to use the identity sec(t) = 1 / cos(t).
So, 1 + sec(t) / 1 + cos(t) becomes 1 + 1/cos(t) / 1 + cos(t).
Next, we'll simplify the expression by multiplying the numerator and denominator by cos(t), which gives us (cos(t) + 1) / (cos^2(t) + cos(t)).
Finally, we can simplify this expression further by factoring out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)).
The cos(t) + 1 in the numerator cancels with the cos(t) + 1 in the denominator, leaving us with 1/cos(t) or sec(t).
To simplify 1 + sec(t) / 1 + cos(t), we use the identity sec(t) = 1 / cos(t). Then, we multiply the numerator and denominator by cos(t), which gives us (cos(t) + 1) / (cos^2(t) + cos(t)).

Therefore, Finally, we factor out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)), which simplifies to 1/cos(t) or sec(t).

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Using the sample space the calculated probabilities are:

(a) P(sum=5 or sum= = 6) = 1/4

(b) P(sum= 14) = 0

(c) P(sum 9 or more) = 5/18

(d) P(sum 12 or less) = 35/36

a. The probability of getting a sum of 5 or a sum of 6 when tossing two dice can be calculated as follows. The possible outcomes for a sum of 5 are (1, 4), (2, 3), (3, 2), and (4, 1). The possible outcomes for a sum of 6 are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). Therefore, there are a total of 9 favorable outcomes out of 36 possible outcomes. Thus, the probability is 9/36, which simplifies to 1/4 or 0.25.

b. The probability of getting a sum of 14 when tossing two dice is zero. Since the maximum possible sum of two dice is 12 (6 + 6), there are no favorable outcomes for a sum of 14. Therefore, the probability is 0.

c. The probability of getting a sum of 9 or more when tossing two dice can be calculated by finding the favorable outcomes. The possible outcomes for a sum of 9 or more are (3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), and (6, 6). There are 10 favorable outcomes out of 36 possible outcomes, resulting in a probability of 10/36, which simplifies to 5/18 or approximately 0.278.

d. The probability of getting a sum of 12 or less when tossing two dice can be calculated by finding the favorable outcomes. Since the maximum possible sum is 12, all outcomes are favorable except for (6, 6). Therefore, there are 35 favorable outcomes out of 36 possible outcomes, resulting in a probability of 35/36 or approximately 0.972.

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Therefore, the simplified form is x^3y^3z^3.

The simplified form of (x^2yz)^2xy^2z^2)/(xyz)^2 is x^3y^3z^3.
Explanation:
To simplify this expression, we first need to expand the numerator:
(x^2yz)^2xy^2z^2 = x^4y^3z^3
Now we can divide the numerator by the denominator:
x^4y^3z^3 / (xyz)^2 = x^4y^2z^2
Finally, we can simplify this expression by combining like terms:
x^4y^2z^2 = x^3y^3z^3

To simplify the given expression, we will apply the exponent rules step-by-step.
Given expression: ((x^2yz)^2 * xy^2z^2) / (xyz)^2
Step 1: Simplify the terms within the parentheses by raising them to the power indicated.
((x^4y^2z^2) * xy^2z^2) / (x^2y^2z^2)
Step 2: Multiply the numerators.
(x^5y^4z^4) / (x^2y^2z^2)
Step 3: Divide the terms with the same base by subtracting the exponents.
(x^(5-2)y^(4-2)z^(4-2))
The simplified expression is x^3y^2z^2.

Therefore, the simplified form is x^3y^3z^3.

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The total amount of Chung's investment at the end of 4 years would be $2804.40.

To calculate the total amount of Chung's investment at the end of 4 years with simple interest, we can use the formula:

Total amount = Principal + (Principal × Rate × Time)

Given:

Principal (P) = $2460

Rate (R) = 3.5% = 0.035 (decimal form)

Time (T) = 4 years

Plugging in the values into the formula:

Total amount = 2460 + (2460 × 0.035 × 4)

= 2460 + (344.4)

= $2804.40

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Answer:

56.2

Explanation:

There is a way to remember the ways to solve for right triangles, SOH CAH TOA which stands for each of the ways to solve for angles or sides:

Sine: Opposite over Hypotenuse

Cosine: Adjacent over Hypotenuse

Tangent: Opposite over Adjacent

In this case, with the information we have, we would use tangent since we have both the opposite side, b, and the adjacent side, a.

It would be the inverse of tangent (tan⁻¹) since you are solving for the angle and not a side.

You would use a calculator to solve this, by dividing b by a.

tan⁻¹(b/a)

tan⁻¹(46.7/31.3) = 56.1686012868

Round to the nearest tenth = 56.2

*Make sure your calculator is in degrees mode or it will give you an incorrect result.

The correct simplified setup of the line integral of F over C is (b) (5 sin t cos t+2 sin t) dt.

The unit circle can be parametrized by x = cos t and y = sin t for t between 0 and pi. Therefore, the top half of the unit circle can be parametrized by x = cos t and y = sin t for t between 0 and pi/2. Using this parametrization, we can write the line integral as ∫(5 sin t cos t+2 sin t) dt, which is equivalent to choice (b).

The correct simplified setup of the line integral of F over C is (b) (5 sin t cos t+2 sin t) dt. Regarding the statement in question 4, none of the choices are correct as they all involve different variables and do not match the given force field. Regarding the statement in question 5, false. The work done by a force field F on an object moving along a path C is given by the line integral ∫F.dr, where dr is the differential displacement along the path.

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Answer:

I didn’t know if I was solving for x or for y but I believe that the answer is x=75-y

Step-by-step explanation:

Solve by simplifying both sides of the equation, then isolating the variable.