adjacent i need help understanding this

The work done by the force is 1/6.To visualize the path followed by the particle, we plot the region R in the xy-plane.The graph of the appropriate region in the xy-plane is shown below: Graph of the region R in the xy-plane.

To use Green's Theorem to find the work done by the force: F(x, y) = x(x + 3y)i + 3xy^2j in moving a particle from the origin along the x-axis to (1,0) then along the line segment to (0,1) and then back to the origin along the y-axis is as follows:

Green's Theorem: ∫C F . dr = ∬R ( ∂Q/∂x - ∂P/∂y ) dA

Where C is the closed curve, P and Q are the components of F, and R is the region bounded by C.

Therefore, we first need to calculate ∂Q/∂x and ∂P/∂y:∂Q/∂x = 3x^2∂P/∂y = xTherefore, the work done by the force is given by:

∫C F . dr

= ∬R ( ∂Q/∂x - ∂P/∂y ) dA

= ∬R ( 3x^2 - x ) dA

We need to evaluate the above expression over the region R. The region R is shown in the figure below:Region RThus, the region R is given by 0 ≤ y ≤ x ≤ 1.To evaluate the double integral, we can integrate first with respect to y and then with respect to x, as follows:

∬R ( 3x^2 - x ) dA

= ∫0¹ ∫0xy ( 3x^2 - x ) dy dx + ∫0¹ ∫x¹ ( 3x^2 - x ) dy dx+ ∫1⁰ ∫0¹ ( 3x^2 - x ) dy dx

= ∫0¹ x(3x^2 - x) dx + ∫0¹ ( x³ - x² ) dx+ ∫1⁰ ( x³ - x² ) dx

= [3/4 x^4 - 1/2 x^2]0¹ + [1/4 x^4 - 1/3 x³]0¹ + [1/4 x^4 - 1/3 x³]1⁰

= ( 3/4 - 1/2 ) + ( 1/4 - 1/3 ) + ( 1/4 - 1/3 )

= 1/6

Therefore, the work done by the force is 1/6.To visualize the path followed by the particle, we plot the region R in the xy-plane.The graph of the appropriate region in the xy-plane is shown below: Graph of the region R in the xy-plane.

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If the set {u1, u2, u3} spans R3 and A = [u1 u2 u3], then the nullity of A is 0, meaning there are no linearly independent vectors that satisfy the equation Ax = 0.

To determine the nullity of matrix A, we need to find the number of linearly independent vectors that satisfy the equation Ax = 0. Since the set {u1, u2, u3} spans R3, we know that any vector in R3 can be expressed as a linear combination of these three vectors. Thus, the equation Ax = 0 has a nontrivial solution if and only if the three vectors u1, u2, and u3 are linearly dependent. If they are linearly dependent, then one of them can be expressed as a linear combination of the other two, and we can eliminate that vector from the matrix A. This means that the nullity of A is equal to the number of linearly dependent vectors in the set {u1, u2, u3}. Since the set spans R3, it must contain three linearly independent vectors, and therefore the nullity of A is 0.

In summary, if the set {u1, u2, u3} spans R3 and A = [u1 u2 u3], then the nullity of A is 0, meaning there are no linearly independent vectors that satisfy the equation Ax = 0.

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The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

Answer:

Rhombus

Step-by-step explanation:

A rectangle has 4 right angles

A Rhombus has 4 congruent sides

A square has 4 congruent sides and 4 right angles

The figure doesn't have 4 right angles, so it can't be a rectangle or square, therefore making it a rhombus.

The following solutions with regard to resolving or simplifying the radii of circular ponds are given below.

Part A: 5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: 5 × 10 + 2√41 meters = 50 + 2√41 meters
Part C: The radius of Pond B is 10√2 meters.
Part D: the radius of Pond B is greater than the radius of Pond A.

Part A: The mistake is in Step 1. To simplify the square root of 164, we need to find its prime factors:

164 = 2 × 2 × 41

So, we can write:

√164 = √(2 × 2 × 41) = 2√41

Using this, we can rewrite Step 1 as:

5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: Using the corrected step from Part A, we can simplify the radius of Pond A as:

5 × 10 + 2√41 meters = 50 + 2√41 meters

So, the radius of Pond A is 50 + 2√41 meters.

Part C: The radius of Pond B is already simplified, so we don't need to do any additional steps. It is:

25√200/5 meters = 5√200 meters

We can simplify this further by finding the prime factorization of 200:

200 = 2 × 2 × 2 × 5 × 5

So, we can write:

√200 = √(2 × 2 × 2 × 5 × 5)

= 2 × 5√2

Using this, we can rewrite the expression for the radius of Pond B as:

5 × 2 × √2 meters

= 10√2 meters

Thus, the radius of Pond B is 10√2 meters.

Part D: We can compare the radii of the ponds using the original expressions by writing:

√164 < 25√200/5

Simplifying both sides:

2√41 < 10√2

Dividing both sides by 2:

√41 < 5√2

Squaring both sides (since both sides are positive):

41 < 25 × 2

41 < 50

So, the inequality is true. Therefore, the radius of Pond B is greater than the radius of Pond A.

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Full Question:

Two circular ponds at a botanical garden have the following radii:

Pond A: Sqrt(164) meters;

Pond B: 25Sqrt(200)/5 meters:

Todd simplified the radius of pond A this way:

5sqrt(164)

Step 1: 5sqrt(100) + Sqrt(164) meters

Step 2: 5(10 + 8)

Step 3: 5(18)

Step 4: 90

One of the steps above is incorrect.

Part A: Rewrite the steps so that it is correct

Part B: Using the corrected step from Part A, simplify the radius of Pond A.

Part C: Simplify the expression for the radius of pond B.

Part D: Write an inequality to compare the radii of the ponds, using the original expressions.

Answer:

200 minutes

Step-by-step explanation:

In order to find the range, you have to subtract the greatest number to the lowest number. In this case, 400 is the smallest number, and 600 is the greatest number. 600-400 is 200 minutes.

This is an example of inferential statistics. Inferential statistics involve making assumptions and predictions about a larger population based on a sample size.

In this example, the teacher is making an assumption that the attitudes of the males and females in the class are representative of the attitudes of the larger population of males and females. To calculate the inferential statistic, the teacher will first calculate the average attitude score for each group (males and females). This can be done by dividing the sum of all the individual attitude scores for a given group by the number of individuals in that group. Then, the teacher would conduct a t-test to determine whether the difference in the average attitude scores of the two groups is statistically significant. The t-test measures the difference between the two groups and determines whether that difference is likely to have occurred by chance or if it is a real difference that is likely to exist in the larger population.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

As the height of warehouse is greater than the height of crate, the crate will fit in the warehouse.

Step-by-step explanation:

Given that

Volume of cube = V = 2197 cubic feet

Side of cube = a =?

Height of ware house = h = 14 feet

In order for the crate to fit in the warehouse the height of crate has to be less than the height of warehouse i.e. a<h

In order to check this we have to find the side/height of crate

So,

\(V = a^3\\2197 = a^3\)

Taking cube root on both sides

\(\sqrt[3]{a^3} = \sqrt[3]{2197}\\\sqrt[3]{a^3} = \sqrt[3]{13^3}\\ a = 13\ feet\)

So the height of cube is 13 feet.

Comparing the height of c and height of ware house we can conclude that

Height of Warehouse > Height of crate

h>a

14>13

As the height of warehouse is greater than the height of crate, the crate will fit in the warehouse.

The given function shows imply that the graph g(x) is shifted two units right and three units up.

Option B is correct.

The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.

From the given information:

Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.

Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.

Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0.  We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.

Combining the two transformations, we have:

Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.

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For question 3, the unique solution is guaranteed if yo = 3. For question 5, the solution is lnx + In(y-x) = c. For the last question, the solution is y = x - 1 + ce^(-x).

For question 3, the initial value problem y' = √(x²-9), y(x) = yo has a unique solution guaranteed by Theorem 1.1 if yo = 3. The reason is that the square root expression inside the differential equation is only defined when x²-9 is non-negative. Since the square root of a negative number is undefined in the real number system, yo cannot be any value that results in x²-9 being negative. Therefore, yo = 3 is the only valid choice.

For question 5, the given differential equation (x-2y)dx + ydy = 0 can be solved by integrating. By integrating the left-hand side of the equation, we obtain the solution lnx + In(y-x) = c, where c is the constant of integration. This is the correct answer (b).

For the last question, the differential equation y' + y = x can be solved using the method of integrating factors. Multiplying both sides of the equation by e^x, we get e^x * y' + e^x * y = xe^x. The left-hand side can be rewritten as (e^x * y)' = xe^x. Integrating both sides with respect to x, we have e^x * y = ∫xe^xdx = x * e^x - e^x + c. Dividing both sides by e^x, we get y = x - 1 + ce^(-x). Therefore, the correct answer is (b), y = x - 1 + ce^(-x).

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Answer:

Dang, too difficult. Anyways,

In a right triangle, if one angle is 45 degrees, it means that the other two angles must be 45 degrees as well, making it an isosceles right triangle. Given that the length of one leg is 4√2 m, we can determine the lengths of the missing sides using the properties of an isosceles right triangle.

Since an isosceles right triangle has two equal legs, the lengths of the vertical leg and horizontal leg will be the same. Let's denote the length of each leg as "m."

Using the Pythagorean theorem, we can find the length of the hypotenuse (the side opposite the right angle) in terms of "m":

hypotenuse^2 = leg^2 + leg^2

hypotenuse^2 = m^2 + m^2

hypotenuse^2 = 2m^2

To find the length of the hypotenuse, we take the square root of both sides:

hypotenuse = √(2m^2) = √2 * m

In summary, for the given isosceles right triangle with one leg measuring 4√2 m, both the vertical leg and horizontal leg will have a length of "m," while the length of the hypotenuse will be √2 * m.

Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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Answer:

A. Domain: (-1, 3, 5)

Step-by-step explanation:

The domain is always the x-inputs or x-values of a function.

Answer:

90 and 80 degrees

Step-by-step explanation:

The hiker's elevation after 150 minutes is 1956.5 feet.

From the information illustrated, the equation of a trend line for the hiker's elevation is y = 8.65x + 659.

where x represents the number of minutes

y represents the hiker's elevation in feet.

Therefore, the elevation after 150 minutes will be:

y = 8.65x + 659.

y = 8.65(150) + 659.

y = 1956.5 feet.

The elevation is 1956.5 feet.

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There are variations in the participation prices of boys and girls across unique sports, with boys having decreased representation in varsity soccer, better representation in freshman basketball, and identical illustration in varsity tennis compared to ladies.

Based on the given statements:

The percentage of boys who play varsity soccer is much less than the share of ladies who play varsity football.

The share of boys who play freshman basketball is extra than the share of girls who play freshman basketball.

The percentage of boys who play varsity tennis is the same as the variety of women who play varsity tennis.

We can finish subsequent:

Boys have a lower representation in varsity football as compared to ladies.

Boys have a higher representation in freshman basketball in comparison to ladies.

The percentage of boys playing varsity tennis is identical to the proportion of women playing varsity tennis.

These statements suggest differences in participation fees and proportions between boys and women in unique sports activities.

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The correct question is:

"The percentage of boys who play varsity soccer is ✔ less than the percentage of girls who play varsity soccer. the proportion of boys who play freshman b-ball is ✔ greater than the proportion of girls who play freshman b-ball. the percentage of boys who play varsity tennis is ✔ the same as the number of girls who play varsity tennis.

What can you conclude from the above statements?"

Answer:

A. N and Q

Step-by-step explanation:

Look at the order of the triangles: MNL and PQR

MNL and PQR

They are both ordered in the middle, whereas others like M and Q are not. For example, M is ordered first and Q is middle.

N and Q match - The correct letters will always align in the order

Answer:

a. ∠N and ∠Q

Step-by-step explanation:

∠N and ∠Q are the pair of angle which are corresponding congruent angles as they have the same angles and matches with each other.

2) The slope of the tangent line at x = 1 is 3.

To differentiate the given function, we can apply the power rule and constant rule.

1. For s(t) = t^3 - 2:

The derivative of s(t), denoted as s'(t), is obtained by differentiating each term separately:

s'(t) = d/dt(t^3) - d/dt(2)

Using the power rule, the derivative of t^3 with respect to t is:

d/dt(t^3) = 3t^2

The derivative of a constant (in this case, 2) is zero:

d/dt(2) = 0

Therefore, the derivative s'(t) is:

s'(t) = 3t^2 - 0

s'(t) = 3t^2

2. For f(x) = 3x + 5:

The derivative of f(x), denoted as f'(x), is obtained by differentiating each term separately:

f'(x) = d/dx(3x) + d/dx(5)

The derivative of 3x with respect to x is:

d/dx(3x) = 3

The derivative of a constant (in this case, 5) is zero:

d/dx(5) = 0

Therefore, the derivative f'(x) is:

f'(x) = 3 + 0

f'(x) = 3

Now, let's find the slope of the tangent line at the given values of the independent variable:

1. For s(t) at t = 7:

Substituting t = 7 into s'(t), we get:

s'(7) = 3(7)^2

s'(7) = 3(49)

s'(7) = 147

The slope of the tangent line at t = 7 is 147.

2. For f(x) at x = 1:

Substituting x = 1 into f'(x), we get:

f'(1) = 3

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Answer:

907

Step-by-step explanation:

Circumference = 34pi

radius, r = 34pi/2pi = 17

Area, A = pi r^2 = pi (17^2) = 289pi=907 approximately

Using models to to illustrate the proportions is similar to reducing or increasing a ratio by a common factor. The solutions to the exercise are given below :

1.)

8 : 6

Reducing each side of the ratio by an half(1/2) :

8 × ½ : 6 × ½

4 : 3

2.)

15 : 3

Reducing each side of the ratio by ⅓:

15 × ⅓ : 3 × ⅓

5 : 1

3.)

12 : 6

Reducing each side of the ratio by (one-third) ⅓:

12 × ⅓ : 6 × ⅓

4 : 2

4.)

11 : 7

Increasing the proportion by 4 :

11 × 4 : 7 × 4

44 : 28

5.)

25 eggs : 3 hens

Increasing the number of hens by 3, then egg production will also triple

25 eggs × 3 : 3 hens × 3

75 eggs to 9 hens

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Answer:

The correct option is;

The variable x has a coefficient

Step-by-step explanation:

The given vertex form of a quadratic function and the quadratic function can be written as follows;

Vertex form of a quadratic function, f(x) = (3·x + 1/3)² + 8/9

The quadratic function, f(x) = 9·x² + 2·x + 1

The vertex form of a quadratic function f(x) = a·x² + b·x + c is f(x) = a·(x - h)² + k

Where;

h = -b/(2·a) = -2/(2×9) = -1/9

k = f(h) = f(-1/9) = 9 × (-1/9)² + 2 × (-1/9) + 1 = 8/9

Which gives the vertex form a s f(x) = 9·(x - (-1/9))² + 8/9

f(x) = 9·(x + 1/9)² + 8/9

Therefore,  f(x) = (3·x + 1/3)² + 8/9 is not the vertex form of f(x) = 9·x² + 2·x + 1 because the variable x has a coefficient.

Answer:

35

Step-by-step explanation:

The exterior sum theorem states the exterior angle is equal to the sum of the opposite interior angles

145 = ?+110

145 - 100 = ?

35 = ?

Answer:

The second and third option are both functions!!

Glad to help!!

Step-by-step explanation:

Therefore, the apparent nth term of the expression is: aⁿ = 5n² - 3n - 2.

The given sequence is not an arithmetic or geometric sequence. However, we can notice that the sequence of differences between consecutive terms is an arithmetic sequence.

The sequence of differences is: 7, 19, 37, 61,...

To find the nth term of this sequence, we can use the formula for the nth term of an arithmetic sequence:

dn = a1 + (n-1) * d

where dn is the nth term of the sequence of differences, a1 is the first term of the sequence of differences, d is the common difference of the sequence of differences, and n is the index of the term we want to find.

So, we have:

dn = 7 + (n-1) * 12

Simplifying this expression, we get:

dn = 5n - 3

Now, we can use this formula to find the nth term of the original sequence. Let's call the nth term an:

an = an-1 + dn-1

where an-1 is the (n-1)th term of the original sequence and dn-1 is the (n-1)th term of the sequence of differences.

We know that a1 = 2 and d1 = 7, so we can use the above formula to find the next terms:

a2 = a1 + d1 = 2 + 7 = 9

a3 = a2 + d2 = 9 + 19 = 28

a4 = a3 + d3 = 28 + 37 = 65

a5 = a4 + d4 = 65 + 61 = 126

Therefore, the apparent nth term of the sequence is: aⁿ = 5n² - 3n - 2.

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Answer:

x=5, -2.

Step-by-step explanation:

abs(2x-3)=7

2x-3=7 or 2x-3=-7

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

2x-3=7

2x=7+3

2x=10

x=10/2

x=5

----------

2x-3=-7

2x=-7+3

2x=-4

x=-4/2

x=-2