Evaluate the line integral by the two following methods.
Image for Evaluate the line integral by the two following methods. Integrate xy dx + x2y3 dy C is counterclockwise aroun
xy dx + x2y3 dy
C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4)
(a) directly
(b) using Green's Theorem

[tex]\huge \boxed{\sf 8+4\sqrt{5} }\\\\\\\sf Using\ the\ distance\ formula \\\\\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]\sf A(0,4)\ and\ B(2,0)\\\\d = \sqrt{(2 - 0)^2 + (0-4)^2}=2\sqrt{5} \\\\B(2,0)\ and\ C(2,-2)\\\\d = \sqrt{(2 - 2)^2 + (-2-0)^2}=2 \\\\C(2,-2)\ and\ D(0,-2)\\\\d = \sqrt{(0 - 2)^2 + (-2-(-2))^2}=2 \\\\D(0,-2)\ and\ E(-2,2)\\\\d = \sqrt{(-2 - 0)^2 + (2-(-2))^2}=2\sqrt{5} \\\\E(-2,2)\ and\ F(-2,4)\\\\d = \sqrt{(-2 - (-2))^2 + (4-2)^2}=2\\\\F(-2,4)\ and\ A(0,4)\\\\ d=\sqrt{(0-(-2))^2+(4-4)^2} =2[/tex]

[tex]\sf Adding\ all\ the\ distances \\\\2\sqrt{5} +2+2+2\sqrt{5}+2+2 =8+4\sqrt{5} =16.94427190...[/tex]

Answer:

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Four of the segments are horizontal or vertical with the length of 2 units:

Two of the segments have same length (parallel segments) with 4 units vertical and 2 units horizontal difference of coordinates:

The perimeter is:

Answer:

one pen costs 0.5 euros

one rubber costs 0.75 euros

Step-by-step explanation:

4p+5r=5.75

p+4r=3.5

  -4r.   -4r

p=3.5-4r

4(3.5-4r)+5r=5.75

14-16r+5r=5.75

14-11r=5.75

-14.     -14

-11r=-8.25

r=0.75

One rubber cost 0.75 euros

Now to find cost of one pen we just fill in what we know

p+4(0.75)=3.5

p+3=3.5

 -3.  -3

p=0.5

1 pen cost 0.5 euros

Hopes this helps please mark brainliest

The year in which only 38,000 items of clothing will be donated to the homeless shelters in new york city. is 2020, using the concept of linear equation.

The above problem is related to a linear equation, A linear equation is a condition in which the highest power of the variable is always 1. It is additionally known as a one-degree equation. The standard form of a linear condition in one variable is of the form Ax + B =0 .from the given graph we can  come  up with the equation which bests fits for x to be the number of the year from 1992 and y  to be the number of clothes donated in thousands, which is  y=-0.375x+48.5

now for the given situation:

-0.375x+48.5 = 38

=>-0.375x= 38-48.5

=-0.375x = -10.5

=>x = -10.5/ 0.375 = 28

so it is 2020

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the complete question attached herewith.

The two consecutive integers that will make the inequality true are 13 and 14.

inequality, is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

If you check for the square root of 181 [tex]\sqrt{181}[/tex] is 13.453

And the two consecutive integers smaller than 13.45 and greater than 13.45 are 13 and 14 respectively.

In conclusion, the two consecutive integers for the expression are 13 and 14.

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The solution to the equation is x = 2/3.

The number of times a number is multiplied by itself is referred to as an exponent.

The given equation is (1/2)ˣ ⁻ ¹ = 2³ˣ ⁻ ⁴.

Solve the equation as follows:

(1/2)ˣ ⁻ ¹ = 2³ˣ ⁻ ⁴

Recall that xᵃ = (1/x)⁻ᵃ, therefore,

2ˣ⁻¹ = 2³ˣ ⁻ ⁴

Since the base of the exponents is the same, it follows:

x - 1 = 3x - 4

3x - x = -1 + 4

2x = 3

x = 2/3

Hence, the solution to the equation is x = 2/3.

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The equation that help use to find the value of x is h(a+b)/2 = lw.

The value of x if both figure have the same area is 4 in

Area can be defined as the region bounded by a plane shape.

To write and solve an equation to find x, we use the formula of area of a trapeziod and the area of a rectangle

From the diagram,

Where:

From the diagram,

Given:

Substitute these values into equation 1 and solve for x

Hence, the equation is h(a+b)/2 = lw, and the values of x  is 4 in.

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The ordered pair that makes both inequalities true is (-2,2)

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

All you have to do is substitute each choice into the equation.

(X,Y) is the format, now plug the numbers that's in that order into both the equations to see if it's true

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Question:

Which ordered pair makes both inequalities true? y < –x + 1 and y > x?

A.-3,5

B.-2,2

C.-1,-3

D.0,-1

The mirror and image has a distance of 90 cm

The image is inverted with a height of 12 cm.

Given,

Concave mirror with a radius of curvature 60 cm

The height of the object = 6 cm

The distance between the object and the mirror = 45 cm

We have to find the location and height of the image;

Here,

For any mirror, the radius of curvature is twice the focal length:

r = 2f

Where

r is the radius of curvature

f is the focal length

Then,

f = r/2 = 60/2 = 30 cm

Focal length = 30 cm

Now,

The distance of the image from the mirror;

The mirror equation is:

1/s' = 1/f - 1/s

Where

s' is the distance of the image from the mirror

f is the focal length

s is the distance of the object from the mirror

Here,

1/s' = 1/30 - 1/45

1/s' = 3/90 - 2/90

1/s' = 1/90

s' = 90 cm

The distance of the image from the mirror is 90 cm

Next,

Height of the image.

For that we have to find the magnification first;-

Magnification, M = - s'/s = - 90/45 = -2

Now,

Magnification in terms of height of the image;

M = y'/y

y' is the height of the image

y is the height of the object

So,

-2 = y'/6

y' = -2 x 6 = -12 cm

That is,

The image is of 12 cm height and which is inverted.

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divide both sides of the equation by one of the variables to solve for that variable.

How do you solve an equation with two variables on both sides?

To solve systems of algebraic equations containing two variables, start by moving the variables to different sides of the equation. Then, divide both sides of the equation by one of the variables to solve for that variable. Next, take that number and plug it into the formula to solve for the other variable.

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The maximum number of functions that can be defined from the power set of A, P(A), to the power set of B, P(B) is 4096.

The Collection of well-defined objects or elements is known as a set. The objects in a set are called elements. The Set contains a finite number of elements. The Set is denoted by any capital letter like A, B etc. Elements of the set can be numbers, alphabets etc.

The elements of the set are listed inside the curly brackets { ..... }. There are various types of sets. The set of all subsets of the set X is called a Power set including the null set, empty set and the set itself. Cardinal number or cardinality denotes the number of elements in the set. Cardinality is denoted by n( X ) where X is a set. The number of subsets of the set is given by 2^n.

As per the question,

⇒  n ( A )   =   3 elements

Number of subsets of A   =   2³

                                          =   8 subsets

⇒   n ( B )   =   2 elements

Number of subsets of B   =   2²

                                          =   4 subsets

By using the product rule,

Total number of functions from P ( B ) to P ( A )   =   8 × 8 × 8 × 8

                                                                                =   4096

Therefore, 4096 is the maximum number of functions that can be defined from the power set of A, P(A) to the power set of B.

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A root of a transformed equation that is not the root of the original equation because it was excluded from the original equation's domain is known as an extraneous solution.

What are extraneous solutions?

A "false" solution to an equation is known as an extraneous solution. Even if we appeared to follow sound procedures when solving the equation, an extraneous solution did not fulfill the original equation.

So,

When we solve an equation, an extraneous solution is a result that does not fulfill the equation. As an illustration, if we square both sides of the equation x = -1, we obtain the value x = 1, which does not satisfy the original equation, indicating that x = 1 is an extraneous solution.

when we wanted to solve the equation √x = -1.  After squaring both sides, we get a value of x = 1.

When we substitute x = 1 into the original equation, we get:

x = -1  [original equation]

√1 = -1  [substitute x = 1]

1 = -1  [this is not true]

Hence,

This equation is called an extraneous solution.

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Answer:

y=x-10

Step-by-step explanation:

y=ax+b - linear equation

y=-x+7

a=-1

y=cx+d - perpendicular equation to y=ax+b

a*c=-1

(-1)*c=-1

c=1

y=x+d

(4,-6) => x=4, y=-6

y=x+d => -6=4+d

d=-10

y=x-10

Boris should navigate 79.74° to go to Island C.

Given,

Boris is on vacation at a tropical bay that has three islands.

Distance between Island A and Island C = 13 miles

Distance between Island B and Island C = 14 miles

Distance between Island A and Island B = 8 miles

Boris rents a boat on Island A and plans to navigate to Island C.

We have to find that at what angle should she navigate to go to Island C

Here,

14² = 13² + 8² - (2 × 13 × 8) Cos A

Cos A = (13² + 8² - 14²) / (2 × 13 × 8)

Cos A = (169 + 64 - 196) / 208

Cos A = 37/208

A = arc Cos 0.178

A = 79.74°

Therefore,

Boris should navigate 79.74° to go to Island C.

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The given question is incomplete. Completed question is given below;

Boris is on vacation at a tropical bay that has three islands. He rents a boat on Island A and plans to navigate to Island C, which is 13 miles away. Based on the figure below, at what angle θ should he navigate to go to Island C? Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth of a degree . × S

Image is attached;

Reponse Rate , is the indicator which is used for review the researcher's overall quality of a data collection efforts .

Reponse Rate:

It provides valuable insight into the accuracy of the data collected. Simply put, the response rate is the number of people who completed the survey divided by the number of people who make up the entire sample group.

It is important to note that response rates can only be calculated for defined sample groups.

Example:

We have a survey with the following stats:

Message sent: 1000

Number of respondents surveyed: 250

Number of surveys completed: 300

Let's calculate the response rate .

response rate = number of surveys completed / number of emails sent

response rate = 30%.

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The slope of a ki run that rise 5 feet for every horizontal change of 12 feet. The horizontal change of 12 feet is 2.0833.

The The slope of a line is "upward thrust over run". That could be 6/30 on this case. That may be simplified to 1/5 (via way of means of dividing each numbers via way of means of 6).That makes the slope 1/5 (or 0.2 as a decimal.

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Diana should reject the null hypothesis because the p-value is less than the value α=0.05.

Given that,

Let's say Diana, a researcher in education at a nearby university, wants to assess the effectiveness of a brand-new Spanish course that combines cultural immersion teaching methods with conventional teaching methods. She chooses a simple random sample of 72 freshmen, matches their IQs and high school GPAs, and then divides them into 36 pairs. She chooses one student from each pair at random to enroll in the new course, while the other student in the pair enrolls in the standard course.

We have to find the p-value.

We know that,

Let

t= difference/standard error =(0.11791)/(0.05242)=2.249

From excel: p value =t distance(2.249,36,2)=0.031

Since p value <0.05

Therefore, Diana should reject the null hypothesis because the p-value is less than the value α=0.05.

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90% confidence interval would be less than a 95% confidence interval.

Given,

A random sample has been taken from a population. A statistician, using this sample, needs to decide whether to construct a 90 percent confidence interval for the population mean or a 95 percent confidence interval for the population mean;

We have to find the difference between the intervals;

Here,

Confidence intervals are a range that depict the accuracy of the measurement. If a statistician chooses to use a 90% C I instead of a 95% C I, it informs you that you have a 10% probability of being incorrect as opposed to a 5% possibility when using the 95%.

That is, a 90% confidence interval would be less than a 95% confidence interval.

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The greatest possible area for the garden is  135200 ft^2 with a shorter side at 260 ft and a longer side at 520 ft

Let L be the length and W be the width of the garden.

So,  L + 2W = 1040

Area = A

= LW

=(1040 - 2W)W

= 1040W - 2W^2

To maximize the area:

take the derivative of A and set = 0

That is:

A' = 1040 - 4W = 0

4W = 1040

W = 1040/4

= 260

And L = 1040 - 2W

= 1040 - 520

= 520

So,

shorter side =260 ft

longer side =520 ft

Computing the greatest possible are using the length of the shorter and the longer side we get:

greatest possible area: =LW=(260)(520)=135200 ft2

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Step-by-step explanation:

A water park water ride pumps 8,000 gallons of water every 2 minutes, How many gallons of water would the ride pump in 100 minutes?

100/2 = 50

50 * 8,000 = 400,000 gallons in 100 minutes

Answer:

400,000 gallons

Step-by-step explanation:

to find the unit rate or how much per minute we divide 8000 by 2

8000/2

4000 gallons per minute

Now multiply by 100

4000*100

400,000

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If the width of a rectangle is 8t-5.5 feet and the length is 5.5t + 7 feet. The perimeter of the rectangle will be 27t+3

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is given that, The width of a rectangle is 8t-5.5 feet and the length is 5.5t + 7 feet.

We have to find find the perimeter of the rectangle.

The perimeter of a rectangle is two times the sum of the length and breadth as,

P = 2(l+w)

P=2(8t-5.5+5.5t + 7)

P=2(13.5t+1.5)

P=27t+3

Suppose the value of t is 1, the perimeter of the rectangle is found as,

P=27×1+3

P=30

Thus, if the width of a rectangle is 8t-5.5 feet and the length is 5.5t + 7 feet. The perimeter of the rectangle will be 27t+3

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The expected number of cars in a randomly selected American household will be 1.75.

Using the probability model, if we ignore some households that own more than 5 cars. Then,

Number of cars            Probability

0                                        0.09

1                                         0.36

2                                        0.35

3                                        0.13

4                                       0.05

5                                       0.02

Multiplying each possibility by its probability

∑xP(x)

= 0x0.09+1x0.36+2x0.35+3x0.13+4x0.05+5x0.02

=1.75

Probability is simply the possibility that something will happen. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several. The study of events that fit into a probability distribution is known as statistics. A probability model is a representation of a random occurrence in mathematics. It is defined by its sample space, occurrences, and related probabilities for each event. When choosing a sample from a population using the randomization principle, also referred to as chance or random selection, the procedure is known as probability sampling. Generally speaking, probability sampling is more challenging, expensive, and time-consuming than non-probability sampling.

Note that the full question is:

What’s the expected number of cars in a randomly selected American household?

(a) Between 0 and 5

(b) 1.00

(c) 1.75

(d) 1.84

(e) 2.00

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Anthony's expected earning would be $175 in a day when he waits in 20 tables.

According to the question,

We have the following information:

Each day Anthony works, Anthony will make a guaranteed wage of $35, however the additional amount that Anthony earns from tips depends on the number of tables he waits on that day. From past experience, Anthony noticed that he will get about $7 in tips for each table he waits on.

Now, for waiting on 20 tables, he will get the fixed amount of 35 dollars and the amount for 20 tables.

So, the total amount will be:

35+7*20

35+140

$175

Hence, Anthony would expect to earn $175 in a day when he waits in 20 tables.

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Step-by-step explanation:

Hello, I need the function in order to give you a exact answer.

Answer:

Step-by-step explanation:

did you watch the video-

Answer:

32, 39, 46

Step-by-step explanation:

Given sequence:

Work out the differences between the terms:

[tex]4 \underset{+7}{\longrightarrow} 11 \underset{+7}{\longrightarrow} 18 \underset{+7}{\longrightarrow} 25[/tex]

As the difference between each term in the sequence is constant, the sequence is an arithmetic sequence with common difference of 7.

To find the next three terms in the given sequence, simply add 7 to the previous term:

[tex]\implies 25 + 7 = 32[/tex]

[tex]\implies 32 + 7 = 39[/tex]

[tex]\implies 39 + 7 = 46[/tex]

Answer:

Step-by-step explanation:

Next three terms are 32, 39, 46

As the different in all of them is of 7 so we add 7 with each term to get the next terms :)

Answer:117,649

Step-by-step explanation:

The answer double will be of 8 is 16, by multiplication.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

The fundamental concept of repeatedly adding the same number is embodied in the process of multiplication. The outcome of multiplying two or more numbers is known as the product of those numbers, and the factors that are multiplied are referred to as the factors. The process of repeatedly adding the same number is made easier by multiplication.

So the double of 8 means adding 2 two times. Or multiplying 8 with 2

8*2 = 16

Hence, double will be of 8 is 16

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Answer:

The simplest ratio of squares to triangles would be: 1 to 5, 1:5, or 1/5.

Either one works, they mean the same thing.

Step-by-step explanation:

In order to find out the simplest form, see how you can divide the numbers with the highest number and the numbers coming out as low as they can. In this case the number to divide the numbers we already have would be 3:

3 divided by 3 = 1

15 divided by 3 = 5

That's why we end up with 1:5.

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The correct option is option A.

Urenium Mining, 60 millions or 10% its uranium has been used.

Mining of Uranium :

In Uranium Mining Uranium is found in small amounts in most rocks and seawater. Uranium mines operate in many countries, but over 85% of uranium is produced in six countries: Kazakhstan, Canada, Australia, Namibia, Niger and Russia.

Currently, the world's uranium mines use a method called in situ leaching. Oxygenated water (or an alkaline, acidic, or oxidizing solution) is circulated through the uranium ore to extract uranium. After uranium has been used in a nuclear reactor for about three years to generate electricity, the spent fuel goes through a series of steps such as temporary storage, reprocessing and recycling before the waste produced is disposed of. It may pass. Collectively, these steps are known as the "back end" of the fuel cycle. About 60 million or 10% of the urenium in the,

reactor was used.

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The Central angle and the radius are not the same.

What is the Radius of a circle?

Any circular object's radius is the measurement from the center to its outermost border or boundary. A radius is a dimension that applies to spheres, semispheres, cones with circular bases, and cylinders with circular bases in addition to circles.

It is possible to define a circle as the locus of a point moving in a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its center. The fixed point is referred to as the center of the circle.

So, According to the question:

The angle formed by any two-circle radii is known as the central angle. The arc length, or the distance between the two places where the two radii cross the circumference, and the radius length must be determined in order to determine the central angle.

Hence,

The Central angle and the radius are not the same.

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