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

Answers

Answer 1

The line integral in both cases is  52/3

Given,

a) The line integral; L = ∫c xy dx + x² y³ dy

 Where C is counterclockwise around the triangle with vertices (0, 0),

(1, 0)  and (1, 4)

Our first line integral is

L₁ = ₁∫₍₀, ₀₎ ⁽¹ ⁰⁾ xy dx + x² y³ dy

The equation of this line is y = 0,  x varies from 0 to 1.

L₁ = 0

Our second line integral is

L₂ = ₁∫₍₁, ₀₎ ⁽¹ ⁴⁾ xy dx + x² y³ dy

The equation of this line is x = 0  and y varies from 1 to 4.

L₂ = 64/3

The third line integral is

L₃ = ∫₁⁰ xy dx + x² y³ dy

The equation of this line is y = 4x  and x varies from 0 to 1.

L₃ = -4

The value of the line integral is

L = L₁ + L₂ + L₃ = 0 + 64/3 + (-4) = 52/3

b) The second part requires the use of Green's Theorem to evaluate:

This is given by:

∫c Pdx + Qdy = ∫ ∫ R Qy - Px dA

∫c xy dx + x² y³ dy = ∫ ∫R 3x² y² - ydA

We choose our region of integration parallel to the y-axis.

∫c xy dx + x² y³ dy

= ∫¹₀ ∫⁴ˣ₀ 3x² y² - y dy dx

= ∫¹₀ x² y³ - 1/4 |y²|²ˣ₀ dx

=  ∫¹₀ 64x⁵ - 4x² dx = 52/3

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Related Questions

Given the two sets A = {a,b,c} and B = {x,y}, calculate 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). Give your answer as an integer, not a formula.

Answers

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,

Set A   =   { a, b, c }Set B   =   { x, y }

⇒  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 researcher wishes to have an indicator of the overall quality of a data collection effort. which indicator should the researcher review?

Answers

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 width of a rectangle is 8t-5.5 feet and the length is 5.5t + 7 feet. Find the perimeter of the rectangle.
CETOS
The perimeter of the rectangle is feet.
(Simplify your answer. Use integers or decimals for any numbers in the expression.)

Answers

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

What is rectangle?

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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Perpendicular to y = -x + 7 through (4, -6)

Answers

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

WORTH 50 POINTS AND BRAINLIEST FOR THE BEST ANSWER!

Directions: Find the perimeter of the polygon with the given vertices.​

Answers

[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:

The perimeter is 8 + 4√5 units

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

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

FA = FE = BC = DC = 2

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

AB = ED = √(4² + 2)² =√20 = 2√5

The perimeter is:

P = 4*2 + 2*2√5 = 8 + 4√5

use the left and right riemann sums with 3 rectangles to estimate the signed area under the curve of y

Answers

Step-by-step explanation:

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

you will begin with a relatively standard calculation. consider a concave spherical mirror with a radius of curvature equal to 60.0 centimeters. an object 6.00 centimeters tall is placed along the axis of the mirror, 45.0 centimeters from the mirror. you are to find the location and height of the image.

Answers

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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Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.

Answers

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

What is Inequality?

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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using the equation for the line of best fit, predict the year in which only 38,000 items of clothing will be donated to the homeless shelters in new york city.

Answers

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.

Mia buys 4 pens and 5 rubbers for £5.75.

Elise buys 1 pen and 4 rubbers for £3.5.

Work out the cost of one pen and one rubber.

Answers

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

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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. How will these intervals differ? Group of answer choices The 90 percent confidence interval will be wider than the 95 percent confidence interval. Which interval is wider will depend on whether the sample is unbiased. Which interval is wider will depend on whether a z-statistic or a t-statistic is used. Which interval is wider will depend on how large the sample is. The 90 percent confidence interval will not be as wide as the 95 percent confidence interval.

Answers

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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Which ordered pair makes both inequalities true y x 1 YX?.

Answers

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

What i the lope of a ki run that rie 5 feet for every horizontal change of 12 feet? Pl how work

Answers

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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Suppose Diana, an educational researcher at a local university, wants to test the impact of a new Spanish course that integrates cultural-immersion teaching techniques with standard teaching practices. She selects a simple random sample of 72 freshmen and divides them into 36 pairs, matched on IQ and high school GPA. She randomly selects one member of each pair to take the new course, while the other member in the pair takes the traditional course.
Next, Diana records the course grade, tallied on a scale from 0 to 4, for all sample members at the end of the semester, and she computes the difference in grades between the members in each matched pair by subtracting the traditional course grade from the new course grade. She wants to determine if the new Spanish course improves or weakens student performance. She runs a matched-pairs t-test to test the null hypothesis, H0:μ=0, against the alternative hypothesis, H1:μ≠0, where μ is the mean course grade difference for the student population.
The sample statistics for Diana's test are summarized in the table.
Variable
description Sample
mean Sample standard
deviation Standard error
estimate
traditional course grade x⎯⎯trad= 3.33496 strad=2.02198 SEtrad=0.33700
new course grade x⎯⎯new=3.45287 snew=2.11043 SEnew=0.35174
difference (new − traditional) x⎯⎯=0.11791 s=0.31452 SE=0.05242
Although Diana does not know the standard deviation of the underlying population of course grade differences, she assumes that the population is normally distributed because the sample data are symmetric, single-peaked, and contain no outliers.
Compute the t-statistic for Diana's matched-pairs t-test. Provide your answer with precision to three decimal places.
Compute the p-value of the t-statistic using software. You may find some software manuals helpful. Provide your answer precise to three decimal places.
t=p =
Select the accurate statement regarding Diana's test decision if she tests at a significance level of α=0.05.
Diana should fail to reject the null hypothesis because the mean grade difference is too small.
Diana should reject the null hypothesis because the p-value is greater than the value α=0.05.
Diana should reject the null hypothesis because the p-value is less than the value α=0.05.
Diana should fail to reject the null hypothesis because the p-value is greater than 0.025.
Diana should fail to reject the null hypothesis because the p-value is greater than the value α=0.05.

Answers

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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What is the double of 8?.

Answers

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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after a uranium based fuel rod has spent 3 years in a reactor, how much of its uranium has been used? group of answer choices 10% 40% 20% 30%

Answers

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

Answers

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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(1/2)^x-1=2^3x-4 what is the answer to this?

Answers

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

What is an exponent?

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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What is 7 to the power of 7 divided by 7?​

Answers

Answer:117,649

Step-by-step explanation:

Is central angle the radius?.

Answers

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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data earns as much money per hour as Diego Diego earns twice as much money per hour as Lynn which graphic represent how much Jada Diego and Lynn earn for different amounts of time works explain how you know be very specific graph a or graph B​

Answers

Answer:

Step-by-step explanation:

did you watch the video-

write and solve an equation to find the value of x so that the figures have the same area. the area of a trapezoid is 1/2h(b1+b2).

Answers

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

What is area?

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,

h(a+b)/2 = lw.......... Equation 1

Where:

h = Height of the trepezioda = Longer parallel side of the trepeziodb = Shorter parallel side of the trepeziodl = Length of the trepeziodw = Width of the trepeziod

From the diagram,

Given:

h = 6 ina = 12 inb = x inl = 12 inw = x in

Substitute these values into equation 1 and solve for x

6(12+x)/2 = 12×x36+3x = 12x12x-3x = 369x = 36x = 36/9x = 4 in

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

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A water park water ride pumps 8000 gallons of water every 2 minutes, How many gallons of water would the ride pump in 100 minutes

Answers

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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Which equations have extraneous solutions?.

Answers

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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What are the next three terms of 4, 11, 18, 25

Answers

Answer:

32, 39, 46

Step-by-step explanation:

Given sequence:

4, 11, 18, 25

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 :)

There are 3 squares and 15 triangles. What is the simplest ratio of squares to triangles?

Answers

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.

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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.

Answers

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;

Anthony is a waiter at a restaurant. Each day he 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. How much would anthony expect to earn in a day on which he waits on 20 tables? how much would anthony expect to make in a day when waiting on tt tables?.

Answers

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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A gardener has 1040 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.

Answers

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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How do you solve equations and inequalities with variables on both sides?.

Answers

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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