5/3 x 6/7 real quick plz

Answers

Answer 1

Answer:

10/7 or 1 3/7. I hope this helps,

Step-by-step explanation:


Related Questions

A population of values has a normal distribution with μ= 106.9 and σ=14.5
You intend to draw a random sample of size n=20

What is the probability that a single randomly selected value is less than 109.8?
P(X < 109.8)
How do you the probability that a sample of size n= 20 is randomly selected with a mean less than 109.8?
P(M < 109.8)

Also, I have to round the answer to the 4th decimal place. How do I do that?

Answers

Step-by-step explanation:

Find the z-score.

z = (x − μ) / σ

z = (109.8 − 106.9) / 14.5

z = 0.2

Use a chart or calculator to find the probability.

P(Z < 0.2) = 0.5793

Find the mean and standard deviation of the sampling distribution.

μ = 106.9

σ = 14.5 / √20 = 3.242

Find the z-score.

z = (x − μ) / σ

z = (109.8 − 106.9) / 3.242

z = 0.894

Use a calculator to find the probability.

P(Z < 0.894) = 0.8145

Yelena needs to swim a total of 8 miles this
week. So far, she swam 5 miles. Use the
equation 5 + m=8 to find how many more
miles Yelena needs to swim.

Answers

Answer:

3 miles

Step-by-step explanation:

5 + m=8

Subtract 5 from each side

5-5 + m=8-5

m = 3

She needs to swim 3 more miles

Answer:

Yelena needs to swim 3 more miles

Step-by-step explanation:

You need to solve for the variable "m", which represents the miles. Based on the information, Yelena swam 5 miles and she needs to swim 8. Solve:

[tex]5+m=8[/tex]

To find the value of m, you need to isolate it on one side of the equation. To do this, you need to get the 8 and 5 on the same side of the equal operation. For this, you need to use reverse operations. This undoes the value from one side and does the same on the other, keeping the equation balanced. Since we have a "positive 5", we take the opposite, which would be a "negative 5". So subtract 5 from both sides of the equation:

[tex]5-5+m=8-5[/tex]

Simplify. The 5's cancel each other out, leaving 0. 8-5 is 3:

[tex]m=3[/tex]

The total miles left that Yelena needs to swim is 3 miles.

:Done


What is the expression

Answers

Answer:

3

Step-by-step explanation:

z - 2x

--------

y

Let x = 3  y = -4 and z  =-6

-6 - 2(3)

--------

-4

-6 -6

---------

-4

-12

-----

-4

3

Answer:

3

Step-by-step explanation:

To solve this, we need to plug in each of the numbers to the equation.

x = 3, y = - 4, z = - 6

[tex]\frac{z-2x}{y} = \frac{-6-2(3)}{-4}[/tex]

Let's solve the parenthesis first. - 2 * 3 = - 6.

[tex]\frac{-6-6}{-4}[/tex]

We then subtract -6 - 6.

[tex]\frac{-12}{-4}[/tex]

Then, we divide (cancel out the negatives).

[tex]-12 / -4 =3[/tex]

Our final answer is 3. Hope this helps!

Triangle+ Triangle + Triangle = 30 Triangle + circle + circle = 20 Circle + Square + Square = 13 Triangle + circle x half square = ?

Answers

Answer:

Below

Step-by-step explanation:

Let T be triangle, C the circle and S the square.

● T + T + T = 30

● 3T = 30

Divide both sides by 3

● 3T/3 = 30/3

● T = 10

So the triangle has a value of 10.

●30 T + C + C = 20C + S + S = 13T +C ×S/2

Add like terms together

●30 T + 2C = 20C +2S= 13T + C×S/2

Replace T by its value (T=10)

● 300 + 2C = 20C + 2S = 130 + C×S/2

Take only this part 20C + 2S = 130 + C × S/2

● 20C + 2S = 130 + C×S/2 (1)

Take this part (300+2C = 20C+2S) and express S in function of C

● 20C + 2S = 300 + 2C

Divide everything by 2 to make easier

● 10 C + S = 150+ C

● S = 150+C-10C

● S = 150-9C

Replace S by (5-9C) in (1)

● 20C + 2S = 130 + C×S/2

● 20C + 2(150-9C) = 130 +C× (150-9C)/2

● 20C + 300-18C= 130 + C×(75-4.5C)

● 2C + 300 = 130 + 75 -4.5C^2

● 2C +300-130 = 75C - 4.5C^2

● 2C -75C + 170 = -4.5C^2

● -73C + 170 = -4.5C^2

Multiply all the expression by -1

● -4.5C^2 +73C+ 170= 0

This is a quadratic equation, so we will use the discriminant method.

Let Y be the discriminant

● Y = b^2-4ac

● b = 73

● a = -4.5

● c = 170

● Y = 73^2 - 4×(-4.5)×170= 8389

So the equation has two solutions:

● C = (-b +/- √Y) /2a

√Y is approximatively 92

● C = (-73 + / - 92 )/ -9

● C = 18.34 or C = -2.11

Approximatively

● C = 18 or C = -2

■■■■■■■■■■■■■■■■■■■■■■■■■

● if C = 18

30T + 2C = 300 + 36 = 336

● if C = -2

30T + 2C = 300-4 = 296

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is false. A sampling distribution is normal only if n30. B. The statement is false. A sampling distribution is normal if either n30 or the population is normal. C. The statement is true. D. The statement is false. A sampling distribution is never normal.

Answers

Answer: Choice B

The statement is false. A sampling distribution is normal if either n > 30 or the population is normal.

==========================================

Explanation:

If the underlying population is normally distributed, then so is the sample distribution (such as the distribution of sample means, aka xbar distribution).

Even if the population isn't normally distributed, the xbar distribution is approximately normal if n > 30 due to the central limit theorem. Some textbooks may use a higher value than 30, but after some threshold is met is when the xbar distribution is effectively "normal".

Choice A is close, but is missing the part about the population being normal. If we know the population is normal, then n > 30 doesn't have to be required.

Help Please. Whoever answers it right with an explanation will get brainliest

Answers

Answer:

The answer is

ab( 11 + 9b)( a - 3b)

Step-by-step explanation:

11a³b - 24a²b² - 27ab³

To factor the expression

First factor ab out

That's

ab ( 11a² - 24ab - 27b²)

Factor the terms in the bracket

Write - 24ab as a difference

That's

ab ( 11a² + 9ab - 33ab - 27b²)

Factor out a from the expression

ab [ a( 11a + 9b) - 33ab - 27b²) ]

Factor -3b from the expression

That's

ab [ a( 11a + 9b) - 3b( 11a + 9b) ]

Factor out 11a + 9b from the expression

We have the final answer as

ab( 11 + 9b)( a - 3b)

Hope this helps you

a sequence of transformations is described below horizontal stretch about a vertical line PQ, a translation, another horizontal stretch about PQ, a reflection over PQ.

Answer Choices:

Angle measures only

Segment lengths only

Both angle measures and segment lengths

Neither angle measures nor segments lengths

Answers

Answer:

Both angle measures and segment lengths.

Step-by-step explanation:

An angle is a shape formed by two rays that meets at a point. The angle is measured by degrees. The angle is formed by the sides of an angle which shares the common endpoint called the vertex. The line is horizontal stretch with a vertical line PQ. It will measure the angle and segments lengths.

Answer:

neither angle measures nor segment lines

23. f(x) is vertically shrank by a factor of 1/3. How will you represent f(x) after transformation?

A. f(3x)
B. 3f(x)
C. 13f(x)
D. f(13x)

Answers

Answer:

Step-by-step explanation:

vertical stretching / shrinking has the following transformation.

f(x) -> a * f(x)

when a >  1, it is stretching

when 0< a < 1, it is shrinking.

when  -1 < a < 0, it is shringking + reflection about the x-axis

when a < -1, it is stretching + reflection about the x axis.

Here it is simple shrinking, so 0 < a < 1.

I expect the answer choice to show (1/3) f(x).

However, if the question plays with the words

"shrink by a factor of 1/3" to actually mean a "stretching by a factor of three", then B is the answer (stretch by a factor of three).

WILL GIVE BRAINLEST PLEASE!!!!!!!! Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table: Color of Tile Purple Pink Orange Number of times the tile is drawn 6 18 26 What is the experimental probability that Jenny will pull out a purple tile? fraction 6 over 50 fraction 44 over 50 fraction 6 over 44 fraction 18 over 44

Answers

Answer:

6/50

Step-by-step explanation:

There are 50 tiles

6 purple

18 pink

26 orange

P( purple) = purple/ total

                = 6/50

Help!!!!!!! Thank you!!!!!!!

Answers

Answer:

D

Step-by-step explanation:

The ratio of yellow paint to blue paint is 4:3. We can make the largest amount of green paint by using all of the 20 quarts of yellow paint so we have to solve for x in 4:3 = 20:x, since 4 * 5 = 20, 3 * 5 = x so we use 15 qts of blue paint, therefore we will have 20 + 15 = 35 qts of green paint.

Answer:

D

Step-by-step explanation:

A scientist needs 120mL of a 20% acid solution for an experiment. The lab has available a 10% solution and a 25% solution. How many milliliters of the 10% solution and how many milliliters of the 25% solution should the scientist mix to make the 20% solution?

Answers

Answer:

40 mL of 10% acid

80 mL of 25% acid

Step-by-step explanation:

x = volume of 10% acid solution

y = volume of 25% acid solution

Total volume is:

x + y = 120

Total amount of acid is:

0.10 x + 0.25 y = 0.20 (120)

Solve by substitution.

0.10 x + 0.25 (120 − x) = 0.20 (120)

0.10 x + 30 − 0.25 x = 24

0.15 x = 6

x = 40

y = 80

Help plz! Jim is climbing a mountain that has a base 150 feet above sea level. If he climbs 233 feet then descends into a cave 64 feet, how far above sea level is Jim

Answers

150+233-64=319
Jim is 319 ft above sea level.

Answer:

150+233-64=319

Jim is 319 ft above sea level.

Step-by-step explanation:

A research center claims that ​% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of adults in that​ country, ​% say that they would travel into space on a commercial flight if they could afford it. At ​, is there enough evidence to reject the research

Answers

Complete Question

A research center claims that ​30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that​ country, ​34% say that they would travel into space on a commercial flight if they could afford it. At ​, is there enough evidence to reject the research center's claim

Answer:

Yes there is  sufficient evidence to reject the research center's claim.

Step-by-step explanation:

From the question we are told that

     The population proportion is  p = 0.30

      The sample proportion is  [tex]\r p = 0.34[/tex]

       The  sample size is  n = 700

The null hypothesis is  [tex]H_o : p = 0.30[/tex]

 The  alternative hypothesis is  [tex]H_a : p \ne 0.30[/tex]

Here we are going to be making use of  level of significance  =  0.05 to carry out this test

Now we will obtain the critical value of  [tex]Z_{\alpha }[/tex] from the normal distribution table , the value is  [tex]Z_{\alpha } = 1.645[/tex]

 Generally the test statistics is mathematically represented as

            [tex]t = \frac{ \r p - p }{ \sqrt{ \frac{ p (1-p)}{n} } }[/tex]

substituting values

              [tex]t = \frac{ 0.34 - 0.30 }{ \sqrt{ \frac{ 0.30 (1-0.30 )}{ 700} } }[/tex]

              [tex]t = 2.31[/tex]

Looking at the values of t  and  [tex]Z_{\alpha }[/tex] we see that [tex]t > Z_{\alpha }[/tex] hence the null hypothesis is rejected

 Thus we can conclude that there is  sufficient evidence to reject the research center's claim.

What is the answer and how is this solved?

Answers

Answer:

Sum : 65

Step-by-step explanation:

In this notation, n is our starting value, and hence we start at 3 and go to 7. Given the set of values : { 3, 4, 5, 6, 7 }, we can substitute in our expression " 4n - 7 " for n and solve. The sum of these values is our solution.

4( 3 ) - 7 = 12 - 7 = 5,

4( 4 ) - 7 = 16 - 7 = 9,

4( 5 ) - 7 = 20 - 7 = 13,

Our remaining values for n = 6 and n = 7 must then be 17 and 21. This is predictable as we have an arithmetic series here, the common difference being 4. As you can see 9 - 5 = 4, 13 - 9 = 4, 17 - 13 = 4, 21 - 17 = 4.

Therefore we have the series { 5, 9, 13, 17, 21 }. This adds to an answer of 65.

Rania graphs the relationship between temperature (in °C) and elevation (in m) in 9 different cities
shown below)

Answers

Answer: 7

Step-by-step explanation:

Answer :

It Is 7 On Khan Academy

◊ YusuCr ◊

:)

Malia measures the longer side of a dollar bill using a ruler at school. Which of the following is most likely the quantity she measured?

Answers

Answer:

6.14 inches

Step-by-step explanation:

The one side of the dollar bill is 6.14 inch. The 6.14 inches of the dollar approximates the 156.1 mm. When Malia measures the longer side of a dollar bill from her rule it will be approximately 6.14 inches in length. The ruler normally has inches and cm sides. Very few rulers have mm scales. The most probable scale that malia would have measure is in inches.

The multiplicative inverse of – 1 in the set {-1,1}is

Answers

Answer: The multiplicative inverse of – 1 in the set {-1,1} is -1.

Step-by-step explanation:

In algebra, the multiplicative inverse of a number(x) is a number (say y) such that

[tex]x\times y=1[/tex]  [product of a number and its inverse =1]

if x= -1, then

[tex]-1\times y=1\Rightarrow\ y=-1[/tex]

That means , the multiplicative inverse of -1 is -1 itself.

Hence, the multiplicative inverse of – 1 in the set {-1,1} is -1.

A manager from a certain well known department store found out the money their customers carry into the store is normally distributed with a mean of $258 dollars and a standard deviation of $35. In a sample of 76 Americans who walked into that store find the probability that a random customer will have more than $260 in his or her wallet

Answers

Answer:

0.30924

Approximately ≈ 0.3092

Step-by-step explanation:

To solve for this question, we use the formula:

z = (x - μ)/σ

where x is the raw score

μ is the sample mean

σ is the sample standard deviation.

From the question,

x is the raw score = 260

μ is the sample mean = population standard deviation = 258

σ is the sample standard deviation

= σ/√N

N = 76 samples

σ = Population standard deviation

= 35/√76

= 4.0146919966

Hence,

z = (x - μ)/σ

= 260 - 258/ 4.0146919966

= 0.4981702212

Approximately = 0.498

We find the Probability using z score table for normal distribution

P(x = z) = P( x = 260)

= P( z = 0.498)

= 0.69076

The probability that a random customer will have more than $260 in his or her wallet is calculated as:

P(x>Z) = 1 - P( z = 0.498)

P(x>Z) = 1 - 0.69076

P(x>Z) = 0.30924

Approximately ≈ 0.3092

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 45 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 25.2 minutes with a standard deviation of 19.1 minutes. Required:a. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour?b. Conduct a hypothesis test at the 5% level of significance. c. What is the p-value for this hypothesis test?

Answers

Answer:

The mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

In this case we need to test whether the mean commute time in the U.S. is less than half an hour.

The information provided is:

 [tex]n=45\\\bar x=25.5\\s=19.1\\\alpha =0.05[/tex]

(a)

The hypothesis for the test can be defined as follows:

H₀: The mean commute time in the U.S. is not less than half an hour, i.e. μ ≥ 30.

Hₐ: The mean commute time in the U.S. is less than half an hour, i.e. μ < 30.

(b)

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

 [tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{25.2-30}{19.1/\sqrt{45}}=-1.58[/tex]

Thus, the test statistic value is -1.58.

(c)

Compute the p-value of the test as follows:

[tex]p-value=P(t_{(n-1)}<-1.58)=P(t_{(45-1)}<-1.58)=0.061[/tex]  

*Use a t-table.

The p-value of the test is 0.061.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.061> α = 0.05

The null hypothesis will not be rejected at 5% level of significance.

Thus, concluding that the mean commute time in the U.S. is less than half an hour.

In a Gallup poll of randomly selected​ adults, 66% said that they worry about identity theft. For a group of 1013​ adults, the mean of those who do not worry about identify theft is closest to​ ________.

Answers

Answer: 669

Step-by-step explanation:

Given, In a Gallup poll of randomly selected​ adults, 66% said that they worry about identity theft.

i.e. The proportion of adults said that they worry about identity theft. (p) = 0.66

Sample size : n= 1013

Then , Mean for the sampling distribution of sample proportion  = np

= (1013) × (0.66)

= 668.58 ≈ 669  [Round to the nearest whole number]

Hence, the mean of those who do not worry about identify theft is closest to​ 669 .

A plot of land has vertices as follows, where each coordinate is a measurement in feet. Find the perimeter of the plot of land. (1,7),(7,7),(7,1),(1,1) please help and explain how to do this type of thing because i am lost

Answers

Answer:

Perimeter of ABCD = 36 ft

Step-by-step explanation:

Given:

A (1,7)

B (7,7)

C (7,1)

D (1,1)

Find:

Perimeter of ABCD

Computation:

Distance between two point = √(x1-x2)² + (y1-y2)²

So,

AB = √(1-7)²+(7-7)²

AB = 6 ft

BC = √(7-7)²+(7-1)²

BC = 6 ft

CD = √(7-1)²+(1-1)²

CD = 6 ft

DA = √(1-1)²+(1-7)²

DA = 6 ft

Perimeter of ABCD = AB + BC + CD + DA

Perimeter of ABCD = 6 + 6 + 6 +6

Perimeter of ABCD = 36 ft

The perimeter of the plot is the sum of side length of the plot of land.

The perimeter of the plot is 24 feet.

Represent the vertices as follows:

[tex]W = (1,7)[/tex]

[tex]X = (7,7)[/tex]

[tex]Y = (7,1)[/tex]

[tex]Z = (1,1)[/tex]

First, we calculate the side length using the following distance formula:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]WX = \sqrt{(1- 7)^2 + (7- 7)^2} = \sqrt{36} = 6[/tex]

[tex]XY = \sqrt{(7- 7)^2 + (7- 1)^2} = \sqrt{36} = 6[/tex]

[tex]YZ = \sqrt{(7- 1)^2 + (1- 1)^2} = \sqrt{36} = 6[/tex]

[tex]ZW = \sqrt{(1- 1)^2 + (1- 7)^2} = \sqrt{36} = 6[/tex]

The perimeter (P) is then calculated as follows:

[tex]P = WX + XY + YZ + ZW[/tex]

So, we have:

[tex]P = 6 + 6 + 6 + 6[/tex]

[tex]P = 24[/tex]

Hence, the perimeter of the plot of land is 24 feet.

Read more about perimeters at:

https://brainly.com/question/394193

-7y=-91 show your work

Answers

Answer:

[tex] \boxed{ \bold{\sf{y = 13}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 7y = - 91}[/tex]

Divide both sides of the equation by -7

⇒[tex] \sf{ \frac{ - 7y}{ - 7} = \frac{ - 91}{ - 7} }[/tex]

Calculate

⇒[tex] \sf{y = 13}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex] \boxed{\sf y = 13} [/tex]

Step-by-step explanation:

Solve for y:

[tex] \sf \implies - 7y = - 91[/tex]

Divide both sides of -7y = -91 by -7:

[tex] \sf \implies \frac{ - 7y}{ - 7} = \frac{ - 91}{ - 7} [/tex]

[tex] \sf \frac{ - 7}{ - 7} = 1 : [/tex]

[tex] \sf \implies y = \frac{ - 91}{ - 7} [/tex]

[tex] \sf \implies y = \frac{ \cancel{ - 7} \times 13}{ \cancel{ - 7}} [/tex]

[tex] \sf \implies y = 13[/tex]

PLzzzz answer quick will give good rate nd say thanks


What is the slope of the line? 5(y+2)=4(x-3)
A 2/3
B 4/5
C 5/4
D 3/2​

Answers

Step-by-step explanation:

Here,

[tex]5y = 4x - 12 - 10[/tex]

[tex]y = \frac{4}{5} x - \frac{22}{5} [/tex]

slope is 4÷5

Answer:

The answer is option B

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

5(y+2)=4(x-3)

To find the slope first expand the terms in the equation

That's

5y + 10 = 4x - 12

Write the equation in the form y = mx+ c

That's

5y = 4x - 12 - 10

5y = 4x - 22

Divide both sides by 5 to make y stand alone

y = 4/5x - 22/5

Comparing with the general equation above the slope of the line is

4/5

Hope this helps you

what is PI numbers?​

Answers

Answer:

These are the first 100 digits of pi: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067

Step-by-step explanation:

Pi goes on continuously forever, so this is a reduced version, by including the first 100 digits.

Which statements about the dilation are true? Check all that apply. Triangle X prime Y prime Z prime. Point X prime is 2 units from the center of dilation C and point Z prime is 3 units from the center of dilation. Triangle X Y Z. Point X is 5 units from point C and point Z is 7.5 units from point C. The center of dilation is point C. It is a reduction. It is an enlargement. The scale factor is 2.5. The scale factor is Two-fifths.

Answers

Pls give brainliest.

Answer:

I only know two right answers.

A: The center of dilation is point C.

C: It is an enlargement.

E: The scale factor is 2/5.

Step-by-step explanation:

These two answers are correct because When you look in the center you see a C.

You tell if it is a reduction because the pre image is small but the image is big.

The center of dilation is point C.

It is an enlargement.

The scale factor is 2/5

The correct options are D, F, H.

What is dilation?

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.

Given:

The transformation of the figure is dilation.

The figure is given in the attached image.

From the diagram:

The center of dilation is point C.

It is an enlargement.

The scale factor is 2/5

Therefore, all the correct statements are given above.

To learn more about the dilation in geometry;

https://brainly.com/question/10713409

#SPJ6

Classify the following random variable according as either discrete or continuous. The temperature in degrees Celsius on January 1st in a certain city
A continuous
B discrete

Answers

Answer:

continuous

Step-by-step explanation:

A quantity like temperature is a continuous random variable. A continuous random variable is different from a discrete random variable because it can take on many values infinitely.

From the question, measuring the Temperature in degrees can take on many different values because there are an uncountable number of possible temperatures that could be taken.

Use Green’s theorem to evaluate line integral along curve C ∮_c〖( 3ydx+2xdy )〗, C : The boundary of 0≤x≤π,0≤y≤sin x

Answers

Answer:

[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = \boxed{\bold{2}}[/tex]

General Formulas and Concepts:
Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Multivariable Calculus

Partial Derivatives

Vector Calculus

Circulation Density:
[tex]\displaystyle F = M \hat{\i} + N \hat{\j} \rightarrow \text{curl} \ \bold{F} \cdot \bold{k} = \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}[/tex]

Green's Theorem [Circulation Curl/Tangential Form]:
[tex]\displaystyle \oint_C {F \cdot T} \, ds = \oint_C {M \, dx + N \, dy} = \iint_R {\bigg( \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} \bigg)} \, dx \, dy[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy}[/tex]

[tex]\displaystyle \text{Region:} \ \left \{ {{0 \leq x \leq \pi} \atop {0 \leq y \leq \sin x}} \right.[/tex]

Step 2: Integrate Pt. 1

Define vector functions M and N:
[tex]\displaystyle M = 3y , \ N = 2x[/tex][Circulation Density] Differentiate [Derivative Rules and Properties]:
[tex]\displaystyle \frac{\partial M}{\partial y} = 3 , \ \frac{\partial N}{\partial x} = 2[/tex][Green's Theorem] Substitute in Circulation Density:
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = \iint_R {2 - 3} \, dx \, dy[/tex]Simplify:
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = - \iint_R {} \, dx \, dy[/tex][Integrals] Substitute in region R:
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = - \int\limits^{\pi}_0 \int\limits^{\sin x}_0 {} \, dy \, dx[/tex]

Step 3: Integrate Pt. 2

We can evaluate the Green's Theorem double integral we found using basic integration techniques listed above:
[tex]\displaystyle \begin{aligned}\oint_C {3y \, dx + 2x \, dy} & = - \int\limits^{\pi}_0 \int\limits^{\sin x}_0 {} \, dy \, dx \\& = - \int\limits^{\pi}_0 {y \bigg| \limits^{y = \sin x}_{y = 0}} \, dx \\& = - \int\limits^{\pi}_0 {\sin x} \, dx \\& = \cos x \bigg| \limits^{x = \pi}_{x = 0} \\& = \boxed{\bold{2}}\end{aligned}[/tex]

∴ we have evaluated the line integral using Green's Theorem.

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Topic: Multivariable Calculus

Unit: Green's Theorem and Surfaces

14. Find the distance between (7,217pi/180 ) and (5,-23pi/36 ) on the polar plane.

Answers

Answer: the distance is  3.49 units

Step-by-step explanation:

There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.

When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:

x = R*cos(θ)

y = R*sin(θ)

Then we have:

(7,217pi/180 )

R = 7

θ = (217/180)*pi

x = 7*cos( (217/180)*pi) = -5.59

y = 7*sin( (217/180)*pi) = -4.21

So this point is (-5.59, -4.21) in rectangular coordinates.

And the other point is  (5,-23pi/36 )

R = 5

θ = -(23/36)*pi

x = 5*cos(  -(23/36)*pi ) = -2.11

y = 5*sin(  -(23/36)*pi ) = -4.53

So this point is (-2.11, - 4.53)

Then the point distance between those points is:

D = I (-2.11, -4.53) - (-5.59, -4.21) I

D = I (-2.11 + 5.59, -4.53 + 4.21) I

D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) =  3.49

What are the approximate solutions of the graphed function?

Answers

Answer:

x = -2.6, x = 2.6

Step-by-step explanation:

The graph crosses the x-axis at approximately 2.6 and -2.6.

The required approximate solution of the function graphed is x = -2.6 and 2.6.

Given that,
A graph of a function is plotted, and the solution of the function is to be determined.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

What is a graph?

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here, the solution of the function is that value of x where the function terminates to zero, So the given curve terminates to zero at two places at x = -2.6 and x = 2.6 from the observation of the graph.

Thus, the required approximate solution of the function graphed is x = -2.6 and 2.6.

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PLS HELP ASAP:Find all the missing elements:

Answers

Answer:

B = 34.2°

C = 105.8°

c = 12.0 units

Step-by-step Explanation:

Given:

A = 40°

a = 8

b = 7

Required:

Find B, C, and c.

SOLUTION:

Using the Law of Sines, find <B:

[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]

[tex] \frac{sin(40)}{8} = \frac{sin(B)}{7} [/tex]

Multiply both sides by 7

[tex] \frac{sin(40)}{8}*7 = \frac{sin(B)}{7}*7 [/tex]

[tex] \frac{sin(40)*7}{8} = sin(B) [/tex]

[tex] 0.5624 = sin(B) [/tex]

[tex] B = sin^{-1}(0.5624) [/tex]

[tex] B = 34.2 [/tex] (to nearest tenth).

Find <C:

C = 180 - (34.2+40°) (sum of angles in a triangle)

C = 180 - 74.2 = 105.8°

Using the Law of Sines, find c.

[tex] \frac{c}{sin(C)} = \frac{b}{sin(B)} [/tex]

[tex]\frac{c}{sin(105.8)} = \frac{7}{sin(34.2)}[/tex]

Multiply both sides by sin(105.8)

[tex]\frac{c}{sin(105.8)}*sin(105.8) = \frac{7}{sin(34.2)}*sin(105.8)[/tex]

[tex] c = \frac{7*sin(105.8)}{sin(34.2)} [/tex]

[tex] c = 12.0 [/tex]

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