Between what two integers is the value of pi ^ 2

The surface integral ∬S F ⋅ dS evaluates to 36π.The closed surface S consists of the bounded cylinder x^2 + y^2 = 4, 0 ≤ z ≤ 3, along with the disks on the top (z = 3) and bottom (z = 0).

To evaluate the surface integral ∬S F ⋅ dS, we need to compute the dot product of the vector field F = ⟨2xy, z=y^2, z^2⟩ with the outward unit normal vector dS for each surface element on S and then integrate over the entire surface.

The closed surface S consists of the bounded cylinder x^2 + y^2 = 4, 0 ≤ z ≤ 3, along with the disks on the top (z = 3) and bottom (z = 0).

The outward unit normal vector dS for the curved surface of the cylinder is given by dS = ⟨2x, 2y, 0⟩, and for the top and bottom disks, the normal vectors are ⟨0, 0, 1⟩ and ⟨0, 0, -1⟩, respectively.

Now, we calculate the dot product of F with dS for each surface element and integrate over the surface. The dot product F ⋅ dS is given by:

F ⋅ dS = 2xy(2x) + y^2(2y) + z^2(0) = 4x^2y + 2y^3

Integrating F ⋅ dS over the curved surface of the cylinder, we use cylindrical coordinates where x = 2cosθ, y = 2sinθ, and z ranges from 0 to 3. The integral becomes:

∫∫(cylinder) (4x^2y + 2y^3) dS = ∫∫(cylinder) (4(2cosθ)^2(2sinθ) + 2(2sinθ)^3) (2dθdz) = ∫(0 to 3) ∫(0 to 2π) (16cos^2θsinθ + 16sin^3θ) dθdz

Evaluating the above integral, we get:

∫(0 to 3) ∫(0 to 2π) (16cos^2θsinθ + 16sin^3θ) dθdz = 36π

Therefore, the surface integral ∬S F ⋅ dS evaluates to 36π.

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Answer:

Juanita borrowed $600 to purchase a computer

Step-by-step explanation:

Grammer

Answer:

what exactly is your question? i would be happy to help, but there is no question present.

Step-by-step explanation:

Answer:

The answer is (3/4)100=75

Hope this helps!

Mark me brainliest if I'm right :)

Answer:

slope = - \(\frac{3}{2}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 1 ) and (x₂, y₂ ) = (8, - 8 ) ← 2 ordered pairs from the table

note that any 2 ordered pairs may be used to calculate m

m = \(\frac{-8-1}{8-2}\) = \(\frac{-9}{6}\) = - \(\frac{3}{2}\)

The expression that completes the equation for the measure of ∠c is ∠c = 180° - (∠a + ∠b)°.

Given that the area of the triangle ABC is d. We are to find the expressions that complete the equation for the measure of ∠c.

In order to find the expression for the measure of ∠c, we should know the formulas for finding the measure of angles in a triangle. In a triangle, the sum of all three interior angles is equal to 180 degrees.

Therefore, we can use the formula given below to find the measure of ∠c:

∠a + ∠b + ∠c = 180°

We know that the area of the triangle ABC is given by

d = 1/2 × base × height

Let the length of base BC be 'a' and the length of altitude drawn on base BC from vertex A be 'h'.

Then we can write:

d = 1/2 × base × height

d = 1/2 × a × h

2d/a = h

Substituting the value of h in the formula for the area of the triangle, we get

d = 1/2 × a × (2d/a)d = d

So, the expression that completes the equation for the measure of ∠c is

∠c = 180° - (∠a + ∠b)

or

∠c = 180° - (∠a + ∠b)°.

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The answer has to be: D) 55/9

Answer:

55/9

Step-by-step explanation:

divide both sides by 2, results in 55/9.

You cant go past 2, so 55/9 (or d) is your answer)

:)

3-44x

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Answer:

25 liters

Step-by-step explanation:

60/12=5

5*5=25

Answer:

25 liters of juice

Step-by-step explanation:

5 liters of juice=12 guests Multiply both sides by 5

25 liters of juice=60 guests

Answer:

Whatever she wants.

I'd say you probably want a Wagoneer, as your username is jeepwagoneer

Answer:

which grade are you in so that i can tell you according to that

i, vì AD//BC nên góc A +góc B =180°

ii, góc A=góc B nên góc C=góc D -> ABCD là hình bình hành

And AB=BC=> ABCD là hình thoi

Answer:

• Given a line segment AB

• open the compass more than half of the distance between A and B, and scribe arcs of the same radius centered at A and B.

• Call the two points where these two arcs meet C and D. Draw the line between C and D.

• CD is the perpendicular bisector of the line segment AB. Call the point where CD intersects AB M.

Answer:

p=12

Step-by-step explanation:

DBC = 180

ABE = 180

ABC + DBA = 180

ABC = (5p -28)

DBA + (12p -4)

CBD = ABC + DBA = 180

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

180 = (5p - 28) + (12p + 4)

180 = 17p - 24

204 = 17p

12 = p

p = 12

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

180 = (5(12) - 28) + (12(12) +4)

180 = 60 - 28 + 144 +4

180 = 180

This student performed better than 68% of the other test-takers in the verbal part and better than 27% in the quantitative part.

Given,

Test-taker scored at the 68th percentile for their verbal grade and at the 27th percentile for their quantitative grade .

Now,

68% percentile : 68% scores equal or less .

27% percentile : 27^ scored equal or less .

Thus option D

This student performed better than 68% of other test taker in verbal and better than 27% in quantitative part .

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Answer:

36 units³

Step-by-step explanation:

The volume of a rectangular prism is given by

Volume, V = l * w * h, where

V = volume like I had stated

L = length of the prism

w = width of the prism

h = height of the prism

Going by the aforelisted parameters, we can apply them to the formula to get our answer straight

Volume, V = 3 * 6 * 2

Volume, V = 36 units³

Therefore, the volume of the prism is 36 units³

Answer:

1

Step-by-step explanation:

Hope this helps!

Lmk if you have any questions!

Have a great day! :)

Answer:

1

Step-by-step explanation:

the y intercept is where the line crosses the y = 0 mark and it crosses it at (1,0) so 1 would be your answer

Answer:

H. 1.8 bc you divide 1 8/9 and you would get 1.8

Step-by-step explanation:

Hoped I helped Im Eve btw. Have an amazing day and consider marking this as brainliest if you do thank you in advanced! :3

Answer: -7

Step-by-step explanation:

The equation is in slope-intercept form (y=mx+b), where m is the slope and b is the y-intercept

Therefore, the m value is -7 and it is the slope

Answer: Review the picture. This is the formula.

Step-by-step explanation: Just multiply the terms and you’ll get the volume. Remember to not measure the diameter but half of that which is the radius! I hope this helps but please comment down below if you need more help!

Answer: V = (1/3)πr2h.

Step-by-step explanation:

Using the t-distribution, it is found that:

a)

The null hypothesis is \(H_0: \mu = 3.1\)

The alternative hypothesis is \(H_1: \mu \neq 3.1\)

b)

c) t = 1.853

d) Since |t| = 1.853 < 2.2, we do not reject the null hypothesis, that is, the sample data does not suggest that there is a difference between the national average and the sample mean of the senior citizens.

Item a:

At the null hypothesis, it is tested if the estimate of 3.1 cups per day is correct, that is:

\(H_0: \mu = 3.1\)

At the alternative hypothesis, it is tested if the estimate is not correct, that is:

\(H_1: \mu \neq 3.1\)

Item b:

This is a two-tailed test, as we are testing if the mean is different of a value, with 12 - 1 = 11 df and a significance level of 0.05,  hence, the critical value is \(t^{\ast} = 2.2\).

Then, the decision rule is:

Item c:

We can find the standard deviation for the sample, hence, the t-distribution is used.

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

The values of the parameters, with the help of a calculator for the sample mean and standard deviation, are given by: \(\overline{x} = 3.425, \mu = 3.1, s = 0.6077, n = 12\)

Hence, the value of the test statistic is:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{3.425 - 3.1}{\frac{0.6077}{\sqrt{12}}}\)

\(t = 1.853\)

Item d:

Since |t| = 1.853 < 2.2, we do not reject the null hypothesis, that is, the sample data does not suggest that there is a difference between the national average and the sample mean of the senior citizens.

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Answer:

(-5,7) (-5,8) (-5,3)

Step-by-step explanation:

Dont know if this will help but here you go

Answer:-a+5ab+8

Step-by-step explanation:

The proportion of the 30 sampled bottles are more than 12 ounces is 0.30. The value is most affected by the error will be mean.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint.

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Answer: A. Yes, their slopes are negative reciprocals

Step-by-step explanation:

x=3 is a vertical line where every y value lands on x=3. (Undefined slope)

y=5 is a horizontal line where every x value lands on y=5 (Zero slope)

Even though the slopes are not numbers they can still be negative reciprocals. The lines are indeed perpendicular and thus the slopes are negative reciprocals. The relationship between undefined slopes and zero slopes is negative reciprocals because 0/1 cannot be inversed because anything divided by 0 is undefined.

Answer:

Answer is 0

Step-by-step explanation:

Well it's just simple, -6 + 6 is 0.

Answer:

-6+6=0

Step-by-step explanation:

The success rate for the sample of 200 customers is 15%. The department store manager can compare this success rate with the established level of 20% .

To calculate the success rate for the sample, we need to determine the proportion of customers who made a purchase return out of the total number of customers in the sample.

Given that the sample size is 200 customers and 30 customers made a purchase return, we can calculate the success rate as follows:

Success Rate = (Number of Successes / Sample Size) * 100

In this case, the number of successes refers to the number of customers who made a purchase return, which is 30. The sample size is given as 200 customers.

Plugging in the values into the formula, we get:

Success Rate = (30 / 200) * 100

Success Rate = (0.15) * 100

Success Rate = 15%

Therefore, the success rate for the sample of 200 customers is 15%.

The department store manager can compare this success rate with the established level of 20% to determine if there is a significant difference between the purchase return level in their store and the established level.

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The normal stress and shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ 11 are σn = 16−15√3 and τ = 2+15√3/4. The maximum shear stress is 17.5.

The stress tensor σ given in the problem is:

σ = 201504−400−1500−1010

The normal stress is given by

σn = σ11cos²θ+σ22sin²θ−2σ12sinθcosθ

where

θ = 30°

θ = 30° is the angle between the direction perpendicular to the plane and the direction of σ11

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
σn = 20cos²(30)+(-15)sin²(30)-2(-4)sin(30)cos(30)

σn = 20cos²(30)+(-15)sin²(30)+4sin(30)cos(30)

σn = 20(3/4)+(-15)(1/4)+4(1/2)(√3/2)

σn = 12−15√3+4√3

σn = 16−15√3

The normal stress is σn = 16−15√3

The shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ11

σ11 is given by:
τ = σ12(sin²θ−cos²θ)+0.5(σ11−σ22)sin2θ

where

θ = 30°

θ=30° is the angle between the direction perpendicular to the plane and the direction ofσ11.

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
τ = −4(sin²(30)−cos²(30))+0.5(20−(−15))sin(60)

τ = −4((1/4)−(3/4))+0.5(20+15)(√3/2)

τ = 4(1/2)+0.5(35)(√3/2)

τ = 2+15√3/4

The shear stress is τ = 2+15√3/4

Maximum shear stress
The maximum shear stress is given by

τmax = 0.5(σ1−σ2)

whereσ1σ1 andσ2σ2 are the first and second principal stresses.

The eigenvalues of the stress tensor σ are found by solving the characteristic equation:

det(σ−λI)=0

Here is a detailed calculation:
σ−λI = [20150−λ−400−1500−λ0−400−15−λ10−λ]

σ−λI = 0(20150−λ)[(−λ)(−λ−15)+0(−400)]−(−4)[0(−λ−15)+(−400)(−λ)]+0[0(−400)+(20150−λ)(−λ)]

σ−λI = 0λ³+35λ²−605λ−1875

σ−λI = 0

λ = −25,5,3

The maximum shear stress occurs on the plane of maximum shear stress which is at 45° 45° to the coordinate axes.

The maximum shear stress is found to be

τmax = 0.5(σ1−σ2)

τmax = 0.5(20−(−15))

τmax = 17.5.

Therefore, the maximum shear stress is τmax = 17.5.

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Answer:

Avas unit rate is for a mile 16.6666666667 minutes. while Mauras is 15 mins

Step-by-step explanation:

It would take Ava 16.6666666667 to run a mile, while it would take Maura 15 minutes to run a mile.

Two clusters can be seen in the scatterplot, and their factors are connected. Y increases, but the growth is gradual, as x increases in the bottom one. As x rises in the upper cluster, y rises as well, but more quickly.

A collection of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can display the degree of link, if any,between the values of measured quantities or phenomena, scatter plots are crucial in statistics. Scatter graphs are used for showing data points on an axis that is vertical and horizontal to show how much one element influences another.

Data visualisation that demonstrates the connection between various variables is known as a scatter plot. To show this data, different components of information are positioned between an x- and y-axis. This type of data visualisation takes its name from the way that each of the information points appears to be "spread" across the graph.

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The complete question attached below,