Use a suitable parametrization to compute directly (without the use of Green's theorem) the outward flux of the vector field F = (5x, -6.) across the circle x2 + y2 = 4 in the plane. (Do not use Green's theorem.)

The maximum value of the data is given as follows:

75.

A box and whisker plot shows these five metrics from a data-set, listed and explained as follows:

The maximum value on the box plot is the end of the plot, hence it is of 75.

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Answer:

The change in latitude, Δφ, from Liverpool to Melbourne is 91.22° south

The change in longitude, Δλ, from Liverpool to Melbourne is 147.95° East

Step-by-step explanation:

The parameters given are;

The latitude of Liverpool is 53.41°

The longitude of Liverpool is -2.99°

The latitude of Melbourne is -37.81°

The longitude of Melbourne is 144.96°

The change in latitude from Liverpool to Melbourne = Δφ

Δφ = 53.41° - (-37.81°) = 53.41° + 37.81° = 91.22°

The change in latitude, Δφ, from Liverpool to Melbourne = 91.22° south

The change in longitude from Liverpool to Melbourne = Δλ

Δλ = -2.99° - 144.96°  = -147.95°

Therefore the change in longitude from Liverpool to Melbourne = 147.95° East.

Answer:

the difference in latitude is 91.22°

the difference in longitude is 147.95°

Explanation:

For Liverpool, London. The latitude is 53.41°, longitude is -2.99°

For  Melbourne, Australia. The latitude is -37.81°, longitude is 144.96°

The negative or positive magnitude of their values shows their position on either sides of the origin of the latitude (equator) and the origin of the longitude (prime meridian).

The latitude measures the relative position of a point, north or south of the equator (latitude 0°). The longitude measures the relative position, east or west of the prime meridian (longitude 0°)

the difference in latitude is 53.41° - (-37.81°) = 53.41° + 37.81° = 91.22°

the difference in longitude = 144.96° - (-2.99°) = 144.96 + 2.99 = 147.95°

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (4, 3)

m = \(\frac{3-0}{4+5}\) = \(\frac{3}{9}\) = \(\frac{1}{3}\) , thus

y = \(\frac{1}{3}\) x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 3) , then

3 = \(\frac{4}{3}\) + c ⇒ c = 3 - \(\frac{4}{3}\) = \(\frac{5}{3}\)

y = \(\frac{1}{3}\) x + \(\frac{5}{3}\) → A

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The equation of the line that passes through (-5, 0) and (4, 3) is

y = (1/3)x + 5/3.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The general equation of a straight line is y = mx + c.

m = slope

c = y-intercept

We have,

A line passes through (-5, 0) and (4, 3)

Slope = m is given by:

m = (d - b) / (c - a)

where (a, b) and (c, d) are the points where the line passes.

Now,

Slope =m = (3 - 0)/(4 - (-5)) = 3/(4+5) = 3/9 = 1/3

We have,

y = mx + c

We can assume any point (-5, 0) or (4, 3) to find the value of the y-intercept.

Case 1.

(-5 , 0) = (x, y)

0 = 1/3(-5) + c

0 = -5/3 + c

c = 5/3

Case 2.

(4, 3) = (x, y)

3 = (1/3)4 + c

3 = 4/3 + c

c = 3 - 4/3

c = 9 - 4 / 3

c = 5/3

We will get the same value for c in both cases.

We have,

m = 1/3 and c = 5/3

The equation of the line can be written as:

y = (1/3)x + 5/3.

Thus the equation of the line that passes through (-5, 0) and (4, 3) is

y = (1/3)x + 5/3.

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Answer:

Non-linear; not a function

Step-by-step explanation:

The line is not straight; it does not pass the vertical line test

Answer:

y = -3x

Step-by-step explanation:

Using the 'y=mx+c' form,

Since m = -3,

y = -3x + c

Substituting (0,0) into the above equation:

0 = 0 + c

Hence,

y = -3x

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To calculate the surface integral of the vector field F(x, y, z) = (cos(2x), e^(-y), vy) over the boundary surface Q of the cube [0, 1], we need to parametrize the surface and then evaluate the dot product of the vector field and the surface normal vector.

The boundary surface Q of the cube [0, 1] consists of six square faces. To compute the surface integral, we need to parametrize each face and calculate the dot product of the vector field F and the surface normal vector. Let's consider one face of the cube, for example, the face with the equation x = 1. Parametrize this face by setting x = 1, and let the parameters be y and z. The parametric equations for this face are (1, y, z), where y and z both vary from 0 to 1.

Now, we can calculate the surface normal vector for this face, which is the unit vector in the x-direction: n = (1, 0, 0). The dot product of the vector field F(x, y, z) = (cos(2x), e^(-y), vy) and the surface normal vector n = (1, 0, 0) is F • n = cos(2) * 1 + e^(-y) * 0 + vy * 0 = cos(2).

To find the surface integral over the entire boundary surface Q, we need to calculate the surface integral for each face of the cube and sum them up. In summary, the surface integral of the vector field F(x, y, z) = (cos(2x), e^(-y), vy) over the boundary surface Q of the cube [0, 1] is given by the sum of the dot products of the vector field and the surface normal vectors for each face of the cube. The specific values of the dot products depend on the orientation and parametrization of each face.

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To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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Answer:

 ^^

Step-by-step explanation:

Answer:

You didn't add the range. I'll use (0<x<2π)

cosx = -1/2

x=-cos-¹(1/2)

x= -60°

Cosine is negative in the second and 3rd quadrants

180-x ---- Second quadrant

x+180 ----- 3rd quadrant

So

Our answer

180-(-60)=240° or 4π/3 second quad

180+(-60) = 120° or 2π/3---- 3rd quad

Answer:

19,600

Step-by-step explanation:

28,000x 0.3=8,400

28,000-8,400=`19,600

i. After 6 years, the amount in the bank account with annual compounding will be $4,238.51.

ii. After 6 years, the amount in the bank account with quarterly compounding will be $4,243.06.

iii. After 6 years, the amount in the bank account with monthly compounding will be $4,245.97.

iv. After 6 years, the amount in the bank account with continuous compounding will be $4,246.93.

To calculate the future amount in the bank account after 6 years with different compounding frequencies, we can use the formula for compound interest: A =\(P(1 + r/n)^(nt)\), where A is the future amount, P is the principal amount, r is the interest rate, n is the compounding frequency per year, and t is the number of years.

i. With annual compounding: A = \(3000(1 + 0.06/1)^(16)\) = $4,238.51.

ii. With quarterly compounding: A = \(3000(1 + 0.06/4)^(46)\)= $4,243.06.

iii. With monthly compounding: A = \(3000(1 + 0.06/12)^(126)\) = $4,245.97.

iv. With continuous compounding: A = \(3000e^(0.066)\) = $4,246.93 (using the formula A = Pe^(rt) where e is the base of the natural logarithm).

These calculations demonstrate how the compounding frequency affects the growth of the investment over time, with more frequent compounding resulting in slightly higher future amounts.

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Answer:

8/9

Step-by-step explanation:

Make 4 as a fraction. It turns to 4/1

2/9 x 4/1 = 8/9

To prove the opposite, we need to show that if G is not a pseudorandom generator (PRG), then Construction 3.17 cannot be EAV-secure.

Assume that G is not a PRG, which means it fails to expand the seed sufficiently. Let's suppose that G is computationally indistinguishable from a truly random function on its domain, but it does not meet the requirements of a PRG.

Now, consider the private-key encryption scheme Π described in Construction 3.17 using G as the pseudorandom generator. If G is not a PRG, it means that its output is not sufficiently pseudorandom and can potentially be distinguished from a random string.

Given this scenario, an adversary A could exploit the distinguishability of G's output and devise an attack to break the security of the encryption scheme Π. The adversary could potentially gain information about the plaintext by analyzing the ciphertext and the output of G.

Therefore, if G is not a PRG, it implies that Construction 3.17 cannot provide EAV-security, as it would be vulnerable to attacks by distinguishing the output of G from random strings. This contradicts Theorem 3.18, which states that if G is a PRG, then Construction 3.17 achieves indistinguishable encryptions.

Hence, by proving the opposite, we conclude that if G is not a PRG, then Construction 3.17 cannot be EAV-secure.

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If your asking to select all that apply, The formula is arc length = θ ( r ) {\displaystyle {\text{arc length}}=\theta (r)} , where equals the measurement of the arc's central angle in radians, and r {\displaystyle r} equals the length of the circle's radius. Plug the length of the circle's radius into the formula.ABC,BAD,DCB

More

For the points A and B, the major arc is the part of the circumference from A to B which contains the points E, D and C

For a circle, take two points on its circumference. That divides the circumference of the considered circle in two parts. Those both parts are called arcs of the circle. The bigger part will be called the major arc, and the smaller one will be called the minor arc.

When the two points are chosen such that they're the endpoints of one of the diameters of the considered circle, then both the arcs are of same length due to symmetry, so there is no concept of major or minor between them.

For this case, there are 5 points, as A, B, C, D, and E.

Since no option is given, so let we take two points which are not on the ends of any diameter.

The points A and B are good enough.

So, the smaller part of the circumference between A and B is the minor arc and the bigger part which contains points like E, D and C is the major arc.

A demonstration is given in the image attached below.

Thus, for the points A and B, the major arc is the part of the circumference from A to B which contains the points E, D and C (the bigger part).

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Answer:

2.1

Step-by-step explanation:

Simplifying

3.4 + -2.8d + 2.8d + -1.3 = 0

Reorder the terms:

3.4 + -1.3 + -2.8d + 2.8d = 0

Combine like terms: 3.4 + -1.3 = 2.1

2.1 + -2.8d + 2.8d = 0

Combine like terms: -2.8d + 2.8d = 0.0

2.1 + 0.0 = 0

2.1 = 0

Solving

2.1 = 0

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

Notice that the given function is an exponential function, also:

therefore, its y-intercept is y=30.

The it looks like the information provided concerning Rheneas' position is lacking. The function you gave, () = 0.43 + 4.32 + 15.7, omits the variable name or the range of possible values for ".

The phrase "east of Knapford Station (for 0)" ends the sentence abruptly.

I would be pleased to help you further with evaluating the expression or answering your query if you could provide me all the details of Rheneas' position, including the variable, the range of values, and any extra context or restrictions.

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Rodger's weekly unemployment amount is $697.54

What is the total of the quarterly wages of two consecutive quarters?

The total of the of the quarterly wages of two consecutive quarters is the sum of first quarter and second quarter wages

total of quarterly wages=$13,950.80+$13,950.80

total of quarterly wages=$27,901.60

unemployment compensation=total of quarterly wages/26

unemployment compensation=$27,901.60 /26

unemployment compensation=$1,073.14

The weekly unemployment amount is 65% of Rodger's state, unemployment compensation

weekly unemployment=65%*$1,073.14

weekly unemployment=$697.54

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Answer:

y=25,000(0.89)^6

Step-by-step explanation:

Answer:

a: y= 25,000(0.89)^6

Step-by-step explanation:

Answer:

Im pretty sure it is E=8

Step-by-step explanation:

Answer:

E=8

Step-by-step explanation:

took the test :)

Answer:

Nolan is wrong.  So is the teacher.

Step-by-step explanation:

See attached image.  There is no valid answer option.

If the "3 sides" of triangle are 14 feet, 19 feet and 23 feet, then the largest angle of the triangle is (d) 87°.

In order to find the largest angle of the triangle, we can use the law of cosines, which is : c² = a² + b² - 2ab×cos(C),

where c is = side opposite the angle we're trying to find (the largest angle), "a" and "b" are the other two sides, and C is = angle opposite side "c".

Substituting the values ,

⇒ c = 23 (the longest side)

⇒ a = 14,

⇒ b = 19,

We get,

⇒ 23² = 14² + 19² - 2(14)(19)×cos(C),

⇒ 529 = 196 + 361 - 532×cos(C),

⇒ -28 = -532×cos(C),

⇒ cos(C) = 0.0526,

Now we use (cos⁻¹) function to find the value of "angle C" in degrees;

⇒ C = cos⁻¹(0.0526),

⇒ C ≈ 87°,

Therefore, the largest angle of the triangle is 87°, correct option is (d).

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Answer:

10yd x 14 yd x 3yd = 420yd ^3

Step-by-step explanation:

When calculating for the volume you multiply all three numbers. That’s why when you write your answer you cube it.

If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.

To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.

To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).

Plugging in the values, we have:

FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06

≈ $12,350

Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.

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The slope of the parametric curve x=-\(2t^3\)+7, y=3t² at the point corresponding to t is -1 divided by t.

To find the slope of the parametric curve x=-\(2t^3\)+7, y=3t², we need to take the derivative of y with respect to x.

To do this, we can use the chain rule:

(dy/dx) = (dy/dt) / (dx/dt)

where (dx/dt) is the derivative of x with respect to t, and (dy/dt) is the derivative of y with respect to t.

Taking the derivatives, we get:

dx/dt = -6t²

dy/dt = 6t

Substituting these values, we get:

(dy/dx) = (dy/dt) / (dx/dt) = (6t) / (-6t²) = -1/t

So, the slope of the curve at the point corresponding to t is -1/t.

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

"Wooden leg" is the correct answer.

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

B. One

Step-by-step explanation:

Since the two angles are already given, the value of the third angle is already fixed. The third angle can be found by the sum of both angles subtracted from 180. Since 2 angles and lengths are already given, there can only be 1 triangle.

Hope this helps!

If not, I am sorry.