Can someone do this for me ill give you brainliest

The divergence of vector field f(x, y, z) is given values div(f) = 1 + zy cos(yz) - z sin(xz) + ye²(Sxy) + xy e²(Sxy) ×cos(Sxy).

To calculate the curl and divergence of the given vector fields, each vector field separately:

a) Vector field f(x, y, z) = (x - y)i + e²(-x)j + xyek

The curl of a vector field F = P i + Q j + R k is given by the following formula:

curl(F) = V × F = (dR/dy - dQ/dz)i + (dP/dz - dR/dx)j + (dQ/dx - dP/dy)k

calculate the curl for vector field f(x, y, z):

P = x - y

Q = e²(-x)

R = xy

compute the partial derivatives:

dP/dz = 0

dQ/dx = -e²(-x)

dR/dy = x

dP/dy = -1

dQ/dz = 0

dR/dx = y

These values into the curl formula,

curl(f) = (x - 0)i + (-e²(-x) - y)j + (-1 - (x - y))k

= xi - e²(-x)j - k

So, the curl of vector field f(x, y, z) is given by curl(f) = xi - e²(-x)j - k.

The divergence of a vector field F = P i + Q j + R k is given by the following formula:

div(F) = V · F = dP/dx + dQ/dy + dR/dz

calculate the divergence for vector field f(x, y, z):

P = x - y

Q = e²(-x)

R = xy

compute the partial derivatives:

dP/dx = 1

dQ/dy = 0

dR/dz = 0

values into the divergence formula,

div(f) = 1 + 0 + 0

= 1

So, the divergence of vector field f(x, y, z) is given by div(f) = 1.

b) Vector field f(x, y, z) = (x + sin(yz))i + (z cos(xz))j + (ye²(Sxy))k

Curl:

Using the same formula as before, Calculate the curl for vector field f(x, y, z):

P = x + sin(yz)

Q = z cos(xz)

R = ye²(Sxy)

Compute the partial derivatives:

dP/dz = y cos(yz)

dQ/dx = -z sin(xz)

dR/dy = e²(Sxy) + xy e²(Sxy) × cos(Sxy)

dP/dy = z cos(yz)

dQ/dz = cos(xz) - xz sin(xz)

dR/dx = y² e²(Sxy) × cos(Sxy)

values into the curl formula,

curl(f) = (y cos(yz) - (cos(xz) - xz sin(xz)))i + ((e²(Sxy) + xy e²(Sxy) × cos(Sxy)) - (z cos(yz)))j + ((z sin(xz) - y² e²(Sxy) ×cos(Sxy)))k

Simplifying further:

curl(f) = (xz sin(xz) + y cos(yz) - cos(xz))i + (e²(Sxy) + xy e²(Sxy) ×cos(Sxy) - z cos(yz))j + (z sin(xz) - y² e²(Sxy) × cos(Sxy))k

So, the curl of vector field f(x, y, z) is given by curl(f) = (xz sin(xz) + y cos(yz) - cos(xz))i + (e²(Sxy) + xy e²(Sxy) × cos(Sxy) - z cos(yz))j + (z sin(xz) - y² e²(Sxy) × cos(Sxy))k.

Divergence:

Using the same formula as before, calculate the divergence for vector field f(x, y, z):

P = x + sin(yz)

Q = z cos(xz)

R = ye²(Sxy)

compute the partial derivatives:

dP/dx = 1 + zy cos(yz)

dQ/dy = -z sin(xz)

dR/dz = ye²(Sxy) + xy e²(Sxy) ×cos(Sxy)

values into the divergence formula,

div(f) = 1 + zy cos(yz) - z sin(xz) + ye²(Sxy) + xy e²(Sxy) ×cos(Sxy)

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Answer:

8x+16

7x-9

_____

15x+7

Step-by-step explanation:

Add or subtract like terms

Answer:

15x+7

No step I did it

You can make 16 headbands using the blue fabric and 5 headbands using the yellow fabric, for a total of 21 headbands.

To calculate this, we need to convert 2/3 yard to feet since the fabric is given in feet. 2/3 yard is equal to 2 feet.

Next, we need to determine how much fabric is needed to make one headband, which is 2 feet.

To find out how many headbands we can make using the blue fabric, we divide the total length of blue fabric (12 feet) by the length needed for one headband (2 feet). 12 feet / 2 feet = 6 headbands per yard of blue fabric. Therefore, with 12 feet of blue fabric, we can make 6 x 12 = 72 headbands.

Similarly, to find out how many headbands we can make using the yellow fabric, we divide the total length of yellow fabric (4 feet) by the length needed for one headband (2 feet). 4 feet / 2 feet = 2 headbands per yard of yellow fabric. Therefore, with 4 feet of yellow fabric, we can make 2 x 4 = 8 headbands.

Therefore, we can make a total of 72 + 8 = 80 headbands.

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Complete Question:

You need 2/3 yard of fabric to create a headband: You have 12 feet of blue fabric and 4 feet of yellow fabric; How many headbands can you make with all of the fabric?

The tangent linear function is:

y + 5.14 = (1/2)*(x - 1.18)

Two lines are parallel if the slope is the same one.

For the line:

x - 2y + 6 = 0

We can rewrite:

2y = x + 6

y = (1/2)*x + 3

The slope is (1/2).

Now, we want to find a line tangent to y = x⁴ - 6x

Parallel to the other one, so we need to differentiate and find the value of x such that the derivative is equal to 1/2

We need to solve:

1/2 = 4*x³ - 6

1/2 + 6 = 4x³

6.5/4 = x³

∛(6.5/4) = x

1.18 = x

Evaluating the function there, we will get:

f(1.18) = 1.18⁴ - 6*1.18 = -5.14

Then the linear function is:

y + 5.14 = (1/2)*(x - 1.18)

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Answer:

following your lead would mean that he has 6 left after the party- but that seems a bit off dont ya think

Step-by-step explanation:

Answer:

K=8.6

Step-by-step explanation:

In a //gram the consecutive angles add up to 180.

So you can set WRD+RDN=180 and then solve for k given the two equations.

Answer:16

well if x=5 and y=1/2 you would have to plug that into the equation 3x+2y which would look like 3(5)+2(1/2) then you would take the time to multiply those out first because P.E.M.D.A.S. which leaves you with 15+1 because 2 times 1/2 is half of 2 which is 1. so 15+1=16!

Step-by-step explanation:

"Mr Clean, Mr Clean."

The parabola has a minimum value of 5.75.

From the question, we have

f(x)=x^2-x+6

a=1, b=-1, c=6

Δ=b^2-4ac

=1-24

=-23<0

So f(x)=0 has no solution.

x=-b/2a=-(-1)/2=1/2

f(1/2)=1/4-1/2+6

=23/4  is the minimum

=5.75

The parabola has a minimum value of 5.75.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The graph of exponential function, is described below.

What is an exponential function?

The mathematical formula f(x) = e^x stands for the exponential function. The term, unless specifically stated otherwise, generally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

The formula for an exponential growth function is y = ab^x, where a > 0 and b > 1. As can be seen in the example of f(x) = 2x below, the graph will ascend. The numbers get smaller as x gets closer to negative infinity, as you can see.

If b > 1 , then the graph's slope is positive and exponential growth is depicted. The value of y approaches infinity as x rises. The value of y approaches zero as x falls.

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Answer:

$54

Step-by-step explanation:

Answer:

Step-by-step explanation:

Bro, for the $500 after the rate add 12 and 12 and do that for all the rate's like when you get to the fraction rate add the fraction rate with the fraction rate

Answer:

yes

Step-by-step explanation:

for the sides to form a triangle then the sum of any 2 must be greater than the third.

10.5 + 8 = 18.5 > 4

10.5 + 4 = 14.5 > 8

8 + 4 = 12 > 10.5

then the 3sides could form a triangle

The probability that more than 20% of the sample are from poverty households is approximately 0.8365.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

We can use the normal approximation to the binomial distribution to solve this problem, given that the sample size is relatively large (n=300) and the probability of success (p=0.22) is not too close to 0 or 1.

Let X be the number of children in the sample who live in poverty households. Then X follows a binomial distribution with parameters n=300 and p=0.22.

The mean of X is given by μ = np = 300 x 0.22 = 66, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(300 x 0.22 x 0.78) ≈ 6.23.

We want to find the probability that more than 20% of the sample are from poverty households, which is equivalent to finding P(X > 0.2n) = P(X > 60).

To use the normal approximation, we can standardize X as follows:

Z = (X - μ) / σ

Then, we have:

P(X > 60) = P(Z > (60 - 66) / 6.23) ≈ P(Z > -0.96)

Using a standard normal table or calculator, we can find that the probability of Z being greater than -0.96 is approximately 0.8365.

Therefore, the probability that more than 20% of the sample are from poverty households is approximately 0.8365.

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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Answer:

x = 19

Step-by-step explanation:

3x - 3 = 6(x - 10)

3x - 3 = 6x - 60 Use dist property

Subtract 3x from both sides

-3 = 3x - 60

Add 60 to both sides

57 = 3x

Divide both sides by 3

19 = x

Answer:

£616

Step-by-step explanation:

700 - 12% = 616

616 is 12% less than 700

There are a few different statistical tests that could be used to compare the mean ages of cases and controls in a case-control study. One commonly used test is the t-test and  Mann-Whitney U test.

t-test compares the means of two groups and evaluates whether they are significantly different from one another. In this case, the two groups would be the cases and controls.

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Answer:

Below

Step-by-step explanation:

4 out of 9 are not broken    first bar not broken chance is then 4/9

  now there are   8 bars left and 3 are not broken    so for the second bar thee is a 3/8 chance of not being broken

4/9 * 3/8 = 12/72 =   1/6

Answer:

it's below because

Step-by-step explanation:

1/6 !!!!!!!!!!!!!!

Answer:

you are so good are this so keeping up

Answer:

k = 12h

Step-by-step explanation:

Since each of the inputs of h can be mutiplied by 12 to get the output k, the equation is k = 12h
Hope this helps :)

Answer:\(V=168\ units^3\)

Step-by-step explanation:

Given

Length of Prism \(l=6\ units\)

Height of prism \(h=7\ units\)

width of prism \(b=4\ units\)

Now Volume of a prism is given by

\(V=l\times b \times h\)

\(V=6\times 4\times 7\)

\(V=168\ units^3\)

Answer:

The answer is 6(7)(4) = 168 Units cubed

Step-by-step explanation:

Hope this helps :)

\(v = (5 \times 3 \times 6.5) + (2 \times 4 \times 6.5)\)

\(v = 15 \times 6.5 + 8 \times 6.5\)

\(v = 97.5 + 52\)

\(v = 149.5 \: \: \: {cm}^{3} \)

Answer:

Step-by-step explanation:

its the next one down

Answer:

100m by 50m.

Step-by-step explanation:

Let the dimension of the rectangular pen be x and y

Area, A(x,y)=xy

Let the side opposite her barn = x

Since she wants to fence only three side

Perimeter = x+2y

Length of Fencing Available = 200m

Therefore: \(x+2y=200 \implies x=200-2y\)

We want to maximize the area of the pen, A(x,y).

Substituting x=200-2y into A(x,y)=xy

\(A(y)=y(200-2y)\\A(y)=200y-2y^2\)

To maximize A(y), we find its derivative and solve for the critical points.

\(A'(y)=200-4y\\$Setting $A'(y)=0\\200-4y=0\\200=4y\\y=50\)

To ensure that this is a maximum, we use the second derivative test.

\(A''(y)=-4\)

This is negative and thus, y=50 is a maximum point.

Recall:

x=200-2y

x=200-2(50)

x=200-100

x=100m

Therefore, the dimensions of the pen that has the largest area are 100m by 50m.

Answer:

37% = 0.37 = 37/100

Step-by-step explanation:

hope this helps :)

Answer:

First box:

1/8 of 5, 5 x 1/8, 5 divided by 8

Second Box:

8 divided by 5, 1/5 of 8,

Third Box:

5 x 8

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The question states that...

\(x=2\\y=2\)

\(2\leq 4(2)-6\\2\leq 8-6\\2\leq 2\)

Yes

Hope this helped! Please mark brianliest :)

Answer:yes

Step-by-step explanation:

Y<_4x-6

2<_4(2)-6

2<_8-6

2<_2

Answer:

\(11\sqrt{797}\pi\)

Step-by-step explanation:

\(A=\pi r \sqrt{h^2+r^2}\)

the radius is 22/2 = 11 in

h is 26 in

substitute: \(\pi \left(11\right)\sqrt{\left(26^2\right)+\left(11^2\right)}\)

= \(11\sqrt{797}\pi\)

Answer:

286π in²

Step-by-step explanation:

The lateral area (A) of the cone is calculated as

A = πrs ( r is the radius and s the slant height )

Here r = 22 ÷ 2 = 11 and s = 26 , then

A = π × 11 × 26 = 286π in²

Answer:

\(\huge \boxed{\mathrm{Option \ C}}\)

Step-by-step explanation:

Length of arc formula = θ/360 × 2\(\pi\)r

The angle is 210 degrees.

The radius is 7 ft.

210/360 × 2\(\pi\)(7)

Simplify the expression.

210/360 × 14\(\pi\)

2940/360\(\pi\)

49/6\(\pi\)

The length of the arc of circle having radius 7 feet is 49π/6 which is option C.

An arc is a part of circumference of a circle which is formed from two radius of the circle. The length of arc is equal to Θr in which r is radius and Θ is angle in radian form.

We have been given the radius of the circle be 7 feet and angle be 210°.

The length of arc will be Θr in which r is the radius and Θ is the angle in radian form.

First we have to convert angle in radian form=210*π/180=7π/6.

Length of arc=7π/6*7

=49π/6

Hence the length of the arc of circle having radius 7 feet is 49π/6 which is option C.

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