HELP PLEASE WITH THE IMAGE BELOW it would mean a lot if someone helped me answer this question and maybe even explain how you got it.

The flux of the vector field F = x³i + y³j + z³k out of the closed surface S can be calculated using the divergence theorem.

In this case, the region W is defined as the space between the spheres x² + y² + z² = 9 and x² + y² + z² = 25, within the cone z = √(x² + y²) with z ≥ 0. To calculate the flux, we need to compute the divergence of F and integrate it over the region W.

The divergence of F is given by div(F) = ∂(x³)/∂x + ∂(y³)/∂y + ∂(z³)/∂z = 3x² + 3y² + 3z².

By applying the divergence theorem, the flux of F out of the surface S can be expressed as the triple integral of the divergence over the region W:

flux = ∭W (3x² + 3y² + 3z²) dV,

where dV represents the volume element.

To evaluate this integral, the specific limits of integration and the coordinate system used for integration need to be determined based on the given surface S and the region W.

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Answer:

Step-by-step explanation:

Given line h:

Dilated line is parallel to original, so will have same slope of -2

y-intercept will change by a scale factor of 4:

So the equation of the new line is:

Answer:

i think it is rise run :)

Step-by-step explanation:

Answer:

gradient =y²-y¹÷x²-x¹

=10-2÷7-3

=2. answer

gradient of the slope

=tan‐¹=opposite/adjacent

tan‐¹=2/1

=tan‐¹(2/1)

=63.4(3 sf)

Given integral is; ∫(2s / (2x+4))dx By factorizing the denominator,

we get; ∫(2s / 2(x+2))dx. However, since the curve approaches zero as x goes to infinity, the total area under the curve is zero.

We can then take out the constant factor of 2 from the numerator and denominator;

∫(s / (x+2))dx

To evaluate this integral, we need to use the substitution method;

Let, u = x + 2, du/dx = 1, dx = du

Now, when x = -5, u = -3When x = ∞, u = ∞

Now, we can substitute these values in the integral to get;

∫(s / (x+2))dx = ∫s(u)

since the integral is indefinite, we need to evaluate it at the limits;

∫(-5 to ∞)s(u)du= s(∞) - s(-3)By using the graph, we can interpret the result.

From the graph, it is clear that the function approaches zero as it goes to infinity.

This means that the area under the curve to the right of the vertical line x = -3 is zero.

Sketch of the graph:

We can see from the graph that the function is a rectangular hyperbola.

Therefore, the integral is equal to s(∞) - s(-3) = 0 - 0 = 0.

The result means that the area under the curve between x = -5 and x = -3 is equal to the area under the curve between x = -3 and x = ∞.

However, since the curve approaches zero as x goes to infinity, the total area under the curve is zero.

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The complete question -:

Use geometry (not Riemann sums) to evaluate the definite integral. Sketch the graph of the integrand, show the region in question, and interpret your result. (2x 6)dx Choose the correct graph below O A 10 10 10 The value of the definite integral (2x+6)jdk as determined by the area under the graph of the integrand is (Type an integer or a decimal.)

For an arithmetic progression, the general formula:

An = A1 + (n -1)d

For progression 1, we have:

d= -30, A1 = 27

A52 = 27 + (52 -1)x(-30) = -1503

For progression 2, we have:

A1 =40, d =-100

A52 = 40 + (52 -1)x(-100) = -5060

Answer:

5

Step-by-step explanation:

7*4= 28

5+2=7

7*4=28

28=28

The given function that represents the decay rate of a radioactive substance in millirems per year is g(t), with t in years. We are to use definite integrals to represent the quantity of the substance that decays over the first 15 years after the spill.

Definite integrals are used to calculate the area under the curve of a function between two given points. So, the quantity of the substance that decays over the first 15 years after the spill is given by the definite integral of the function g(t) from 0 to 15.3.1 The quantity of the substance that decays over the first 15 years after the spill is given by the definite integral of the function g(t) from 0 to 15.

So, we can represent it as∫₀¹⁵g(t) dt. Note: The symbol ∫ is the integral symbol, ₀ is the lower limit, and ¹⁵ is the upper limit of the definite integral.

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Answer:

6

Step-by-step explanation:

The prime factorization of 12x is 3*2*2x. The prime factorization of 18 is 2*3*3. The same thing that appears in both prime factorizations is 3*2, or 6.

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In 1995, we would anticipate a per capita consumption of 54.3 pounds of chicken.

So,

Let us first calculate the slope of the linear function:

The required linear function can be written as:

When we simplify this, we get:

To calculate per capita consumption in 1995, enter t=15 into this function.

Therefore, in 1995, we would anticipate a per capita consumption of 54.3 pounds of chicken.

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The correct question is given below:

For 1983 through 1989, the per capita consumption of chicken in the u.S. Increased at a rate that was approximately linear. In 1983, the per capita consumption was 39.7 pounds, and in 1989 it was 47 pounds. Write a linear model for per capita consumption of chicken in the u.S. Let t represent time in years, where t = 3 represents 1983. Let y represent chicken consumption in pounds. What would you expect the per capita consumption of chicken to be in 1995? What would you expect the per capita consumption of chicken to be in 1995?

Answer:

13,860

Step-by-step explanation:

List all prime factors for each number.

Prime Factorization of 11 shows:

11 is prime.

Prime Factorization of 35 is:

5 x 7

Prime Factorization of 36 is:

2 x 2 x 3 x 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 3, 5, 7, 11

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 3 x 5 x 7 x 11 = 13860

LCM(11, 35, 36) = 13,860

Answer: x=16

Step-by-step explanation:

To find the axis of symmetry you need to find the value for x. the equation to find x is x=\(\frac{-b}{2a}\). Now solve-

x= \(\frac{-b}{2a}\)=\(\frac{-(-96)}{2(3)}\)=\(\frac{96}{6}\)=16

Kylie earns 5.80 dollars more than Kayla per hour

Answer:

12

Step-by-step explanation:

Rewriting input as fractions if necessary:

7/12, 3/2

For the denominators (12, 2) the least common multiple (LCM) is 12.

LCM(12, 2)

Therefore, the least common denominator (LCD) is 12.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

7/12 = 7/12 × 1/1 = 7/12

3/2 = 3/2 × 6/6 = 18/12

Answer:

9 comic books

Step-by-step explanation:

23 - 5 = 18

18/2 = 9 comic books

Answer:

AC = 56

Step-by-step explanation:

Um, so basically the answer is given to you, no work required. The problem states that the two lines are equal, so AC must equal 56 as well. :P

But let's solve it anyway:

5x + 1 = 56

5x = 56 - 1

5x = 55

x = 11

AC = 5(11) + 1

AC = 55 + 1

AC = 56

-Chetan K

Answer:

A) Negative Correlation. B) C. C) B

Step-by-step explanation:

As the line of best fit is travelling downwards, it is a negative correlation, if the line of best fit is travelling upwards, it is a positive correlation, if the points on the graph are all over the place, there is no correlation.

As there are only three types of correlation, the strongest is always the positive.

The answer is B because there is no correlation and that means that there shouldn't be a line of best fit.

Diagram B because there is no correlation and the strongest is always the positive.

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

The line of best fit is travelling downwards, it is a negative correlation, if the line of best fit is travelling upwards, it is a positive correlation, if the points on the graph are all over the place, there is no correlation.

As there are only three types of correlation, the strongest is always the positive.

The answer is B because there is no correlation and that means that there shouldn't be a line of best fit.

Hence, Diagram B because there is no correlation and the strongest is always the positive.

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By looking at the degree, we conclude that we have 4 roots.

Here we want to see how many roots the function:

x⁴ - 2x³ - 6x² + 22x - 15 = 0

The numer of roots (repeated, complex, or real) is given by the degree of the g

In this case we can see that the maximum exponent is 4, so the degree is 4, which means that we have 4 roots

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Answer: A, B and D.

Step-by-step explanation:

We have two numbers, x and y.

And we know that:

x + y is a negative number.

Then it can happen if:

1) x and y are negative numbers.

remember that when we add two negative numbers, for example -2 and -3 we have:

-2 + (-3) = -5

The sum of two negative numbers is always negative.

2) we have a positive and a negative number, but the absolute value of the negative number is larger than the absolute value of the positive.

For example, if we have -5 and 3.

The positive number is 3 and the negative is -5

and I-5I > I3I

Then when we add those:

-5 + 3 = -2

The result is also a negative number.

Then the correct options are:

A. Both numbers are negative.

B. x is negative, and |x| > |y|. (here says that the negative number is larger in absolute value than the other)

D. y is negative, and |x| < |y|. (this is similar as above, but in this case the negative number is y)

Answer:

x = 32 degrees

Step-by-step explanation:

since there is a line intersecting both of the lines you would do the opposite number to solve the problem. basically what i am trying to say is.

A straight line equals 180 degrees

and the given angle is 148 degrees

so just subtract.

180 degrees - 148 degrees = 32 degrees

so x = 32 degrees

to see if it is reasonable, look at the angle

if you look you can see that it is an acute angle

so, since 32 degrees is an acute angle, the answer is also reasonable.

so like i said,

x = 32 degrees

The interior angles of parallel lines and a transversal are the angles between the parallel lines.

The value of x is 32 degrees

Alternate interior angles of a parallel line add up to 180 degrees.

So:

\(\mathbf{148 + x = 180}\)

Subtract 148 from both sides

\(\mathbf{148 - 148+ x = 180 - 148}\)

Evaluate like terms

\(\mathbf{x = 32}\)

Hence, the value of x is 32 degrees

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The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

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Answer:

Step-by-step explanation:

Dang kid

Answer:

x=16

Step-by-step explanation:

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

The extended power series solution of the differential equation (1+x²)y'' + xy' +2y = 0 using manual computation is \(y(x) = a_{-3}x^{-3} + a_{-2}x^{-2} + \sum(n=0 \;to \;\infty) a_nx^n\) and using matlab is sol = dsolve(ode, y(0) == 1, subs(diff(y,x), 0, 0)).

To find the extended power series solution of the given differential equation, we assume a power series solution of the form y(x) = ∑(n=0 to ∞) aₙxⁿ

First, we differentiate y(x) to find y'(x) and y''(x):

y'(x) = ∑(n=0 to ∞) (n+1)aₙxⁿ

y''(x) = ∑(n=0 to ∞) (n+1)(n+2)aₙxⁿ

Substituting these expressions into the differential equation:

(1+x²)y'' + xy' + 2y = ∑(n=0 to ∞) [(n+1)(n+2)aₙ + (n+1)aₙ]xⁿ + ∑(n=0 to ∞) 2aₙxⁿ = 0

Now, equating the coefficients of like powers of x to zero, we get the following recursive relation:

(n+1)(n+2)aₙ + (n+1)aₙ+ 2aₙ = 0

Simplifying the equation, we obtain:

aₙ [(n+1)(n+2) + (n+1) + 2] = 0

Since this equation must hold for all values of n, we have two possibilities:

Setting aₙ = 0 for all n gives the trivial solution.

Solving the equation (n+1)(n+2) + (n+1) + 2 = 0 for the roots of n gives the non-trivial solution. By solving the quadratic equation, we find two distinct roots: n = -3 and n = -2.

Therefore, the extended power series solution of the differential equation is given by:

\(y(x) = a_{-3}x^{-3} + a_{-2}x^{-2} + \sum(n=0 \;to \;\infty) a_nx^n\), where aₙ are arbitrary constants.

In MATLAB, we can use the 'dsolve' function to find the solution to the differential equation. The syntax would be:

syms y(x)

ode = (1+x²)diff(y,x,2) + xdiff(y,x) + 2*y == 0;

sol = dsolve(ode);

The output 'sol' will provide the symbolic solution to the differential equation. To obtain a numerical solution, we can substitute initial conditions or specific values of the arbitrary constants into the solution.

For example, if we want to find the numerical solution with initial conditions y(0) = 1 and y'(0) = 0, we can use:

sol = dsolve(ode, y(0) == 1, subs(diff(y,x), 0, 0));

The output 'sol' will give the numerical solution to the differential equation satisfying the given initial conditions.

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Answer:

1.5

Step-by-step explanation:

3.8-2.3=1.5