This is very easy. will give brainliest!!

Using the divergence theorem to compute the flux of the vector field f through the surface S. The flux of the vector field f through the surface S, where S is the sphere \(x^2 + y^2 + z^2 = a^2\) oriented outward, the flux of f through S is simply 0.

Using the divergence theorem to compute the flux of the vector field f through the surface S. The divergence theorem states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the vector field over the volume enclosed by the surface. In this case, since the surface S is a sphere, we can use spherical coordinates to evaluate the volume integral.

The divergence of the vector field f is given by

div f = ∂x + ∂y + ∂z.

Evaluating this in spherical coordinates, we get

div f = (1/r^2) ∂(r^2x)/∂r + (1/r^2) ∂(r^2y)/∂θ + (1/r^2sinθ) ∂(z)/∂φ. Substituting the components of f, we get div f = 3.

The volume enclosed by the surface S is the interior of the sphere, which has volume \((4/3)\pi a^3\). Therefore, the flux of f through S is\((3/4\pi a^3)\) times the volume integral of the divergence of f over the interior of the sphere, which is \((3/4\pi a^3)\) times 3 times the volume of the sphere, i.e., \(3a^3\). Hence, the flux of f through S is 9, which means that the net flow of f through S is outward. However, since S is already oriented outward, the flux of f through S is simply 0.

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For the expression y5y3−(y−2)4 the correct value is in the first tile, and for the expression (y−2)4+y3y5 the correct value is in the fifth tile.

Exponents that should be integers are known as integer exponents in mathematics. It could be either a positive or negative integer. The positive integer exponents specify how many times the base number should be multiplied by itself in this case.

We have:

\(=\rm y^5y^3-(y^{-2})^4\)

\(= \rm y^{5+3}-(y^{-2\times4})\)

\(= \rm y^{8}-(y^{-8})\)

\(= \rm y^{8}-\dfrac{1}{y^{8}}\)

\(\rm y^5y^3-(y^{-2})^4 = y^{8}-\dfrac{1}{y^{8}}\)

Similarly,

\(\rm (y^{-2})^4 + \dfrac{y^3}{y^{5}} = \rm \dfrac{1}{y^{8}} + \dfrac{1}{y^{2}}\)

Thus, for the expression y5y3−(y−2)4 the correct value is in the first tile, and for the expression (y−2)4+y3y5 the correct value is in the fifth tile.

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Two unit vectors that make an angle of 60 degrees with v = (3, 4) are approximately (2.5000, 4.3301) and (-2.5000, -4.3301).

To find two unit vectors that make an angle of 60 degrees with vector v = (3, 4), we can use trigonometry and vector operations.

Step 1: Calculate the magnitude of vector v:

|v| = sqrt(3^2 + 4^2) = 5

Step 2: Convert the given angle of 60 degrees to radians:

θ = 60 degrees * (π/180) = π/3 radians

Step 3: Calculate the components of the unit vector in the same direction as v:

u1 = cos(θ) = cos(π/3) ≈ 0.5000

u2 = sin(θ) = sin(π/3) ≈ 0.8660

Step 4: Multiply the components by the magnitude of v to obtain the unit vectors:

u1 = u1 * |v| ≈ 0.5000 * 5 ≈ 2.5000

u2 = u2 * |v| ≈ 0.8660 * 5 ≈ 4.3301

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Answer:

D. 96

Step-by-step explanation:

the answer is irrational

The number 11.47723 is rational if it is an integer or decimal

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.

Since 11.47723 is an integer or decimal from above, 11.47723 is also a rational

Answer:

X=9 so D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

70 and 12x + 2 are same- side interior angles and are supplementary, thus

12x + 2 + 70 = 180 , that is

12x + 72 = 180 ( subtract 72 from both sides )

12x = 108 ( divide both sides by 12 )

x = 9 → D

x/12 + 3 < 7 = x<48 this is the only one i can do because i cant do the others sorry

25% off means the new price of the item is 75% of the originl price ( 100% - 25% = 75%)

Multiply the original price by 75%:

20 x 0.75 = 15

The sale price is £15

S.P:25x/100

0.25x=20

x=20/0.25

x=80

The partial fraction decomposition of the integrand for the integral of x² - 2x - 1 / (x - 3)²(x² + 9) dx is of the form: A / (x - 3) + B / (x - 3)² + (Cx + D) / (x² + 9), where A, B, C, and D are constants.

First, factorize the denominator: (x - 3)²(x² + 9). This gives us three distinct linear factors: (x - 3), (x - 3), and (x² + 9).

Write the partial fraction decomposition using the distinct linear factors as denominators. In this case, we have two (x - 3) terms and one (x² + 9) term:

x² - 2x - 1 / (x - 3)²(x² + 9) = A / (x - 3) + B / (x - 3)² + (Cx + D) / (x² + 9).

Multiply both sides of the equation by the common denominator (x - 3)²(x² + 9) to eliminate the denominators.

Simplify the numerators and equate the corresponding coefficients on both sides of the equation.

Solve the resulting system of equations to find the values of A, B, C, and D.

Substitute the values of A, B, C, and D back into the original partial fraction decomposition.

Therefore, the partial fraction decomposition of the integrand for the given integral is: A / (x - 3) + B / (x - 3)² + (Cx + D) / (x² + 9), where A, B, C, and D are constants

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Answer:

Net Profit after tax Rs 15,000

Step-by-step explanation:

The computation of the net profit after tax is shown below:

Gross profit Rs. 1,25,000

Less:

Selling and distribution expenses Rs. 21,000

General and administrative expenses Rs. 75,000

Interest on loan Rs. 5,000

Gain on sale of plant Rs. 4,000

Profit before tax Rs 20,000

Less: income tax expense at 25% of Rs 20,000 Rs 5000

Net Profit after tax Rs 15,000

Answer:

There isn't a graph so this can't be answered

Step-by-step explanation:

In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.

That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.

We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.

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Answer:

symemetric property

Step-by-step explanation:

Yes, a probability distribution is given because the sum of all probabilities is equal to 1, the mean of the random variable is 1.584, the standard deviation of the random variable is 1.422.

It is a statistical concept that describes how much the data deviates from its mean or average value. A small standard deviation indicates that the data points are closely clustered around the mean, while a large standard deviation indicates that the data points are more spread out. The standard deviation is commonly used in many fields, such as finance, engineering, and social sciences, as a way to describe the variability of data. It is often used in conjunction with other statistical measures, such as mean, median, and mode, to better understand the distribution of data.

Yes, a probability distribution is given because the sum of all probabilities is equal to 1.

Mean = Σ(x * P(x))

Mean = (0 * 0.106) + (1 * 0.352) + (2 * 0.394) + (3 * 0.148)

Mean = 0 + 0.352 + 0.788 + 0.444

Mean = 1.584

Therefore, the mean of the random variable is 1.584.

To find the standard deviation, we can use the formula:

SD = √Σ[(x - Mean)² * P(x)]

SD = √[(0 - 1.584)² * 0.106 + (1 - 1.584)² * 0.352 + (2 - 1.584)² * 0.394 + (3 - 1.584)² * 0.148]

SD = √[2.025632]

SD = 1.422

Therefore, the standard deviation of the random variable is 1.422.

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Answer:

2000 percent.

Step-by-step explanation:

First we find the calculation of the equation, this will be equal to 100 percent.

1/8 * 16 = 2

Next we divide 2 by 100, to find how much is 1 percent.

2 / 100 = 0.02

Finally, we divide 40 by 0.02 to find out the total percent it it made up of.

40 / 0.02 = 2000

The final answer is 2000 percent.

this is just a quick additon to "24mhomme" good posting above

\(\cfrac{1}{8}\cdot 16 \implies \cfrac{16}{8}\implies 2 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} Amount&\%\\ \cline{1-2} 2 & 100\\ 40& x \end{array} \implies \cfrac{2}{40}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 1 }{ 20 } ~~=~~ \cfrac{ 100 }{ x }\implies x=\stackrel{ \% }{2000}\)

Answer:

51

Step-by-step explanation:

Divide 170 by 10 you get 17,now that is 10% of 170, and 3 times 10% is 30% 10 3 times 17 equals 51.

Answer: 51

Step-by-step explanation:

turn 30 into a fraction and multiply it by 170, take off the 0 on 170 and it's basically 17 × 3, which is 51

Answer:

184

Step-by-step explanation:

Answer: 184

Step-by-step explanation:

A P E X

Answer:

yes

Step-by-step explanation:

Answer:

No, she did not multiply the x-tiles by the negative integer tiles correctly.

Step-by-step explanation:

Approximately 37 child tickets were sold that day.

Let's assume the number of child tickets sold is represented by 'x'. Since the problem states that four times as many adult tickets were sold as child tickets, the number of adult tickets sold would be 4x.

The cost of each child ticket is $5.50, so the total revenue from child tickets would be 5.50x.

Similarly, the cost of each adult ticket is $9.40, so the total revenue from adult tickets would be 9.40(4x) = 37.60x.

The total revenue from all tickets sold is given as $1594.70, so we can write the equation:

5.50x + 37.60x = 1594.70

Combining like terms:

43.10x = 1594.70

To solve for x, we divide both sides of the equation by 43.10:

x = 1594.70 / 43.10

Calculating the value:

x ≈ 37

Therefore, approximately 37 child tickets were sold that day.

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Answer:

The correct answer is C. (2, 3)

The absolute maximum and minimum values of \(f(x, y) = 4xy^2\) on the set D can be found by analyzing the critical points and the boundary of D. The maximum value is attained at the point (1,0) and the minimum value is attained at the point (-1,0).

To find the absolute maximum and minimum values of f(x,y) = 4xy^2 on the set D, we first need to identify the boundary of D. Since no boundary was given, we assume that D is the entire xy-plane. Next, we find the critical points of f by setting its partial derivatives with respect to x and y equal to zero:

\(fx(x,y) = 4y^2 = 0\)

\(fy(x,y) = 8xy = 0\)

The first equation gives us y = 0, and the second equation gives us x = 0 or y = 0. Therefore, the critical points are (0,0) and (x,0) for any nonzero value of x.

To determine whether these critical points correspond to a maximum, minimum, or saddle point, we use the second partial derivative test. The Hessian matrix of f is

H(x,y) = [0 8y; 8y 0]

At (0,0), the Hessian is indefinite, so this point is a saddle point. At (x,0), the Hessian is negative definite for x < 0 and positive definite for x > 0, so these points are local minima and maxima, respectively. Finally, we need to check the values of f at the critical points and the boundary of D to determine the absolute maximum and minimum values of f. We have f(0,0) = 0, f(x,0) = 0, and f(1,0) = 0. On the boundary of D, we have\(f(x,y) = 4xy^2\), which tends to infinity as |x| or |y| tends to infinity. Therefore, the absolute maximum value of f on D does not exist, but the minimum value is 0 and is attained at (0,0), (x,0) for any nonzero value of x, and (-1,0). The maximum value of f on the set D is attained at (1,0) and is 0.

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Answer:

27/28

Step-by-step explanation:

The unit rate of the beef if it cost $14.40 for 4.5 pounds of beef is $3.2 per pound

The unit rate is the cost of each unit of an item at a particular time.

Cost of 4.5 pounds of beef = $14.40

Unit rate of beef = Total cost / Total pounds

= $14.40 / 4.5

= $3.2 per pound

Check:

Cost of 4.5 pounds of beef = unit cost of beef × pounds of beef

= $3.2 × 4.5

= $14.4

In conclusion, the unit rate of beef is given as $3.2 per pound.

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The amount of money that he will make for 2 hours of baby sitting work is $18

The function is

f(x) = 4x + 10

The function f(x) is the amount of money Francis makes when babysitting for x hours

The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is dependent variable then the other variable will independent variable

The function

f(x) = 4x + 10

The number of hours x = 2 hours

Substitute the values of x in the function

f(2) = 4(2) + 10

f(2) = 8 +10

f(2) = $18

Hence, the amount of money that he will make for 2 hours of baby sitting work is $18

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Answer:

Y x X=Q-T=The slope simple!

Step-by-step explanation:

Answer:

5280 feet=1 mile, so she was traveling 78(5280) feet per hour.

To find the feet per minute divide by 60 to get 78(5280)/60 or 6864 feet per minute.

Pls give me branilest

Approximate percent increase in how much the student pays with Optin 2 versus Option is 20%

$540 plus 15% sales tax now.=$515

Pay exactly $120 now and then $58 each month for 9 months=$642

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