A) Consider the vector field
F(x,y,z) = (-8yz, -7xz, -xy).
Find the divergence and curl of
B) Consider the vector field
F(x,y,z) = (5x^2, 9(x+y)^2, -3(x+y+z)^2).
Find the divergence and curl of

Answer:

512

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

1)  \(2^{3} * \frac{4^{3} }{5^{0}}\)

2)  \(8 * \frac{4^{3} }{5^{0}}\)

3)  \(8 * \frac{64 }{1}\)

4)  \(\frac{512 }{1}\)

5)  \(512\)  

∫∫∫e f(x, y, z) dV can be expressed as ∫∫∫e f(x, y, z) dz dy dx for the given solid e bounded by y = 4 - \(x^{2}\) \(z^{2}\) and y = 0.

To express the integral as an iterated integral, we consider the order of integration. In this case, we start with the innermost integral, which integrates with respect to z. The limits of integration for z are determined by the bounds of the solid e, which are given by the surfaces y = 0 and y = 4 - \(x^{2}\) \(z^{2}\)

Next, we move to the middle integral, integrating with respect to y. The limits of integration for y are determined by the intersection points of the surfaces y = 0 and y = 4 - \(x^{2}\) \(z^{2}\). In this case, y ranges from 0 to the value of y determined by the equation 4 - \(x^{2}\) \(z^{2}\) = 0.

Finally, we integrate with respect to x, where the limits of integration for x are determined by the bounds of the solid e. These bounds can be determined by finding the values of x that satisfy the equation 4 - \(x^{2}\) \(z^{2}\) = 0.

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4 9/10

explanation:

1: Simplify both sides of the equation.

x+−2/5=9/2

2: Add 2/5 to both sides.

x+−2/5+2/5=9/2+2/5

x=4 9/10

Answer:

3 units

Step-by-step explanation:

DC = \(\frac{1}{3}\) EC

5x - 9 = 6 ⇒ x = 3 units

The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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Answer:

36

Step-by-step explanation:

4/9 x = 16

9/4 * 4/9 x = 16 * 9/4

x = 36

Answer:

1 , 2

Step-by-step explanation:

Since 0.506 is a decimal, any whole number would be greater.

Answer:

y= -4/3x

Step-by-step explanation:

hope this helps :)

Answer:

100% increase

Step-by-step explanation:

The equation is, as we see (120-60)/60=x/100. If we multiply the whole equation by 100, we get (120-60)/60*100=x. We simplify to get a 100% increase.

An equation for this line in the point-slope form will be y-7 = -2(x + 4).

What is the Point-slope form?

The equation of the straight line has its slope and given point. If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation. Point-slope is a specific form of linear equations in two variables:

y - y₁ = m(x - x₁)

Which is the required equation of a line in a point-slope form.

We need to find the equation of the line that passes through (-4, 7) and whose slope is -2.

Well, we will simply plug m = -2, x₁= -4, and y₁  = 7 into point-slope form.

y-y₁ = m(x-x₁)

Now substitute;

y-7 = -2(x - (-4))

y-7 = -2(x + 4)

Therefore, an equation for this line in the point-slope form will be y-7 = -2(x + 4).

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The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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Answer: True

Step-by-step explanation: because bias can lead to personal errors

The measure of angle ∠4 is 115°, we can conclude that the measure of corresponding angle ∠2 is also 115°.

Corresponding angles are formed when a transversal intersects two parallel lines. In the given figure, if the lines on either side of the transversal are parallel, then angle ∠4 and angle ∠2 are corresponding angles.

The key property of corresponding angles is that they have equal measures. In other words, if the measure of angle ∠4 is 115°, then the measure of corresponding angle ∠2 will also be 115°. This is because corresponding angles are "matching" angles that are formed at the same position when a transversal intersects parallel lines.

Therefore, in the given figure, if the measure of angle ∠4 is 115°, we can conclude that the measure of corresponding angle ∠2 is also 115°.

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Answer:

x = 5

Step-by-step explanation:

4x + 8 - 9x = -17

combine like terms:

-5x = -25

divide both sides of the equation by -5:

x = 5

Answer:

x=5

Step-by-step explanation:

4x-9x+8=-17

-5x+8=-17

subtract 8 from both sides and you get:

-5x=25

divide 5 from both sides, and you get x=5! :)

Answer:

\( - 26 \sqrt{3} \)

I'm sure about the answer.

The correct answer is a. The mean of the sampling distribution is always equal to the population mean.

This is known as the central limit theorem, which states that as the sample size increases, the sampling distribution will approach a normal distribution with a mean equal to the population mean. However, the standard deviation of the sampling distribution (option b) is not always equal to the population standard deviation and the shape of the sampling distribution (option c) is not always approximately normal, as it depends on the sample size and the underlying population distribution. Therefore, option d is incorrect. The correct is (a). The mean of the sampling distribution is always equal to the population mean. This is due to the fact that a sampling distribution is created by taking multiple random samples from the population, and as the number of samples increases, their mean tends to converge to the population mean. Options (b) and (c) are not always true, as the standard deviation and shape of the sampling distribution depend on the sample size and the underlying population distribution.

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The range of the assumed equation of the absolute value function is -∞ < y ≤ 7

The question is incomplete, so I will provide a general explanation

Assume that the absolute value function is given as:

f(x) = |x + 1| + 7

Set the absolute value to 0

f(x) ≥ 0 + 7

Evaluate

f(x) ≥ 7

This means that the smallest value of the function is 7

Hence, the range of the absolute value function is -∞ < y ≤ 7

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The value of angle z in the figure is 137 degrees.

The sum of angles on a straight line equals 180 degrees.

The supplemetary angles are defined as the angles having the summation of 180 degrees.

The angles made by the straight lines are termed supplemetary angles.

From the diagram;

Angle 43 degree and angle z are on a straight line.

Meaning the two angles are supplemetary angles.

Hence, the sum of angle 43 and angle z gives 180 degrees.

43 + z = 180

Subtract 43 deom both sides

43 - 43 + z = 180 - 43

z = 180 - 43

z = 137 degrees.

Therefore, angles z measures 137 degrees,

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Liam has 34 silver coins and 18 gold coins in his collection of 52 coins. He has 16 more gold coins than silver coins.

Let's assume that Liam has x silver coins in his collection. According to the given information, Liam has 16 more gold coins than silver coins. Therefore, the number of gold coins he has would be x + 16.

The total number of coins Liam has is given as 52. So, we can write the equation:

x + (x + 16) = 52

Simplifying the equation, we get:

2x + 16 = 52

Subtracting 16 from both sides, we have:

2x = 36

Dividing both sides by 2, we find:

x = 18

Hence, Liam has 18 silver coins. Since he has 16 more gold coins than silver coins, he has 18 + 16 = 34 gold coins.

Therefore, Liam has a collection of 34 gold coins and 18 silver coins, totaling 52 coins in all.

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The equation that has a vertex at (3, -2) and a directrix of y = 0 is:

y + 2 = -1/8(x - 3)^2

The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

In this case, the given vertex is (3, -2), so we have h = 3 and k = -2. Plugging these values into the vertex form, we get:

y = a(x - 3)^2 - 2

Since the directrix is y = 0, we know that the parabola opens downward. Therefore, the coefficient 'a' must be negative.

Hence, the equation that satisfies these conditions is:

y + 2 = -1/8(x - 3)^2

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When a swimming coach needs to choose a team for a relay race then the number of ways they can arrange 444 of the 666 swimmers is 3.53×\(10^{1735}\)

There are a total of 444\(C_{444}\) (or 6.64 x \(10^{847}\)) ways to select 444 swimmers from the pool of 666.

Once the swimmers have been chosen, they need to be arranged in a strategic sequence.

This can be done in 444! (or 5.34 x \(10^{906}\)) ways.

Therefore, the total number of unique ways to arrange 444 of the 666 swimmers is

6.64 x \(10^{847}\) x 5.34 x \(10^{906}\)

3.53 x \(10^{1735}\)

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The missing angle represented by 6 is 107 degrees

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that, when combined, create a straight line, then they are supplementary angles.

Angles on a straight line are supplementary and hence the potion that has 6 is equal to say x

x + 73 = 180

x = 180 - 73

x = 107 degrees

Supplementary angles can be found in many geometric shapes, such as triangles, quadrilaterals, and polygons.

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Answer:

See below.

Step-by-step explanation:

The volume of the box is given by the expression.

V(x) = x^3 - 2x^2 - 15x

To find the possible dimensions of the box, we need to solve for the values of x that make the volume positive. A box with negative volume is not physically meaningful.

Setting V(x) > 0, we get.

x^3 - 2x^2 - 15x > 0

Factorizing the left-hand side, we get.

x(x^2 - 2x - 15) > 0

Now, we can find the values of x that make each factor positive.

For x > 0, both factors are positive.

For x^2 - 2x - 15 > 0, we can factor it as (x - 5)(x + 3) > 0. This inequality is true when x < -3 or x > 5.

Therefore, the possible dimensions of the box are.

x > 0 and x < -3, or

x > 0 and x > 5.

However, we need to remember that the dimensions of a physical box must be positive. Therefore, the only valid solution is,

x > 0 and x > 5.

So the possible dimensions of the box are.

Length, width, and height > 5 units.

Answer:

Factor the polynomial.

x

(

x

−

5

)

(

x

+

3

Step-by-step explanation:

Answer:

180 lb for an adult

Answer:

180 lb.

Step-by-step explanation:

This is due to the fact that 1.5 tons is literally 3,000 pounds and someone would have to be morbidly obese to weigh that much, 50 lbs. is underweight for an adult, 160 oz is 10 lbs which is even more underweight, which leaves 180 lbs as the last resort as well as the one that makes the most sense.

Brainliest please

The reason behind the statement m∠TRS + m∠TRV = 180° is; Angle Addition Postulate

Angle addition postulate states that if D is the interior of ∠ABC, therefore, the sum of the smaller angles equals the sum of the larger angle, which from the attached image is;

m∠ABD + m∠DBC = m∠ABC.

From the attached image, we want to prove that x = 30°.

Now, T is the interior of straight angle ∠VRS.

m∠VRS = 180° (straight line angle)

Thus, from angle addition postulate, we can say that;

m∠TRS + m∠TRV = 180°.

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Answer:

angle addition postulate

Step-by-step explanation:

The answer above is correct.

Answer:

\(\frac{1}{10} * 0.5 = 0.05\)

Step-by-step explanation:

The problem asks "what is the value of _____ of _______"

Step 1: Know The word "of" means to multiply.

So you just need to multiply the first number by the second number.

Example:

The value of 1/6 of 4 is 1/6 * 4 = 2/3.

Answer: if you meant: 125, 729, 225, 512.

The answer is 225

Step-by-step explanation:

\(\sqrt[3]{125}\) = 5

\(\sqrt[3]{729}\) = 9

\(\sqrt[3]{512}\) = 8

\(\sqrt[3]{225}\) = 6.08220199557

The probability distribution for bn is:

n | P(bn)

1 | 1/6

2 | (5/6)(1/6)

3 | (5/6)^2(1/6)

4 | (5/6)^3*(1/6)

... | ...

k | (5/6)^(k-1)*(1/6)

... | ...

where k can be any positive integer. Note that this is a geometric distribution with p=1/6.

The sample space for this experiment consists of the sequence of rolls required to obtain the first 6. For example, if a 6 appears on the first roll, then the sample space consists of the single element {6}. If a 6 does not appear on the first roll, then the sample space consists of all possible sequences of rolls that do not include a 6 until the final roll, which is a 6.

More formally, we can represent the sample space as follows:

S = {6, (not 6)(6), (not 6)(not 6)(6), (not 6)(not 6)(not 6)(6), ...}

where (not 6) represents any roll that is not a 6, and each element of the sample space consists of a sequence of (not 6) rolls followed by a 6.

Now, let bn denote the event that n rolls are required to complete the experiment, i.e., the experiment ends with a 6 on the nth roll. The probability of success on any roll is 1/6, and the probability of failure (i.e., rolling a number other than 6) is 5/6. Therefore, the probability of requiring exactly n rolls to obtain the first 6 is:

P(bn) = (5/6)^(n-1) * (1/6)

This is because we must roll a non-6 number on the first n-1 rolls (with probability 5/6 for each roll), and then roll a 6 on the nth roll (with probability 1/6).

Therefore, the probability distribution for bn is:

n | P(bn)

1 | 1/6

2 | (5/6)(1/6)

3 | (5/6)^2(1/6)

4 | (5/6)^3*(1/6)

... | ...

k | (5/6)^(k-1)*(1/6)

... | ...

where k can be any positive integer. Note that this is a geometric distribution with p=1/6.

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