Can somebody pls help me on this

The curl and the divergence of the vector field is illustrated below.

The term vector in math contains both position and magnitude.

Here we need to find the curl and the divergence of the vector field.

While we looking into the given question, we have the function

=> F(x, y, z) = <ex, exy, exyz>

AS per the concept of convergence, here we have consider that F=⟨P,Q,R⟩  is a vector field in  R3  and  Px, Qy,  and  Rz  all exist here then the divergence of F is defined by as,

=> div F = Px + Qy + Rz

=> div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z.

The term curl in vector field is defined as a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space

And the curl of the vector field is calculated as,

=> curl F = (Ry−Qz)i + (Pz−Rx)j + (Qx−Py)k

=> curl F = (∂R/∂y−∂Q/∂z)i + (∂P/∂z−∂R/∂x)j + (∂Q/∂x−∂P/∂y)k.

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The rectangular block has a perimeter of 10 units. The triangle's perimeter is 7.5 units.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area.

Here,

area=6 units

length on scale=5-2

=3 units

3*w=6

w=2 units

perimeter=2*(3+2)

=10 units

length of side of triangle=2.5 units

perimeter=2.5+2.5+2.5

=7.5 units

The perimeter of rectangle block is 10 units. The perimeter of triangle is 7.5 units.

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Answer:

They are not traveling at the same speed (Graph attached)

Step-by-step explanation:

(Assuming that the graph and table are the two different cars)

If you look at the graph and the table, you can already see that the value for 8 in the graph is 2, when the value for 8 in the table is 1, meaning that they are not at the same speed.

To graph the table, you need to find the equation first, which is y = 8x because the corresponding value for 1 in the table is 8 and the slope (or the value next to x) is equal to the unit rate, or the value corresponding to 1. Next, you can graph it by finding two points, (0,0) and (1,8), and putting a straight line through them (or use an online graphing calculator).

(Graph is attached)

Answer:

b=-3

Step-by-step explanation:

hope this helps!

Answer:

x=36°

the sine rule enables us to find missing angles and sides when given an angleand 2 known sides

In a sample of 10,000 observations from a normal population, about 27 would be expected to lie beyond three standard deviations of the mean, therefore, the correct option is b.

For a normal distribution, about 99.7% of the data is expected to lie within three standard deviations of the mean. This is known as the empirical rule or the 68-95-99.7 rule.

Using this rule, we can estimate the number of observations beyond three standard deviations of the mean for a sample of 10,000. Since the distribution is normal, we know that the mean and standard deviation completely describe the distribution.

Assuming the sample is representative of the population, we can use the empirical rule to estimate the number of observations beyond three standard deviations of the mean. Since three standard deviations from the mean cover 99.7% of the data, the remaining 0.3% of the data would be expected to lie beyond three standard deviations.

Therefore, the correct answer is c. about 27, since 0.3% of 10,000 is approximately 27.

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Answer: Check below

Step-by-step explanation:

Okay so the Pythagorean Theorem was made by some old guy and the formula is a^2+b^2=c^2. You ALWAYS have to subtract the leg of the triangle when your finding a leg. You squareroot the square of the two legs if your finding the hypotnuse. The Theorem can be used to find any side of the triangle ONLY IF its a right triangle. An adult might use it in real life like when your an architect trying to find how much material you should use to make something thats in the shape of a right triangle.

Ps. Sorry if there's a bunch of grammar mistakes since this is kinda rushed

Answers:

==================================================

Explanation:

Part a)

If we ignore the $39 rental fee, then it costs 0.75x dollars to drive x miles. However, we cannot ignore that fee which means we tack it on to get 0.75x+39 to represent the total cost.

Therefore, y = 0.75x+39 is the cost function

If your teacher insists you use other variables (instead of x and y), then be sure to follow those instructions.

------------------

Part b)

Plug in x = 200 to find y

y = 0.75x+39

y = 0.75*200+39

y = 189 dollars is the total cost

Answer:

b. two solutions

Step-by-step explanation:

Answer:

Two Solutions.

Step-by-step explanation:

12(x - t)

if x = 7 and t = 2

12(x - t) = 12(7 - 2) = 12 * 5 = 60

Answer:

60

Answer:

(a) \(4\frac{1}{5}\)

(b)  \(7\frac{7}{24}\)

Step-by-step explanation:

One way of operating with mixed numbers is to first convert them into improper fractions, and operate with them following the simple rules of fraction multiplication, and at the end convert the answer into mixed number.

(a) For this operation let's first convert \(5\,\frac{2}{5}\) into an improper fraction:

\(5\frac{2}{5} =5+\frac{2}{5} =\frac{25}{5} +\frac{2}{5} =\frac{27}{5}\)

Now perform the requested operation:

\(\frac{7}{9} \,*\,\frac{27}{5} =\frac{189}{45} =\frac{21}{5} =4\frac{1}{5}\)

(b) Start by converting both mixed numbers into improper fractions and then operate as indicated:

\(1\frac{3}{4} =\frac{4+3}{4} =\frac{7}{4} \\4\frac{1}{6} =\frac{24+1}{6} =\frac{25}{6}\)

\(\frac{7}{4} *\frac{25}{6} =\frac{175}{24} =7\frac{7}{24}\)

Division is the antithesis of multiplication. When you divide twelve into three equal groups, you get four in each group when you multiply three groups of four to create twelve.

The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups. The basic objective of splitting is to determine how many equal groups are created or how many people are in each group after a fair distribution.

The phrase to use is "divide in half," not "divide by half," when discussing splitting something into two equal portions. In mathematics, multiplying by two is equivalent to dividing by half. Additionally, see "multiply by two."

The French term "douzaine," which denotes a group of 12, is where the word "dozen" originates.

2 dozen apples equals 24, and 24 divided by 8 is 3.

Therefore, the answer is 3.

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Answer:

x-18°+24°=180°[co interior angle]

x+6°=180°

x=180°-6°

x=174°

answer

Answer:

x = 2

Step-by-step explanation:

4 x + (negative 4) = negative 2 x + 8

4x + (-4) = - 2x + 8

4x - 4 = - 2x + 8

4x + 2x = 8 + 4

6x = 12

\(x = \frac{12}{6} \\ \\ x = 2\)

Answer:

C. x = 2

Step-by-step explanation:

On edge

Answer:

The answer is 1

Step-by-step explanation:

Remember PEMDAS,  1+2 is 3. 2x3 is 6, then 6 divided by 6 is 1.

Answer:

1

Step-by-step explanation:

6 / 2(1 + 2)

6 / 2(3)

6 / 6 = 1

Part a

we have the function

R=-0.1x^3+11x62-100x

using a graphing tool

Part b

we have that

The value of x cannot be a negative number

The value of R can be a negative number

therefore

part c

the answer part c is the option A and C

Answer:

28,028 in3

Step-by-step explanation:

Given:

Cost of an item with VAT = Rs 1,356

Cost of that item without VAT = Rs 1,200.

To find:

The VAT.

Solution:

We have,

Cost of an item with VAT = Rs 1,356

Cost of that item without VAT = Rs 1,200.

We know that,

VAT = Cost of an item with VAT - Cost of that item without VAT

       = 1356 - 1200

       = 156

Therefore, the value of VAT is $156.

The inequality \(x^2 - 2 \leq 4x + 10\) is satisfied when x is in the interval (-∞, -2] or [6, +∞).

To solve the inequality \(x^2 - 2 \leq 4x + 10,\)  we can rearrange it to bring all terms to one side of the inequality sign:

\(x^2 - 4x - 12 \leq 0\)

Next, we can factorize the quadratic equation:

(x - 6)(x + 2) ≤ 0

Now, we can find the critical points by setting each factor equal to zero:

x - 6 = 0 --> x = 6

x + 2 = 0 --> x = -2

The critical points divide the number line into three intervals: (-∞, -2), (-2, 6), and (6, +∞).

To determine the sign of the expression (x - 6)(x + 2) in each interval, we can choose a test point within each interval and substitute it into the expression:

For x = -3: (-3 - 6)(-3 + 2) = (-9)(-1) = 9 > 0

For x = 0: (0 - 6)(0 + 2) = (-6)(2) = -12 < 0

For x = 7: (7 - 6)(7 + 2) = (1)(9) = 9 > 0

From this, we can determine the solution to the inequality:

(-∞, -2] U [6, +∞)

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Answer:

$31.80

Step-by-step explanation:

The ball will cost 100% of its price plus 6% of its price for a total of 106%.

To use percentages as a factor and multiply, they must be divide by 100, making the multiplication factor version of 106% 1.06.

Multiply the cost of the ball by your multiplication factor:

30 x 1.06 = 31.8

Money is written to two decimal places, making your answer $31.80

Answer:

$31.80

Step-by-step explanation:

First, find how much the sales tax is

$30 × 6%

Convert the percentage into a decimal

30 × 0.06

1.8

$1.80

Add the sales tax to the original cost

$30 + $1.80

$31.80

Answer:

x = -16

Step-by-step explanation:

52= 1/2x+15−3.25x−7

Combine 1/2x and −3.25x to get −11/4 x.

52= −11/4x+15−7

Subtract 7 from 15 to get 8.

52=−11/4x+8

Swap sides so that all variable terms are on the left hand side.− 11/4x+8=52

Subtract 8 from both sides.

− 11/4x=52−8

Subtract 8 from 52 to get 44.

−11/4 x=44

Multiply both sides by − 4/11

​ the reciprocal of − 11/4

​x=44(−4/11)

​Express 44(−4/11 ) as a single fraction.

x= 44(−4)

​Multiply 44 and −4 to get −176.

x= −176/11

​Divide −176 by 11 to get −16.

According to Pythagorean theorem, the length of BE is 2√(61) units.

To solve this problem, we need to use the Pythagorean Theorem, which tells us that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we can see that triangle ABE is a right triangle, with AB as the hypotenuse and BE and AE as the other two sides. Therefore, we can use the Pythagorean Theorem to find the length of BE.

To do this, we first need to find the length of AE. Since triangle ADE is a right triangle with a hypotenuse of length 4 and one leg of length 2, we can use the Pythagorean Theorem to find the length of the other leg, which is AE. Specifically, we have:

AE² + 2² = 4² AE² + 4 = 16 AE² = 12 AE = √(12) = 2√(3)

Now we can use the Pythagorean Theorem again to find the length of BE. Specifically, we have:

BE² + (2√(3))² = AB² BE² + 12 = (2AB)²

[since AB = AC = CD = DE = 4]

BE² + 12 = 16² BE² + 12 = 256 BE² = 244 BE = √(244) = 2√(61)

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Answer:

D. 6x + 3

Step-by-step explanation:

A perimeter is just the sum of all sides of a shape.

First, write an equation to add all sides of the triangle:

(x + 4) + (3x - 2) + (2x + 1)

What is inside the parentheses is all already simplified. Also, it is addition, so the order in which we add does not matter. So, we can now get rid of the parentheses and combine like terms:

x + 3x + 2x + 4 -2 + 1

6x + 3

And that's our final answer: 6x + 3

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Answer:

The car is going at 8.125 m/s²

Step-by-step explanation:

Answer:

2.26m/s^2

Step-by-step explanation:

65km/hr = 18.05m/s

\(a = \frac{v - u}{t} \)

v = 18.05m/s

u = 0 m/s

t = 8s

\(a = \frac{18.05 - 0}{8} \)

\(a = \frac{18.05}{8} \)

a = 2.26m/s^2

Answer:

the answer is A

Step-by-step explanation:

Answer:

9.42

Step-by-step explanation:

Breaking the phrase down:

'Nine' would be the number 9 in the ones place.

'And' represents the decimal in a number. ('.')

'Forty-Two Hundredths" is 0.42.

So, "nine and forty-two hundredths" would be 9.42.

Hope this helps.

The dimensions of the rectangle will be 4 and 6.

From the information given, we are told that the area is given by x² + 2x - 24. We will expand this as follows:

x² + 2x - 24

x² + 6x - 4x - 24

x(x + 6) + 6(x - 4)

x - 4 = 0

x = 0 + 4

Therefore, the other dimension will be:

= 24/4

= 6

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An interval variable is one that has numerical values and still makes sense when you average the data values. This type of variable is used in statistics and data analysis to measure continuous data, such as temperature, time, or weight.

Interval variables are based on a scale that has equal distances between each value, meaning that the difference between any two values is consistent throughout the scale.

Interval variables can be used to create meaningful averages or means. The arithmetic mean is a common method used to calculate the average of interval variables. For example, if a researcher is studying the temperature of a city over a month, they can use interval variables to represent the temperature readings. By averaging the temperature readings, the researcher can calculate the mean temperature for the month.

In summary, interval variables are essential in statistics and data analysis because they can be used to measure continuous data and create meaningful averages. They are based on a scale with equal distances between each value and are commonly used in research studies.

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