Fill in the missing term on each line. Simplify any fractions.
2p + 4 = 6
2p=______ Subtract 4 from both sides ***
p=_______ Divide both sides from 2***

Using the divergence theorem we can compute that the outward flux of the vector field is 16π .

The outward flux of F over the solid cylinder and z = 0 is

∫∫F·ds  = ∫∫∫ DivF dv

F = 2xy² i   +  2x²y j + 2xy k

Div F  =  D/dx (2xy²)  +   D/dy (2x²y )

Div F  =  2y²  +  2x²

In cylindrical coordinates   dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ

Using the parametric form of the surface equation

x = rcosθ        y =  r sinθ      and z = z

Div F  = 2r² sin²θ  + 2r²cos²θ

∫∫∫ DivF dv  =  ∫∫ [2r²sin²θ  + 2r²cos²θ] × rdrdθ

∫∫ 2r² [sin²θ  + cos²θ] × rdrdθdz   ⇒  ∫∫ 2r³ drdθ

Integration limits

0 < r < 2          0 < θ < 2π

2∫₀² r³ ∫dθ

(2/4) × (2)⁴ × 2π

The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.

In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.

Therefore the flux is 16π .

To know more details about flux visit:

brainly.com/question/16840837

#SPJ4

Answer:

268 units³

Step-by-step explanation:

V = 4/3 (pi)r³

V = 4/3 (3.14) (4³)

V = 4/3 (3.14) (64)

V = 4/3 (200.96)

V = 268

The number of regions created when constructing a Venn diagram with three overlapping sets is 8.

In a Venn diagram, each set is represented by a circle, and the overlapping regions represent the elements that belong to multiple sets.

When three sets overlap, there are different combinations of elements that can be present in each region.

For three sets, the number of regions can be calculated using the formula:

Number of Regions = 2^(Number of Sets)

In this case, since we have three sets, the formula becomes:

Number of Regions = 2^3 = 8

So, when constructing a Venn diagram with three overlapping sets, there will be a total of 8 regions formed.

Each region represents a unique combination of elements belonging to different sets.

These regions help visualize the relationships and intersections between the sets, providing a graphical representation of set theory concepts and aiding in analyzing data that falls into multiple categories.

Therefore, the correct answer is 8.

To know more about Venn diagram refer here :

https://brainly.com/question/318076803

#SPJ11

Answer:

28

Step-by-step explanation:

let the number be n then increased by 20 = n + 20 and

n + 20 = 48 ( subtract 20 from both sides )

n = 28

The correct answer is S = {A, D, D, I, T, I, O, N}.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The sample space is the set of all possible outcomes of an experiment or event.

In this case, the experiment is choosing one card from a set of eight labeled cards.

The sample space for this experiment is the set of all possible cards that can be chosen.

In the given problem, there are eight cards labeled A, D, D, I, T, I, O, N.

The sample space is the set of all possible cards that can be chosen, which is {A, D, D, I, T, I, O, N}.

This is because each card is distinct and can be chosen independently of the others.

Therefore, the correct answer is S = {A, D, D, I, T, I, O, N}.

To know more about probability visit :

https://brainly.com/question/13604758

#SPJ1

Answer: A( A,D, D,I, I,N,O,T)

Step-by-step explanation:

Order does not matter!!

Answer:

Step-by-step explanation:

This is not a triangle at all. You must have typed the angles incorrectly. A triangle's angles have to add up to 180 and yours only add up to 160...

yes they both have the same midpoint of (1,2)

For the midpoint of JK

\((\frac{-2+4}{2}, \frac{1+3}{2} )\)

\((\frac{2}{2}, \frac{4}{2} )\)

(1,2)

then for LN

\((\frac{0+2}{2}, \frac{3+1}{2} )\)

\((\frac{2}{2}, \frac{4}{2} )\)

(1,2)

18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.

19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.

If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.

The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.

The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.

This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.

Learn more about Daily Fluid Requirements (DFR) here:

https://brainly.com/question/28334028

#SPJ4

The Length of CD is 27.875 cm.

We have,

AB=24 cm, BD= 17 cm, AD = 13 cm

and, ACD=90Degrees

Using Pythagoras theorem

AD² = AC² + CD²

13² = AC² + (x-17)²

169 = AC² + x² + 289 - 34x

- x² + 34x - 120 = AC²

AC² = (x-4)(x-30)

Again,

AB² = AC² + CB²

24² = (x-4)(x-30) + x²

576 =  - x² + 34x - 120 + x²

34x = 696

x= 10.875

Thus, the length of CD is

= 10.875 + 17

= 37.875 cm

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ1

We have proven that BC = DE using the Segment addition postulate

The segment addition postulate states that given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC

The reasons for the proof are given below:

Statement                                Reason

BD = BC + CD                          Segment addition postulate

CE = CD + DE                           Segment addition postulate

BD = CE                                    Given

BC + CD = CD + DE                  Substitution property

BC = DE                                   Subtraction property

Hence, we have proven that BC = DE using the Segment addition postulate

Learn more on Segment addition postulate here: https://brainly.com/question/2134445

#SPJ1

Answer:

-29.4

Step-by-step explanation:

(-2.1)(-1.4) - 29.4 - 2.94

2.94 - 29.4 - 2.94

          -29.4

The factor that provides the basis for the grading of newly diagnosed malignant tumours is degree of differentiation.

The level of differentiation impacts an individual's capacity to control their emotions, thoughts, individuality, and connections to others. The degree of any differential equation can be obtained when it is expressed as a polynomial; otherwise, the degree cannot be defined.

The mechanisms by which immature cells develop into mature cells with particular roles are described in biology. This indicates the degree to which tumour tissue resembles the healthy tissue from which it originated in the context of cancer. Compared to poorly or undifferentiated cancer cells, well-differentiated cancer cells resemble normal cells more and grow and spread more slowly. Tumour grading systems, which vary for each form of cancer, use differentiation.

To know more about degree of differentiation, visit:

https://brainly.com/question/28104656

#SPJ4

Answer:

2 and 3.

Step-by-step explanation:

5.5 would be between t and 6, not 2 and 3. Answer is 2 and 3

Answer:

-4 1/26

Step-by-step explanation:

You will want to Reduce the expression, if possible, by cancelling the common factors.

Therefore, the length of each side of the hexagon is 5√2. Hence, the area of the regular hexagon is 150 square units.

Area is a mathematical term that refers to the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters, square feet, or square inches, depending on the system of measurement used. The area of a shape is determined by multiplying its length and width, or by using a specific formula depending on the shape of the object. Knowing the area of an object can be useful in many fields, including architecture, engineering, and mathematics.

Here,

To find the area of the regular hexagon, we need to know the length of its sides. Since the hexagon is regular, all of its sides are congruent. We can find the length of the sides by using the distance formula between two adjacent vertices. Let's find the distance between vertices A and B, which are adjacent vertices of the hexagon:

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(7 - 0)² + (1 - 0)²]

= √(49 + 1)

= √50

= 5√2

To find the area of the hexagon, we can divide it into six equilateral triangles. Each of these triangles has a base of 5√2 and a height of (5√2)/2. The area of one triangle is:

A = (1/2)bh

= (1/2)(5√2)((5√2)/2)

= 25

Therefore, the area of the regular hexagon is:

A = 6A(triangle)

= 6(25)

= 150

To know more about area,

https://brainly.com/question/13194650

#SPJ1

Answer:

B

Step-by-step explanation:

Answer:

9x9x9x9x9x9x9, theres your answer

Answer:

Da Answer Is : 9 × 9 × 9 × 9 × 9 × 9 × 9

The solution to the equation log base 16 x + log base 4 x + log base 2 = 7 is x = 256.

To solve the equation:

log base 16 x + log base 4 x + log base 2 = 7

We can use the properties of logarithms to combine the terms on the left-hand side into a single logarithm.

log base 16 x can be rewritten as log base 2 (x) / log base 2 (16) = log base 2 (x) / 4

log base 4 x can be rewritten as log base 2 (x) / log base 2 (4) = log base 2 (x) / 2

Therefore, the original equation becomes:

log base 2 (x) / 4 + log base 2 (x) / 2 + log base 2 (2) = 7

Simplifying, we get:

log base 2 (x) × (1/4 + 1/2) + 1 = 7

log base 2 (x) × 3/4 + 1 = 7

log base 2 (x) × 3/4 = 6

log base 2 (x) = 8

Now, we can use the definition of logarithms to rewrite the equation as an exponential equation:

\(2^{8}\) = x

x = 256

Therefore, the solution to the equation log base 16 x + log base 4 x + log base 2 = 7 is x = 256.

to know more about the equation:

brainly.com/question/29538993

#SPJ1

396,667.5 is the total of all whole numbers between 1 and 890.

To find the sum of the whole numbers from 1 to 890, we can use the formula for the sum of an arithmetic series:

S = n(a1 + an) / 2

Where S is the sum, n is the number of terms, a1 is the first term, and an is the last term. In this case, n = 890, a1 = 1, and an = 890. Plugging these values into the formula, we get:

S = 890(1 + 890) / 2

S = 890(891) / 2

S = 793335 / 2

S = 396667.5

Therefore, the sum of the whole numbers from 1 to 890 is 396,667.5.

To know more about numbers click on below link :

https://brainly.com/question/29766862#

#SPJ11

Answer:

please somebody also helpp me

Answer:

9-16y

Step-by-step explanation:

9-x^2y when x=4

plus in 4: 9- (4)^2y

=9-16y

The probability that all the numbers rolled are distinct is 0.015.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that suppose six 6-sided dice are rolled. The probability of the numbers rolled are distinct is calculated as,

Probability = 6! / 6⁶

Probability = ( 720 ) / ( 46656)

Probability = 5 / 324

P = 0.015

Therefore, the probability that all the numbers rolled are distinct is 0.015.

To know more about probability follow

https://brainly.com/question/24756209

#SPJ1

Without the individual probability of a passenger showing up, we cannot calculate the exact probability of the number of people who show up exceeding the capacity of the plane

To solve this problem, we need to determine the probability that more than 65 people (the capacity of the plane) will show up from the 70 booked passengers.

Step 1: Identify the relevant information
- Maximum capacity of the plane: 65
- Number of people booked: 70

Step 2: Calculate the probability of each possible outcome
To exceed the capacity, at least 66 passengers must show up. We need to calculate the probability of 66, 67, 68, 69, and 70 passengers showing up. However, we don't have information on the individual probability of a passenger showing up. If we had this information, we could use the binomial probability formula.

Step 3: Express the final answer
Unfortunately, without the individual probability of a passenger showing up, we cannot calculate the exact probability of the number of people who show up exceeding the capacity of the plane. Please provide the probability of a passenger showing up so we can give you an accurate answer.

Learn more about probability here:

https://brainly.com/question/27992840

#SPJ11

Answer:

709

Step-by-step explanation:

473 + 236 = 709

Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

The velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.

To find the velocity of the particle at the first instance it is at the origin, we need to find the value of t when x(t) = 0.

Since the particle is at the origin when x(t) = 0, we have:

\(0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1 = 0\)

Using numerical methods or graphing the equation, we find that the roots are approximately t ≈ -0.618, t ≈ 1.532, t ≈ 3.143, and t ≈ 2.944.

Since t > 0, the first instance the particle is at the origin corresponds to t ≈ 2.944 (the smallest positive real root).

Now, to find the velocity of the particle at this instance, we need to find the derivative of the position function x(t) with respect to time t, which gives us the velocity function v(t):

v(t) = dx/dt

\(v(t) = d/dt (0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1)\\v(t) = 2t^3 - 4.5t^2 - 4t + 6\)

Now, we can find the velocity at t ≈ 2.944:

\(v(t = 2.944) = 2(2.944)^3 - 4.5(2.944)^2 - 4(2.944) + 6\)

v(t ≈ 2.944) ≈ 16.885

So, the velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.

learn more on velocity :

https://brainly.com/question/29290259

#SPJ4

A solution to the equation \(x^2\)=5

a. Using exponents: ±\(\sqrt{5}\)

b. Using radicals:±\(\sqrt{5}\)

a. Using exponents:

We can solve the equation \(x^2\) = 5 by taking the square root of both sides of the equation:

\(x^2\) = 5

Taking the square root of both sides, we get:

\(\sqrt{x^2}\) = \(\sqrt{5}\)

x = +/- \(\sqrt{5}\)

Therefore, the solutions to the equation \(x^2\) = 5 using exponents are x = \(\sqrt{5}\) or x = -\(\sqrt{5}\).

b. Using radicals:

We can also solve the equation \(x^2\) = 5 using radicals. To do this, we take the square root of both sides of the equation:

\(\sqrt{x^2}\) = \(\sqrt{5}\)

Since the square root of \(x^2\) is equal to the absolute value of x, we can write:

|x| = \(\sqrt{5}\)

Therefore, the solutions to the equation \(x^2\) = 5 using radicals are x = \(\sqrt{5}\) or x = -\(\sqrt{5}\).

To learn more about exponents, refer:-

https://brainly.com/question/30066987

#SPJ4

Answer: it is b

Step-by-step explanation:

A sample of 68  is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean for the standard deviation of 40 hours

Since a level =1-0.96/2 =0.02, here the  Z value of 1-a = 1-0.02= 0.98 , for which z=2.055 .Now we know that the formula for margin is:

M = z*σ/√n, where σ is the standard deviation and n is the sample size since we are provided with the standard deviation of  40  and M=10. so,

=> 10= 2.055*40/√n

=>10√n= 2.055*40

=>√n =  82.2/10

=>n=67.6 ,which is almost  68

To know more about standard  deviation refer to the  link brainly.com/question/23907081

#SPJ4