please help with #2 and #3

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 .

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The constant of proportionality in this proportional relationship is (D) 5/12.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.

Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

So, the constant of proportionality formula:

y = kx ⇒ k = y/x

Now, calculate as follows:

(A)

k  = y/x

k = 5/6 / 2

k = 5/6 * 1/5

k = 5/12

(B)

k  = y/x

k = 5/3 / 4

k = 5/3 * 1/4

k = 5/12

Similarly, we can say that (C) and (D) will also be k = 5/12.

Therefore, the constant of proportionality in this proportional relationship is (D) 5/12.

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Complete question:
What is the constant of proportionality in this proportional relationship?

x 2 4 6 8

y 5/6 1 2/3 2 1/2 3 1/3

Responses

a. 12

b. 5

c. 12/5

d.5/12

The approximate number of price increases needed to maximize profit is 2.5

From the question, we have the following parameters that can be used in our computation:

x = number of price increases

y = Profit

Also from the question, we have

Begins at (0, 50)

Increases to (2.5, 81.25)

Decrease through (6.531, 0)

This means that

Maximum = (2.5, 81.25)

Recall that

x = number of price increases

So, we have

x = 2.5

Hence, the number of price increases is 2.5

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Answer:42/5.

21*8=168

4*5=20

168 divided by 20 is 8.4 which is 42/5

Emma and Ryan both have 125/32 pizzas.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given, Emma has [tex]3\frac{1}{8}[/tex]  slices of pizza.

Simplifying to improper fraction;

Emma has 25/8 slices of pizza.

And Ryan has 1/4 x The amount of pizza Emma has, slices of pizza.

That means, Ryan has 1/4 x (25/8) slices of pizza.

Applying multiplication of fraction.

That is, 25/32 slices of pizza.

To find the total amount of pizza;

add the number of pizza,

25/8 + 25/32

To add the number:

First, we take LCM,

25/8 + 25/32

= (100+ 25) / 32

= 125/32

Therefore, they both have 125/32 pizzas.

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The standard size of the rectangle's area is x² + 12x + 35

Given:

a diagram that depicts the polynomial that denotes a rectangle's length and width.

The rectangle's area is equal to its length x width.

Given that length is equal to x + 7 and width is equal to x + 5, the area is equal to length plus width.

Add the numbers in brackets: Area = x2 + 5x + 7x + 35

Area = x2 + 12x + 35

A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. We are surrounded by numerous rectangular objects. The length and width of a rectangular shape are the two dimensions that define it. The rectangle's length and width are its longer and shorter sides, respectively. We will learn about the properties of the rectangle shape in this chapter.

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Full Question = Express the area of the entire rectangle.

Your answer should be a polynomial in standard form.

x+7 x+5

The zeros of the function, along with their multiplicities and effects, are given as follows:

The zeros of the function are given by the zeros of the linear factors.

The linear factors are given as follows:

Then the zeros are given as follows:

Then the multiplicities are given by the exponents, and the effects are defined according to the multiplicities, as follows:

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Answer: B they are parallel

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Lines that are both perpendicular to a given line are parallel.

p = 9

see explanation in image

using law of sines

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Length of p to the nearest 10th of an inch is 8.9 inches.

Sines law of a triangle defines that the ratio of the side lengths of a triangle to the sine of the opposite angles to the side lengths are equal.

a / sin A = b / sin B = c / sin C

where a, b and c are the sides opposite to A, B and C respectively.

Given is a triangle ΔPQR.

Given, ∠Q = 37° and ∠R = 12°.

Sum of the interior angles of a triangle is 180°.

∠P = 180° - (37° + 12°)

     = 131°

Using the sine law,

p / sin P = q / sin Q

p / sin (131°) = 7.1 / sin (37°)

p = (7.1 / sin (37°)) × (sin (131°))

  = 8.9 inches

Hence the length of p is 8.9 inches.

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The point is located (d) outside the target in relation to the target

From the question, we have the following parameters that can be used in our computation:

This means that we substitute (-1,-6) for x and y in the circle equation = (x + 5)² + (y + 5)² = 16.

So, we have the following representation

(x + 5)² + (y + 5)² = 16.

Substitute the known values in the above equation, so, we have the following representation

(-1 + 5)² + (-6 + 5)² = 16.

Evaluate the sum

(4)² + (-1)² = 16.

Evaluate the exponent

16 + 1 = 16.

Evaluate the sum

17 = 16

17 is greater than 16

Hence, the point is not in the target

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The equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 5xy is [tex]e^{\frac{5x^2}{2} }[/tex] .

The slope of the curve is 5xy.

Therefore:

dy/dx =  5xy

dy/y = (5x)dx

Then,

The integrate both sides giving us

ln(y) = (15x²)/2 + C

Since, the curve passes through (0,1) .

Therefore, x=0 and y=1 for solving 2

ln(1) = 0/2 + C

0 = 0 + C

⇒ C = 0

We now,

substitute C back in and isolate y

ln(y) = (15x²)/2

⇒ y = e(15x²) / 2

Therefore, The answer is y = [tex]e^{\frac{5x^2}{2} }[/tex]

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The steps of the perpendicular bisector construction in order from 1 to 4 are;

1) Open the compass

2) Draw arcs above and below the segment to be bisected

3) Draw arcs from the other endpoint of the segment to be bisected

4) Join the intersection of the arcs with a line

A perpendicular bisector is a line, that is perpendicular to another line, and which divides the other line into two congruent segments.

The steps of a perpendicular bisector construction includes;

1) Opening the compass to a radius that is more than half the length of the segment to be bisected

2) With the radius of the compass opening in step 1, place the compass at one endpoint of the segment to be bisected and draw arcs above and below the the segment to be bisected

3) With the same radius of the compass from step 1, place the compass at the other endpoint and draw arcs above and below the segment to be bisected to intersect the arcs drawn in step 2

4) With a straightedge, draw a straight line joining the point of intersection of the arcs in step 3. The line is the perpendicular bisector of the segment.

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Triangles can be proven congruent by using the congruency theorems - SSS, SAS, ASA, and AAS.

Congruency is shown by the sign (≅). It is when the given figures have the same shape and size.  

To prove that the given triangles are congruent there are some rules, one of which it must satisfy in order to prove its congruency. The theorems are stated below-

SSS rule: if 3 sides of the given triangles are equal, then the triangles are congruent.

SAS rule: if 2 sides and an angle of the given triangles are equal, then the triangles are congruent.

ASA rule: if 2 angles and a side (in the middle of the angles)of the given triangles are equal, then the triangles are congruent.

AAS rule: if 2 angles and a side(adjacent to the angles) of the given triangles are equal, then the triangles are congruent.

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Answer:

it is 9

Step-by-step explanation:

The formula of an equation is a mathematical expression that is used to represent the relationship between two or more variables

It is written in the form of a mathematical statement that expresses the relations between the variables. The equation is written using symbols such as +, -, =, and other mathematical operators to denote the relationships between the variables. The equation can be used to solve problems and to find unknown values. By using the equation, it is possible to determine the values of the unknowns given the values of the knowns. for an example such as x+2=4.

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The examples of functions in real life situation is given below .

In the question,

we have to give few examples for functions in real life .

the term Function is defined as as a relationship between two variables where for every input variable there is one output variable.

the examples are :

Example 1 :

Suppose that a car is driving at a constant speed of 30 mph.

the total distance "d" is equal to the rate, 30 times the time "t" ,that we drive for . the function for the relationship between our distance, d, and the time for driving is

d = f(t) =30 × t  .

Example 2:

Suppose that the cost for 1 bag is $9 , then the function for the cost of "x" bags can be written as

Cost = f(x) = 9x .

Therefore , the real life situations examples are shown above.

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The rate the level in the tank falling when the height of the syrup level is 3 feet is 8/π feet per minute. The result is obtained by using the rate of change concept.

A conical tank containing syrup is draining.

Find the rate of syrup level falling (dh/dt) when h = 3 ft!

See the picture in the attachment!

By the similar triangles, we get

r/h = 2/6

r/h = 1/3

r = 1/3 h

Find the volume of the syrup left at a certain height.

V = 1/3 πr²h

V = 1/3 π(1/3 h)²h

V = 1/3 π(1/9) h² h

V = 1/27 πh³

The rate of syrup level falling is

dV/dt = dV/dh . dh/dt

dV/dt = d/dt [1/27 πh³] . dh/dt

dV/dt = 1/27 π 3h² dh/dt

8 = 1/27 π 3(3)² dh/dt

8 =  π dh/dt

dh/dt = 8/π ft/min

Hence, the rate of syrup level falling is 8/π feet per minute.

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Answer:

(-4,-7)

Step-by-step explanation:

Multiply both sides of the first equation by-5 or 2 (I'll use 5) and both sides of the second equation by - 2 or 3 (I'll use -2).

3x - 2y = 2

5(3x-2y)= 5(2)

-15x - 10y = 10

2x - 5y = 27

-2(2x - 5y) = -2(27)

-4x + 10y = -54

Now you see that the absolute values of the y-values of the 2 equations match up . They are still the same equations but scaled up.

-15x + 10y = 10

-4x - 10y = -54

Add to eliminate y.

-11x = 44

Divide both sides by -11.

[tex]\frac{-11x}{-11} = \frac{44}{-11}[/tex]

x = -4

Plug back in to either equation to solve. I'll use the first equation.

3x - 2y = 2

x = - 4

3(-4) - 2y = 2

-12 - 2y = 2

Add 12 on both sides.

-12 + 12 - 2y = 2 + 12

- 2y = 14

Divide -2y on both sides.

[tex]\frac{-2y}{-2} = \frac{14}{-2}[/tex]

y = -7

(-4,-7)

Answer:

175 yards

Step-by-step explanation:

70/2 = 35

35 x 5 = 175

Answer:

Step-by-step explanation:

urmom

y=-3/4x-9/2 is the equation of a line that goes through both transformed points.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

we must translate the given point (x,y) into the translation given. We begin with the 90 degree clockwise rotation such that

90 degree clockwise rotation = (x, y) => (y, -x)

we translate the coordinate (y, -x)

2 units to the right such that

(y-4, -x - 2)

So the coordinate of points changed (1,2) and (-4,6) from (-2, -3) and (2, -6)

m=-6-(-3)/2-(-2)

m=-3/4

Now let us find the y intercept.

-3=-3/4(-2)+b

-3=3/2+b

-3-3/2=b

-9/2=b

Hence, y=-3/4x-9/2 is the equation of a line that goes through both transformed points.

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The dimensions of the rectangular( length and width) are 14m and 15m.

Here we have to find the dimension of the length and width.

Data given:

Fencing = 58m

Area = 210 m²

Let us assume the length be x

By this, we get the width as:

width = 58 - 2x / 2

         = 29-x

As the area is 210 m²

The formula to find the area of the rectangular is:

Area = length ×width

210 = x ( 29 -x)

x² - 29 x + 210 = 0

Formula to find the value of x from the quadratic equation:

x = -b ±[tex]\sqrt{b^{2} - 4ac }[/tex]

For the general equation ax² + bx + c =0

As the equation is:

x² - 29x + 210 = 0

a = -1

b = -29

c = -210

So,

x = 29 ±[tex]\sqrt{(29)^{2} - 4(-1)(-210) }[/tex] / 2(-1)

  = 29± 1/-2

  = 14, 15

29 - x = 15, 14 (for the value of x = 14 and 15 respectively)

Therefore the dimensions are 14m and 15m.

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The easiest way to solve 4 linear equations is to use the substitution method. This involves substituting the values of one equation into the other equations until you are left with a single equation that can be solved for the remaining variable.

if you have the following four linear equations:

A + B = 10

A - B = 2

A + C = 12

A - C = 3

You can substitute A = 10 - B into the third and fourth equations to get:

10 - B + C = 12

10 - B - C = 3

Then you can add the two equations together and solve for C:

2B + 2C = 15

2C = 15 - 2B

C = (15 - 2B) / 2

Once you have C, you can substitute it into one of the other equations to solve for B:

A + B = 10

A = 10 - C

B = 10 - (15 - 2B) / 2

B = 5 - (15 - 2B) / 2

2B = 10 - 15

2B = -5

B = -2.5

Now you have both B

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Answer:

31.992 dollars

Step-by-step explanation:

39.99 times 80%

=31.992

The Total Square Footage of the House is 780 sq. ft.

What is Area?

The quantity area indicates the extent of a region on a planar or curved surface. 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.

Solution:

Area of Living Room = 20*15 = 300 sq. ft.

Area of Kitchen = 12*10 = 120 sq. ft.

Area of Bedroom 1 = 12*12 = 144 sq. ft.

Area of Bedroom 2 = 12*10 = 120 sq. ft.

Area of Bathroom = 8*12 = 96 sq. ft.

Total Area is 300 + 120 + 144 + 120 + 96 = 780 sq. ft.

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If the radius of the base of a cone is decreasing at rate of 2 cm/minute and the height is kept constant at 9 cm, the rate of change of the volume at radius 13 cm is 489.4 cm³/minute

To calculate the rate of change, we need to take the derivative of the variables with respect to time.

The volume of a cone is given by:

V = 1/3 . πr²h

Where:

r = radius of the base

h = height

Since the height of the cone is held constant, then the derivative with respect to time is:

dV/dt = 1/3 h. 2πr dr/dt

Parameters given:

dr/dt = 2 cm/minute

h = 9 cm

r = 13 cm

Hence,

dV/dt = 1/3 x 9 x 2π x 13 x 2

dV/dt = 489.4 cm³/minute

Hence, at radius 13 cm, the rate of change of the volume is 489.4 cm³/minute

It looks like there was typos in your question, most probably your question was:

The radius of the base of a cone is decreasing at a rate of 2 centimeters per minute. The height of the cone is fixed at 9 centimeters. At a certain instant, the radius is 13 centimeters. What is the rate of change of the volume of the cone at that instant (in cubic centimeters per minute)?

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Answer:

The last graph that is a straight line represents y as a function of x

Step-by-step explanation:

In order for a graph to be considered a function, it can't intercept the same value twice. To test this, use the vertical line test to see if the graph hits the line twice. If it does, then it is not a function. But if the line hits the graph only once, then it is a function.

Answer:

31%

Step-by-step explanation:

total number of candy bars in the beginning =  28

number of milkyway bars in the beginning = 9

probability = 9/28 x 100 = 32% (rounded)

number of candy bars after = 27

number of milkway bars after = 8

probablity = 8/27 x 100 = 30 (rounded)

total probablity = (30+32)/200 x 100 = 31

Answer:

all integers greater than or equal to 11