show (separately) how the integral and differential forms of the continuity equation can be simplified for application to fluid problems involving: (a) steady flow, (b) steady, incompressible flow,

The solution to the given differential equation is a 3-dimensional vector function which satisfies the given initial conditions. The vector function consists of three components, one for each dimension in the equation.

The given differential equation is a 3-dimensional vector equation, of the form ()=⟨12−12,2−1,1⟩. The initial conditions are (1)=⟨0,0,12⟩ and ′(1)=⟨8,0,0⟩. The solution to this equation is a 3-dimensional vector function, ()=⟨, ,⟩. The first component of the vector function is a function of the independent variable, and must satisfy the initial condition (1)=⟨0,0,12⟩. This means that the first component of the vector function must be equal to 0 at x=1. The second component must satisfy the initial condition ′(1)=⟨8,0,0⟩. This means that the second component of the vector function must be equal to 8 at x=1. The third component of the vector function must also satisfy the initial condition (1)=⟨0,0,12⟩. This means that the third component of the vector function must be equal to 12 at x=1. Once the initial conditions have been satisfied, the  equation can be solved to find the vector function.

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Answer:

0.712GB

Step-by-step explanation:

1 day = 24hrs = 24*60 seconds

speed 890KB per 18 seconds

so 24*60/18 = 80 *890KB= 71200KB

1GB = 100000KB

so 0.712GB

Answer:

13.86

Step-by-step explanation:

You have the exact value, just compute it and round the number to get your approximate

Answer:

13.86

Step-by-step explanation:

You'll most likely need the calculator since ✓192 is not a perfect square.

Calculating it

✓192 = 13.856

Rounding it two places would be 13.86

Step-by-step explanation:

Nope. Actually, every single even number except 1 is composite actually

Answer:

No

Step-by-step explanation:

2 is a prime number, but all other even numbers are composite, since they're all multiples of 2

The arc angle mWX is 9 degrees.

An inscribed angle is the angle that is formed by the intersection of two chords on the circumference of a circle. Therefore, inscribed angles subtended by the same arc are equal.

Hence,

3x - 20 = 15x - 64

3x - 15x = - 64 + 20

- 12x = -44

divide both sides by -12

x = -44 / -12

x = 3.7

Let's find the arc angle

Hence,

mWX = 3(3.7) - 20

mWX = 11 - 20

mWX = 9 degrees

The answer can't be negative.

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Answer: 38.3 cm

Step-by-step explanation:

To find the size of a rectangular monitor measured diagonally, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Here are the steps to calculate the diagonal size of the monitor:

Therefore, the size of the rectangular monitor that is 30 centimeters wide by 24 centimeters high is approximately 38.3 cm. to the nearest centimeter.

The size of the given mirror as a rectangular diagonal is 38.41 cm which is almost 39 cm.

We know that;

d=√ {(l)^2 + (w)^2}.........(i), where,

d= diagonal of the rectangle,

l= length of the rectangle = 30 cm

w= width of the rectangle = 24 cm.

Therefore, Substituting the values of each in equation (i), we get;

d=√{(30)^2+(24)^2} cm,

or, d = 38.41 cm

So, the size of the rectangular mirror measured diagonally is 38.41 cm which is almost 39 cm.

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The equation in slope intercept form is : [tex]y = \frac{1}{8} x - 223.05[/tex]

The slope intercept form is a process used to determine the equation of a straight line in the coordinate plane. It can be used to determine the equation of a line when given the slope of the straight line and the y-intercept

The slope-intercept form of a line is:

y = mx+b

where m is the slope of the line and b is an intercept of the y-axis.

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]m = \frac{26.7 - 23.2 }{1998- 1970}[/tex]

[tex]m = \frac{1}{8}[/tex]

So,

[tex]y = \frac{1}{8} x + b[/tex]

To find b we get the point (1970, 23.2) and introduce it in the previous equation.

[tex]23.2= \frac{1}{8} (1970)+ b[/tex]

⇒ 23.2 - 246.25 = b

⇒ b = - 223.05

Then, the equation is : [tex]y = \frac{1}{8} x - 223.05[/tex]

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The square root of 9 is 78 less than 9 squared

The square root of 9 is calculated as

                     √9 = √(+ 3)² or√(- 3)²

                           = + 3 or - 3

Let's calculate the square of 9:

                      9² = 81

We need to calculate here, how much the square root of 9 is less than the square of 9 or we can say the difference between the square of 9 and the square root of 9. So, let's say that difference is denoted by d

                                 d = 9² - √9

When √9 = +3

                                 d = 81 - 3

                                 d = 78

When √9 = -3

                                 d = 81 - (-3)

                                 d = 81 + 3

                                 d = 84

Hence, the value of the difference between the square of 9 and the square root of 9 is 78 or 84.

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It is going to be more expensive for 9 teams to buy these baseballs.

It has been mentioned in the problem that Ms.Bush charges $4 per baseball. This means that we need to pay $4xn dollars where n is the number of baseballs. According to the question, the member of baseball depends on the number of teams as well. More teams mean more baseballs will be bought.

Since it is obvious that 9 is greater than 6, so, it automatically means that it is going to be more expensive for 9 teams to buy these baseballs as compared to 6 teams.

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Answer:

n = 6.42105263158

Step-by-step explanation:

324 - 202 = 122

122 ÷ 19 = 6.42105263158

That seems like a very large decimal place for a school related math problem if I'm doing this correctly.  When you say increased by you mean addition right?

The value of x in the isosceles triangles is 169 degrees

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

A series of isosceles triangles are drawn between two red line segments

Also, we have

a = 11°

Because the triangles are isosceles triangles, we have the following equation

x + a = 180

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

x + 11 = 180

Evaluate the like terms

x = 169

Hence, the value of x is 169

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a) The enlargement needed to be done is 25%.

b) The succession time should be at least t=9 to get a final copy that is less than 15% of the original size.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Let the size of the page be q, when it is reduced to 80%, its size becomes

= 80% x q

= 0.80(q)

= 0.80q

When you want to return it into its original size q,

x(0.80q) = q

x = q / 0.80q

x = 1.25

x= 125%

Hence, the enlargement needed to be done is 25%.

b) The size of the page after t number of copying done is given by

C(t) = [tex]C_0(0.80)^t[/tex]

So, C(t) / [tex]C_0[/tex] = [tex](0.80)^t[/tex]

0.15 ≤  [tex](0.80)^t[/tex]

Taking log on both side

log (0.15) ≤ log [tex](0.80)^t[/tex]

log (0.15) ≤ t log (0.80)

log (0.15) /log (0.80)  ≤ t

0.80 ≤ t

Hence, the succession time should be at least t = 9 to get a final copy that is less than 15% of the original size.

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the simple form of the given number will be 8√3.

What is square root?

A value known as the square root of a number is one that, when multiplied by itself, yields the original number. An alternative to square rooting a number is to use it. Therefore, the concepts of squares and square roots are connected. The original number is equal to the square root of any integer, which is equivalent to a number.

Let's assume that m is an integer that is positive, such that (m.m) = (m2) = m.

A square root function in mathematics is described as a one-to-one function that accepts a positive number as input and outputs the square root of the specified input number.

The given number is √192

= √ (2*2*2*2*2*2*3)

=8√3

Hence the simple form of the given number will be 8√3.

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The required Linear function among the following option is D) y=|x|.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A)  y=3x³

It is cubic function.

B) y=¼x

It is inverse function.

C) Y=x²

It is a quadratic function.

D) y=|x|

It is a modulus function, but after remove the Mode in x, we get

y = x and y = -x

So, Here power on x is one. It is Linear function as well.

Thus,  y=|x| is linear function.

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Answer:

x = 40

Step-by-step explanation:

We can set up the following equations to represent the problem:

x = number of quarters

x + 16 = number of dimes

0.25x + 0.1(x + 16) = 12.45

Solving for x, we get:

x = 40

So there are 40 quarters and 56 dimes in the coin bank.

Answer: 7 is the 10% of 70

Step-by-step explanation:

1. write 10% as 10/100 as we convert in this form to find the percentage.

2. 10/100 x 70 = 7

therefore the answer is 7

The required end behavior of the graph of y = f(x) is given as, x → ∞, y→-∞ and when x → -∞, y →∞. Option B is correct.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
As we can see in the graph of y =f(x)

As x approaches -∞ y approaches ∞, and as As x approaches ∞ y approaches -∞

Thus, the required end behavior of the graph of y = f(x) is given as, x → ∞, y→-∞ and when x → -∞, y →∞. Option B is correct.

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Answer:

x=291/X

Step-by-step explanation:

it mean 29=xX-262

xX=29+262

xX=291

x=291/X

The coordinates of the points A and B, after scaling becomes

A(x, y) → A'(2x, 2y)

B(x₁, y₁) → B'(2x₁, 2y₁)

        {K} = L{final}/L{initial}

Given is that shape is being enlarged using a scale factor of 2 and centre (6, 3).

Assume the coordinates of the point are A(x, y) and B(x₁, y₁). After scaling, the coordinates will become -

A(x, y) → A'(2x, 2y)

B(x₁, y₁) → B'(2x₁, 2y₁)

Therefore, the coordinates of the points A and B, after scaling becomes

A(x, y) → A'(2x, 2y)

B(x₁, y₁) → B'(2x₁, 2y₁)

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There are 81 different ways to place 5 distinguishable balls in 3 indistinguishable boxes using combinations.

Given that in how many ways we can put 5 balls in 3 boxes if balls are distinguishable, but the boxes are not.

To find the number of ways we will use the concept of combination.

Combinations can be defined as the entire outcomes of an event where the order of outcomes does not matter.

Given Data

The number of balls is 5 balls.

The number of boxes is 3 boxes.

The balls are distinguishable, but the boxes are not distinguishable.

According to the question, the expression for the number of ways is,

P = [tex]\frac{n^N}{n}[/tex]

Putting the values in the formula we get,

P = [tex]\frac{3^5}{3}[/tex]

P = 81

Hence the number of the ways are 81.

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Answer:

The median is 79.

Step-by-step explanation:

The following are the respective values of the angles:

∠5 = 44°

∠3 = 117°

x = 60°

x = 157°

angles (∠5 + ∠6)° and ∠2 are corresponding angles and are equal so;

∠5 + 90° = 134°

∠5 = 134° - 90°

∠5 = 44°

angles (∠5 + ∠6)° and ∠3 are alternate angles and are equal so;

∠3 = ∠5 + ∠6

∠3 = 27° + 90°

∠3 = 117°

(x + 5) + 90° + (180° - 155°) = 180° {sum of interior angles of a triangle}

x + 5 + 90° + 25° = 180°

x + 120° = 180°

x = 180° - 120°

x = 60°

x = 22° + (180° - 45°) {exterior angle of a triangle equals two opposite interior angles}

x = 22° + 135°

x = 157°

Therefore, the following are the values of the angles: ∠5 = 44, ∠3 = 117°, x = 60°, and x = 157° respectively.

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Answer:

x-5/10 - 2(x-3)/5 = 3(x-4)/15= x=-15/4

According to the question, the closing balance for quarter 2 is £82,750.

A quarter is one fourth of a year. It is typically a three month period, usually consisting of January, February, and March; April, May, and June; July, August, and September; or October, November, and December. The terms of a quarter can vary depending on the context. For example, in the United States, quarters are commonly referred to as “fiscal quarters,” and begin on the first day of October, January, April, and July. In this case, each quarter covers a three-month period.

Inflows for quarter 2: 540,000 x 1.075 = £581,000

Outflows for quarter 2: 495,000 x 1.05 = £519,250

Closing balance for quarter 2:

Opening balance + Inflows - Outflows =

20,000 + 581,000 - 519,250 = £82,750

Therefore, the closing balance for quarter 2 is £82,750.

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The cubic function whose graph passes through the given points is defined as follows:

y = -2(x³ - 4x² + x + 6).

The cubic function is defined by the Factor Theorem, as a product of it's linear factors.

The x-intercepts of the function are given as follows:

Hence the linear factors of the function are given as follows:

As a product of the linear factors, the function is defined as follows:

y = a(x + 1)(x - 2)(x - 3)

y = a(x² - x - 2)(x - 3)

y = a(x³ - 4x² + x + 6).

When x = 0, y = -12, hence the leading coefficient a is obtained as follows:

6a = -12

a = -2.

Thus:

y = -2(x³ - 4x² + x + 6).

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The value of m for the given equation is 18. The solution has been obtained by solving the linear equation.

What is a linear equation?

A linear equation is the one with the highest degree of one. This demonstrates that there are no variables in a linear equation with an exponent bigger than one. On the graph, such an equation yields a straight line.

We are given an equation as 2 = m/2 - 7

On solving the equation for m, we get

⇒2 = m/2 - 7

⇒2 = (m - 14)/2

⇒2*2 = (m - 14)

⇒4 = m - 14

⇒m = 18

Hence, the value of m for the given equation is 18.

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Therefore , the solution of the given problem of hexagon comes out to be 2700 meters square is the area of hexagon.

It is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles.

Here,

Given :

=> 300 meters

and

2400 meters

So,

=> area = 2400 +300 = 2700 meters square

Therefore , the solution of the given problem of hexagon comes out to be 2700 meters square is the area of hexagon.

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The mathematical expression boole’s inequality for a sequence of events a1, a2, . . . , an then the bounds are known as Bonferroni inequalities [13].

Arithmetic sequence is [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1

The given equation about an arithmetic sequence is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1

Boole's inequality(or the union bound) states that for any at most countable collection of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the events in the collection.

The objective is to prove the statement using principle of mathematical induction.

The principle of mathematical induction statement that a statement [tex]p_{n}[/tex] about positive integer n, is true if satisfies the following two conditions:

[tex]p_{1}[/tex] is true

If [tex]p_{k}[/tex] is true, then [tex]p_{k+1}[/tex] is true

Consider the statement for n > 1

[tex]p_{n}[/tex] : [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d

Here, it is known that [tex]a_{n}[/tex] is an arithmetic sequence with [tex]a_{1}[/tex] as first term and 'd' as common difference.

Recall that in any arithmetic sequence, each term is determined by adding 'd' to previous term.

Hence, the second term is determined by adding 'd' to first term.

[tex]a_{2}[/tex] = [tex]a_{1}[/tex] + d

For [tex]p_{2}[/tex] , substitute n = 2 in the given statement to verify it for first positive integer.

[tex]p_{n}[/tex] : [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d

[tex]p_{2}[/tex] : [tex]a_{2}[/tex] = [tex]a_{1}[/tex] + (2-1) d

[tex]p_{2}[/tex] : [tex]a_{1} +d[/tex] =   [tex]a_{1} +d[/tex]

This has given a true statement.

Hence, the statement is verified for [tex]p_{1}[/tex].

Therefore,

The mathematical expression boole’s inequality for a sequence of events a1, a2, . . . , an then the bounds are known as Bonferroni inequalities [13].

Arithmetic sequence is [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1

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