In fig if x+y=w+z then prove that AOB is a line.​

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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Answer:

you would take 10 and divide that by 16 to get .63, so you take .63 and minus that from 100 and you get 37. so the officer had a 37% decrease.

Step-by-step explanation:

Answer:

4 according to the numbers you provided integer x the = 4

Step-by-step explanation:

The equations that have one solution are: 5x – 1 = 3(x + 11) and 4 = 2(x – 3). (option a and c)

Linear equations are mathematical expressions involving variables raised to the power of 1, and they form a straight line when graphed.

5x – 1 = 3(x + 11)

To determine if this equation has one solution, we need to simplify it:

5x – 1 = 3x + 33

Now, let's isolate the variable on one side:

5x – 3x = 33 + 1

2x = 34

Dividing both sides by 2:

x = 17

Since x is uniquely determined as 17, this equation has one solution.

4(x – 2) = 4x

Expanding the parentheses:

4x – 8 = 4x

The variable x cancels out on both sides, resulting in a contradiction:

-8 = 0

This equation has no solution. In mathematical terms, we say it is inconsistent.

8(x – 9) = 4(x – 6)

Expanding the parentheses:

8x – 72 = 4x – 24

Subtracting 4x from both sides:

4x – 72 = -24

Adding 72 to both sides:

4x = 48

Dividing both sides by 4:

x = 12

As x is uniquely determined as 12, this equation has one solution.

4 = 2(x – 3)

Expanding the parentheses:

4 = 2x – 6

Adding 6 to both sides:

10 = 2x

Dividing both sides by 2:

5 = x

Since x is uniquely determined as 5, this equation has one solution.

2(x – 4) = 5(x – 3)

Expanding the parentheses:

2x – 8 = 5x – 15

Subtracting 2x from both sides:

-8 = 3x – 15

Adding 15 to both sides:

7 = 3x

Dividing both sides by 3:

7/3 = x

The value of x is not unique in this case, as it is expressed as a fraction. Therefore, this equation does not have one solution.

2(x – 1) + 3x = 5(x – 2) + 3

Expanding the parentheses:

2x – 2 + 3x = 5x – 10 + 3

Combining like terms:

5x – 2 = 5x – 7

Subtracting 5x from both sides:

-2 = -7

This equation leads to a contradiction, which means it has no solution.

Hence the correct options are a and c.

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The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

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

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

Answer

18,080

Explantion

400x10=4000x4=16000

400x5=2000

2000+16000=18000

400×.2=80

cause 20% of 400 is 80

so total is 18,080

Answer:3,393 tickets

Step-by-step explanation:

You can use the butterfly method to solve this.

Answer: c = 149 + 0.02p

Step-by-step explanation:

From the question,

P = purchase price of the boat

C = Mick's commission

From the scenario in the question, the commission earned by Mick will be:

c = 149 + (2% × p)

c = 149 + (0.02p)

c = 149 + 0.02p

Answer:c

Step-by-step explanation:

Answer:

17.23

Step-by-step explanation:

The area of the surface that lies above the triangle with vertices (0, 0), (2, 0), and (2, 4) is 12 square units.

For the area of the surface that lies above the triangle with vertices (0, 0), (2, 0), and (2, 4), we need to calculate the surface integral over that region.

Let's denote the surface as S and the vector function that represents the surface as 'r' = ⟨x, 2y + 1, 4z^2 + x^2 - 5⟩.

The area of the surface S can be calculated using the surface integral formula:

A = ∬S dS

We can use the parameterization of the surface to express dS in terms of the parameters u and v. Since the surface is defined by two variables, we can choose a parameterization that represents the triangle. Let's choose u as x and v as y.

The vertices of the triangle in terms of u and v are:

P(u=0, v=0) = (0, 0, -5)

Q(u=2, v=0) = (2, 1, -5)

R(u=2, v=4) = (2, 9, 11)

To calculate the area, we can set up the surface integral using the parameterization:

A = ∬S dS = ∬R(u,v) |∂r/∂u x ∂r/∂v| dA

where R(u, v) is the parameterization of the surface and dA is the area element.

∂r/∂u = ⟨1, 0, 0⟩

∂r/∂v = ⟨0, 2, 0⟩

|∂r/∂u x ∂r/∂v| = |⟨0, 0, 2⟩| = 2

The integral becomes:

A = ∬R(u,v) 2 dA

To calculate the area, we need to integrate over the region R(u, v) defined by the triangle:

0 ≤ u ≤ 2

0 ≤ v ≤ 4

0 ≤ u + v ≤ 4

Now, we can calculate the integral:

A = ∫[0,2] ∫[0,4-u] 2 dudv

Integrating with respect to v first, we get:

A = ∫[0,2] [2v]_[0,4-u] du

A = ∫[0,2] (8 - 2u) du

A = [8u - u^2]_[0,2]

A = (8(2) - (2)^2) - (8(0) - (0)^2)

A = (16 - 4) - 0

A = 12

Therefore, the area of the surface that lies above the triangle with vertices (0, 0), (2, 0), and (2, 4) is 12 square units.

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the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).

To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.

Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.

Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.

Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

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To determine whether two ratios represent quantities that are proportional, we need to check if their values are equal. Let's examine each pair of ratios:

   5/7 and 7/14:

   To check if these ratios are proportional, we simplify them to their simplest forms. The first ratio is already simplified, but the second ratio can be simplified to 1/2. Since 5/7 is not equal to 1/2, these ratios are not proportional.

9/10 and 10/9:

By simplifying both ratios, we find that they are equal to each other in their simplest forms. Therefore, 9/10 and 10/9 are proportional.

56/64 and 36/48:

After simplifying both ratios, we get 7/8 for the first ratio and 3/4 for the second ratio. Since 7/8 is not equal to 3/4, these ratios are not proportional.

21/28 and 12/16:

Upon simplifying, we obtain 3/4 for both ratios. Therefore, 21/28 and 12/16 are proportional.

In summary, out of the four given pairs of ratios, only the ratios 9/10 and 10/9, as well as 21/28 and 12/16, represent quantities that are proportional. It is important to simplify the ratios to their simplest forms before comparing them to determine proportionality.

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Answer:

Step-by-step explanation:

yes

Answer: See explanation

Step-by-step explanation:

At sit and Stay School, 12 lessons cost $96. The unit rate for each lesson will be:

= $96/12 = $8

At Canine Community Center, 25 lessons cost $125. The unit rate will be:

= $125/25 = $5

The better deal is at Canine Community as it's cheaper.

The unit rate for lessons at Sit and Stay School is $8 per lesson

The unit rate for lessons at Canine Community Center is $5 per lesson

The lower unit rate is $5 which is that of Canine Community.

The lessons at Canine Community are the better deal.

Step-by-step explanation:

Pythagoras

c² = a² + b²

c being the Hypotenuse (the line opposite of the 90° angle) of the right-angled triangle.

9² = 5² + side²

81 = 25 + side²

56 = side²

side = sqrt(56) = sqrt(4×14) = 2×sqrt(14)

Answer:

30 + 12.5x >= 135

X >= 8.4 points

Step-by-step explanation:

30 + 12.5x > = ( more or equal) 135

12.5x >= 135 - 30

12.5x >= 105

X >= 105/12.5

X >= 8.4

The inequality that determines the number of visits Nevaeh can make to earn her first free movie ticket.

30 + 12.5v ≥ 135

The number of visits must be 9 or greater.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Signing up rewards points = 30

Points for each visit = 12.5

Minimum points required for a free movie ticket = 135

Let the number of visits = v

Now,

The inequality that determines the number of visits Nevaeh can make to earn her first free movie ticket.

30 + 12.5v ≥ 135

Solve for v.

30 + 12.5v ≥ 135

12.5v ≥ 135 - 30

12.5v ≥ 105

v ≥ 105/12.5

v ≥ 8.4

This means that,

The number of visits must be greater than or equal to 9.

We can cross-check.

30 + 12.5 x 9

30 + 112.5

142.5

Thus,

The inequality that determines the number of visits Nevaeh can make to earn her first free movie ticket.

30 + 12.5v ≥ 135

The number of visits must be 9 or greater.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

This statement is true. Statistical inference is the process of deriving conclusions about a population from a sample.

The process of statistical inference uses probability theory to draw conclusions from data. It is important to note that the conclusions drawn from a sample of data may not be accurate conclusions about the entire population.Statistical inference involves several steps. First, a random sample of data is selected from the population. Second, the data is analyzed to identify patterns and trends that may exist in the population. Third, a statistical model is used to make inferences about the population based on the sample data. In statistical inference, we use the following equation to calculate the probability of a certain event occurring: P(A|B)=P(B|A)P(A)/P(B), where A and B are two events. In this equation, P(A|B) is the probability that event A occurs given that event B has already occurred. P(B|A) is the probability that event B occurs given that event A has already occurred. P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.Statistical inference is a powerful tool for drawing conclusions from data.

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The economic and political doctrine that emphasizes free trade and the constitutional guarantee of individual rights, such as freedom of speech and religion, is called liberalism.

Liberalism is a political and economic ideology that promotes individual freedom, limited government intervention, and free market principles. It emphasizes the importance of protecting individual rights, including civil liberties such as freedom of speech, religion, and assembly. Liberalism advocates for a system of governance that ensures equality under the law and encourages free trade and open markets. Economic liberalism promotes free trade and opposes government restrictions or regulations on business and commerce. It supports the idea of a market economy where prices are determined by supply and demand and individuals have the freedom to engage in economic activities. In the context of politics, liberalism advocates for democratic principles, constitutionalism, and the protection of individual rights as essential components of a just and prosperous society.

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Answer:

y= (x+7)(x+3)

Step-by-step explanation:

This is intercept form, which is y=a(x-p)(x-q). p and q are the zeros, and I assumed a=1

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

A polynomial with the highest power of 2 is called a quadratic equation.

The quadratic function whose zeroes are -7 and -3 is

y = x² + 10x + 21

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

A polynomial with the highest power of 2 is called a quadratic equation.

A quadratic function whose zeroes are -7 and -3.

This means the quadratic function has zeroes.

x = -7

x + 7 = 0 ____(1)

x = -3

x + 3 = 0 _____(2)

Let the quadratic function be f(x) = y.

From (1) and (2) we get,

y = (x + 7)(x + 3)

y = x² + 3x + 7x + 21

y = x² + 10x + 21

Thus,

The quadratic function whose zeroes are -7 and -3 is

y = x² + 10x + 21

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Answer:2.25 + 4.5 = 6.75 cups of flour

2.25

Step-by-step explanation: 1 batch is already 2.25 in decimal form so just infer from there.. divide 2.25 from .5 and get 4.5 then add to the one batch you've already received .. 4.5 + 2.25 = 6.75 and just convert into a fraction 6 3/4

Answer:

x= 8

Step-by-step explanation:

Half of a circle or a straight line is equal an angle of 180 degrees. Therefore, both the measurements of angles RPS and QPR are equal to 180 degrees.

3x + 12 + 7x + 88 = 180

Add like terms

10x + 100 = 180

-100. -100

10x = 80

/10. /10

x = 8

Answer:

sorry if this is wrong but i think its 9 17/89

if the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph., then the visitor  would run 14 .45 miles  before swimming to minimize the time it takes to reach the island .

we are given that an island is 1 mi due north of its closest point along a straight shoreline., where the visitor is staying at a cabin on the shore that is 15 mi west of that point, in some point the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph. Considering x be the distance the visitor runs. so the total time will be :

Time (T)= x/6 + √((15-x)²+1²)/2.5

Differntiating both sides respect to  x , we get

dT/dx = 1/6 -(15-x)/√(15-x)²+1)/2.5

=>1/6 = (15-x)/√(15-x)²+1)/2.5

=>6(15-x) = 2.5√(15-x)²+1)

Now considering   15 - x = y, we get  

=>6y = 2.5√(y²+1)

=>36y² = 6.25y² + 6.25

=>29.75y² = 6.25

y = √(25/119),  therefore ,x = 15 - √(25/119) = 14 .45

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Answer:

12.7=s

Step-by-step explanation:

First, write the equation and combine like terms.

7-45=-3s

-38=-3s

Next, divide both sides by 3.

-38=-3s

/-3  /-3

12.7=s (I rounded the answer.)

Hope this helps! Have a great day C:

The approximate length of the diameter of the pizza in inches would be 96. 93 inches.

To find the approximate length of the diameter of the pizza, we can use the relationship between the circumference and the diameter of a circle.

The circumference of a circle is calculated using the formula C = π x d.

In this case, we are given the circumference of the jumbo pizza as approximately 301.5 inches:

301.5 inches = π x d

d = 301.5 inches / π

d = 301.5 inches / 3.14

d = 96. 93 inches

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Answer: y=3/5x -1.5

Step-by-step explanation:

hope this helps!

The equation of line is y = ( 1/2 )x - 3/2 and the slope is m = ( 1/2 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P = P ( 1 , -1 )

Let the second point be represented as Q = Q ( -5 , -4 )

Now , the slope of the line between the points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -4 - ( -1 ) ) / ( -5 - 1 )

On simplifying the equation , we get

Slope m = ( -3 / -6 )

Slope m = 1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -1 ) = ( 1/2 ) ( x - 1 )

On simplifying the equation , we get

y + 1 = ( 1/2 )x - 1/2

Subtracting 1 on both sides of the equation , we get

y = ( 1/2 )x - 3/2

Hence , the equation of line is y = ( 1/2 )x - 3/2

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By using this algorithm, we can efficiently determine whether a graph with 15 vertices is 2-colorable or not.

To prove Lemma 1, we need to show that if a small subset of vertices in a graph with 15 vertices is 2-colorable, then the entire graph can be 2-colored. Similarly, if a small subset of vertices in a graph with 15 vertices is not 3-colorable, then the entire graph is not 3-colorable.

We can prove this by using a brute force algorithm, where we exhaustively search over all small subsets of 15 vertices. If we find a subset that is 2-colorable, we can use this to 2-color the entire graph. Conversely, if we find a subset that is not 3-colorable, we can conclude that the entire graph is not 3-colorable.

This algorithm is justified by Lemma 1, which states that the 2-colorability of a small subset of vertices implies the 2-colorability of the entire graph, and the non-3-colorability of a small subset of vertices implies the non-3-colorability of the entire graph.

Therefore, by using this algorithm, we can efficiently determine whether a graph with 15 vertices is 2-colorable or not.

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the expression 9y^5 - 10y^3 is a polynomial. Specifically, it is a polynomial of the fifth degree (or order) since the highest exponent of the variable y is 5.

A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication, but not division or negative exponents.

In the given expression, we have two terms: 9y^5 and -10y^3. Each term is a monomial (a single term) and can be written in the form of coefficient times variable raised to a non-negative integer exponent.

The coefficient of the first term is 9, and the variable is y raised to the power of 5. Similarly, the coefficient of the second term is -10, and the variable is y raised to the power of 3.

Both terms satisfy the criteria of a polynomial, and the expression can be simplified as:

9y^5 - 10y^3

Therefore, the expression 9y^5 - 10y^3 is a polynomial. Specifically, it is a polynomial of the fifth degree (or order) since the highest exponent of the variable y is 5.

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