Half of a number increased by fifteen is five. What is the number?

To compute the circulation and outward flux for the given vector field, f = ∇ × (2 + y^2), over the boundary of the half annulus region, we need to calculate the circulation and flux separately. For the circulation, we evaluate the line integral of the vector field around the boundary curve in a counterclockwise direction.

For the outward flux, we compute the surface integral of the vector field across the region's boundary.

To calculate the circulation on the boundary, we need to evaluate the line integral of the vector field f along the boundary curve in a counterclockwise direction. The boundary curve in this case is the outer and inner boundaries of the half annulus, which are given by r = 2 and r = 8, respectively, with 0 ≤ θ ≤ π.

The circulation can be computed using the line integral formula:

Circulation = ∮ f · dr

To evaluate this line integral, we parametrize the boundary curve using polar coordinates. Then, we substitute the parametric equations into the vector field f and evaluate the integral over the specified range.

For the outward flux across the boundary, we need to calculate the surface integral of the vector field f over the half annulus region. The outward flux can be computed using the surface integral formula:

Flux = ∬ f · dS

To evaluate this surface integral, we use the divergence theorem, which states that the flux across a closed surface is equal to the volume integral of the divergence of the vector field over the region enclosed by the surface. However, since the region in question is an open half annulus, we need to consider only the flux across the boundary.

In conclusion, to compute the circulation on the boundary, we evaluate the line integral of the vector field f along the boundary curve. For the outward flux, we calculate the surface integral of the vector field over the boundary of the half annulus region using the divergence theorem.

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The correct answer is polygon has rotated 42° after 7 minutes.

To understand how much the polygon has rotated after 7 minutes, we can break it down into smaller increments.

Since the clock has 60 sides, each minute corresponds to a rotation of 360°/60 = 6°. Therefore, after 1 minute, the polygon rotates by 6°.

After 7 minutes, the polygon would have rotated by 7 * 6° = 42°. This is because each minute adds an additional 6° of rotation.

Hence, after 7 minutes, the polygon has rotated 42°. This means that it has moved 42° clockwise or counterclockwise from its starting position.

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Answer:

42°

Step-by-step explanation:

To find the differential of f(x,y) at the point (1,3), we need to compute its partial derivatives with respect to x and y at that point, and then combine them with the differentials of x and y using the formula:

df = (∂f/∂x) dx + (∂f/∂y) dy

where df is the differential of f, dx and dy are small changes in x and y, and (∂f/∂x) and (∂f/∂y) are the partial derivatives of f with respect to x and y, respectively.

∂f/∂x = \((1/2) (x^2 + y^3)^(-1/2) * 2x = x / \sqrt{ (x^2 + y^3)}\)

∂f/∂y = \((1/2) (x^2 + y^3)^{-1/2} * 3y^2 = (3y^2) / (2 \sqrt{(x^2 + y^3))\)

Now, we can plug in the values x = 1, y = 3 to get the partial derivatives at the point (1,3):

∂f/∂x (1,3) = 1/10

∂f/∂y (1,3) = \((27/10)\sqrt{10}\)

we have df = (∂f/∂x) dx + (∂f/∂y) dy = \((1/10) dx + (27/10)\sqrt{10}dy\)

Note that we didn't specify the values of dx and dy, as they represent small changes in x and y around the point (1,3). The differential df represents the corresponding small change in f around that point.

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A) The third fundamental form of a differentiable surface is a mathematical concept that characterizes the intrinsic geometry of the surface. It is defined in terms of the second derivatives of the surface's parameterization. Geometrically, the third fundamental form measures the rate of change of the surface's unit normal vector as one moves in the direction of the surface.

Proof:

The third fundamental form, denoted as III, is given by the equation:

III = -N · (d²r/du²) · (d²r/dv²) / |dr/du × dr/dv|,

where N is the unit normal vector to the surface, r(u, v) is the parameterization of the surface, and d²r/du² and d²r/dv² are the second derivatives of r with respect to u and v, respectively. |dr/du × dr/dv| represents the magnitude of the cross product of the partial derivatives of r.

B) The properties of the third fundamental form include:

1. Invariance under reparameterization: The third fundamental form is invariant under changes in the parameterization of the surface. This property ensures that the geometric information encoded by the third fundamental form remains consistent regardless of how the surface is parameterized.

2. Symmetry: The third fundamental form is symmetric with respect to the two variables u and v. In other words, swapping the roles of u and v does not change the value of the third fundamental form.

3. Relationship with the second fundamental form: The third fundamental form is related to the second fundamental form, which characterizes the extrinsic curvature of the surface. More specifically, the third fundamental form is expressed in terms of the second fundamental form as:

III = -N · L,

where L is the linear operator defined as:

L = (d²r/dv²) · S · (d²r/du²) - (d²r/dv²) · S · (d²r/dv²),

and S is the shape operator associated with the surface.

The proofs for these properties involve calculations using the definition and properties of the second fundamental form, as well as manipulation of the differential operators. These proofs require a more detailed understanding of differential geometry and are beyond the scope of this brief explanation.

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The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%. Here, we have to depend on the principles of standard normal distribution to find the percentage of probability,


Let us take  z-score for a starting salary of $31,000 as

z = (31000 - 25000) / 5000
= 1.2

Now after using a standard normal distribution table , the probability of a z-score of 1.2 or greater is approximately 0.1151
Converting it into percentage
0.1151 x 100
= 11.51%
The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%.

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I need help too ;-; some one plsssssssss

A fraction represents a part of a whole.40/70, 21/70 are the same fractions like 4/7 and 3/10 with same denominator.

A fraction represents a part of a whole

We need to write 4/7 and 3/10 with the same denominator

The given fractions are 4/7 and 3/10

in 4/7

If numerator and denominator is multiplied with 10

4/7*10/10

we get

40/70

i.e 4/7=40/70

Now

in 3/10

If numerator and denominator is multiplied with 10

3/10*7/7

we get

21/70

i.e 3/10=21/70

Therefore 4/7=40/70 and 3/10=21/70 are two fractions with same denominator.

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Step-by-step explanation:

To solve the given equations, let's assign variables to each equation and solve them step by step.

Let's assume:

a = x

b = y

c = z

d = w

e = v

From the given equations:

a * b = 1 -> x * y = 1 (Equation 1)

b * c = 4 -> y * z = 4 (Equation 2)

c * d = 9 -> z * w = 9 (Equation 3)

d * e = 16 -> w * v = 16 (Equation 4)

e * a = 25 -> v * x = 25 (Equation 5)

Now, let's solve the equations using substitution:

From Equation 1 (x * y = 1), we can rewrite it as y = 1/x.

Substituting y in Equation 2, we get (1/x) * z = 4, which gives us z = 4x.

Substituting z in Equation 3, we have (4x) * w = 9, which gives us w = 9/(4x).

Substituting w in Equation 4, we get (9/(4x)) * v = 16, which simplifies to v = (16 * 4x)/9.

Finally, substituting v in Equation 5, we have [(16 * 4x)/9] * x = 25.

Simplifying the equation, we get:

(64x^2)/9 = 25.

To solve for x, we can cross multiply and solve the quadratic equation:

64x^2 = 225.

Dividing both sides by 64, we get:

x^2 = 225/64.

Taking the square root of both sides, we have:

x = ±(√(225/64)).

So, x = ±(15/8).

Now, substituting the values of x in the respective equations, we can find the values of y, z, w, and v.

For x = 15/8:

y = 1/(15/8) = 8/15

z = 4 * (15/8) = 30/4 = 15/2

w = 9/(4 * (15/8)) = 9/(30/8) = 9 * (8/30) = 12/5

v = (16 * 4 * (15/8))/9 = (60/2)/9 = 60/18 = 10/3

For x = -15/8:

y = 1/(-15/8) = -8/15

z = 4 * (-15/8) = -30/4 = -15/2

w = 9/(4 * (-15/8)) = 9/(-30/8) = -9 * (8/30) = -12/5

v = (16 * 4 * (-15/8))/9 = (-60/2)/9 = -60/18 = -10/3

Therefore, the possible solutions for the variables are:

x = 15/8, y = 8/15, z = 15/2, w = 12/5, v = 10/3

or

x = -15/8, y = -8/15, z = -15/2, w = -12/5, v = -10/3.

Note: The solution includes both positive and negative values for the variables.

To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

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Answer:

x ≤ 7 or x > 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Answer:

Step-by-step explanation:

3/(3+2) = 3/5

B is 3/5 of the distance from A to C.

Interpolate the coordinates of B:

Difference of x-coordinates = 6-(-4) = 10

3/5 of 10 = 6

x-coordinate of B = (x-coordinate of A) + 6 = -4 + 6 = 2

Difference of y-coordinates = 4-(-3) = 7

3/5 of 7 = 21/5

y-coordinate of B = (y-coordinate of A) + 21/5 = 6/5

B(2, 6/5)

\(f(x) = \dfrac{x+1}{x^2-7x-8} \\~\\~\\f(x) = \dfrac{x+1}{(x-8)(x+1)} \\~\\~\\f(x) = \dfrac{1}{x-8}\)

\(\text{avg} = \dfrac{f(a)-f(b)}{a-b} \\~\\~\\\text{avg} = \dfrac{\left(\dfrac{1}{3-8}\right)-\left(-\dfrac{1}{2+8}\right)}{3-(-2)} \\~\\~\\\text{avg} = \dfrac{\left(\dfrac{1}{-5}\right)-\left(-\dfrac{1}{10}\right)}{5} \\~\\~\\\text{avg} = \dfrac{1}{2}-1 \\~\\~\\ \text{avg} = -\dfrac{1}{2}\)

Answer:

$140

Step-by-step explanation:

Total Amount of chocolate = 100 Pounds

Amount of chocolate in one box = 1 1/4 Pounds =  5/4 Pounds

Number of boxes = 100/(5/4) = 80 boxes

Cost of one box = $1.75

Total selling price = 80×1.75 = 140

The total selling price for all the boxes of chocolate is $140

Answer: $140

Step-by-step explanation:

Convert

1 1/4 --> 1.25

Solve

100/1.25= 80

80*1.75= $140

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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$11.2425 money she save on the purchase of the tires.

The basic way to calculate a discount is to multiply the original price by the decimal form of the given percentage rate. To calculate the sale price of any item, we need to subtract the discount from the original price.

Both bought 2 new tires for her race car

each tire originally cost is $74.95

she received a 15% discount

=74.95 × 15%

=74.95 × 0.15

=11.2425

$11.2425 money she save on the purchase of the tires.

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Answer:

50

110

90

=250

Step-by-step explanation: 90+50+110

I HOPE THIS HELPS

Answer:

x=40

Step-by-step explanation:

100+2x=180

80=2x

x=40

Answer:

40°, because 180 minus 100 is 80, then divided 80 by 2 (because there is two 2's) and you get 40

Step-by-step explanation:

Bleh :b

Answer:

an attractive force that acts between all objects without contact

Step-by-step explanation:

an attractive force that acts between all objects without contact

You are pulled down by gravity when you jump

Answer:

an attractive force that acts between all objects without contact

The force of gravity, first discovered by Isaac Newton, is one of the four fundamental forces. It is a force that is always attractive, and it is exerted between all objects that have mass. Also, the force is exerted even when the two objects are not in contact.

The magnitude of the force of gravity between two objects is given by where

G is the gravitational constant

m1 and m2 are the masses of the two objects

r is the distance between the two objects

Step-by-step explanation:

MRK ME BRAINLIEST PLPZZZZZZZZZZZZZZZZ

Audience reach is a metric that is used to measure of the total audience size for a specific provide platform.

Audience reach answers the question of how many people have had the opportunity to consume (i.e. read, watch, and/or hear) news coverage of whatever you're watching. This metric is based on known circulation, viewership, audience size and followers of media outlets or social media users who publish the content in question. For the audience size of the publication/social media user providing the content is identified and then this number is added to the audience size of all other outlets publishing the content to give the total audience reach.

Hence, required answer is audiance reach.

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Answer:

a

Step-by-step explanation:

Answer:

aaaaaaaaaaaaa is the correct answerrrrr

Step-by-step explanation:

i´m a singer of cource

Answer:

I hope the image helps!

The largest prime number that divides the given expression is 229.

We can factorize the given expression as follows:

\($0! \times 1 \times 1! \times 2 \times 2! \times 3 \times 3! \times \cdots \times 50! \times 50$\)

Now, we can cancel out all the factorials from both sides, leaving us with:

\($1 \times 1 \times 2 \times 2 \times 3 \times 3 \times \cdots \times 50 \times 50$.\)

The largest prime factor of any composite number is the largest prime factor of its prime factorization. By the fundamental theorem of arithmetic, we know that the prime factorization of any composite number is unique.

The prime factorization of a number can be found by dividing the number by prime numbers and keeping dividing the quotient by prime numbers until the quotient is prime.

Now, we can start dividing the given number (the product of all numbers from 1 to 50) by the smallest prime number, 2, and keep dividing the quotient by the next prime number until the quotient is prime.

The largest prime factor of the given expression is the largest prime factor of the final quotient.

The final quotient is

\(2^{24} \times 3^{12} \times 5^9 \times 7^7 \times 11^5 \times 13^4 \times 17^3 \times 19^3 \times 23^2 \times 29^2 \times 31^2 \times 37^2 \times 41^2 \times 43^2 \times 47^2 \times 53^2 \times 59^2 \times 61^2 \times 67^2 \times 71^2 \times 73^2 \times 79^2 \times 83^2 \times 89^2 \times 97^2 \times 101^2 \times 103^2 \times 107^2 \times 109^2 \times 113^2 \times 127^2 \times 131^2 \times 137^2 \times 139^2 \times 149^2 \times 151^2 \times 157^2\)

\(\times 163^2 \times 167^2 \times 173^2 \times 179^2 \times 181^2 \times 191^2 \times 193^2 \times 197^2 \times 199^2 \times 211^2 \times 223^2 \times 227^2 \times 229^2$\)

The largest prime factor of the final quotient is the largest prime factor of the prime factorization, which is 229.

So the largest prime number that divides the given expression is 229.

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The inequality expression of the volume of the balloon is V < 4,400

From the question, we have the following statement:

The initial volume of the balloon is 4,400 cubic centimeters

Also, we understand that:

The balloon leaks out over time

This means that the volume of air in the balloon decreases over time.

So, we have the following representation

V = Less than the initial volume

Rewrite as

V < 4400

Hence, the volume of the balloon at any time after it starts leaking is V < 4,400

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Answer:

OCD473

Step-by-step explanation:

Answer:

1920

Step-by-step explanation:

Volume of larger rectangular prism: 10 * 8 * 14 = 1120

Volume of smaller rectangular prism: 10 * 10 * 8 = 800

Volume of whole prism: 1120 + 800 = 1920

Hence, your answer is 1920

12.566

Hope this helped :T

The sum οf the angle measures οf 7 οf the sectiοns is 315 degrees.

An angle is a geοmetric figure fοrmed by twο rays that share a cοmmοn endpοint, called the vertex. It is usually measured in degrees οr radians and describes the amοunt οf rοtatiοn between the twο rays.

If we arrange eight chairs arοund a circle that has eight sectiοns, each sectiοn will have a central angle οf 360 degrees / 8 = 45 degrees.

Tο find the sum οf the angle measures οf 7 οf the sectiοns, we can add the central angles οf thοse 7 sectiοns:

7 x 45 degrees = 315 degrees.

Therefοre, the sum οf the angle measures οf 7 οf the sectiοns is 315 degrees.

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Answer: Solution

= 0

Step-by-step explanation:

Answer:

-25/3

Step-by-step explanation:

khan said so