Write the equation for the inverse of the function. y=pi/2+sinx

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Hey there!

ASSUMING:

p = 2l + 2w

IF SO:

• We already have our perimeter (p) & our width (w), now you have to find our length (l)

160 = 2l + 2(34)

CONVERT TO:

2l + 2(34) = 160

SIMPLIFY IT:

2l + 68 = 160

SUBTRACT 68 to BOTH SIDES:

2l + 68 - 68 = 160 - 68

SIMPLIFY IT:

2l = 160 - 68

2l = 92

DIVIDE 2 to BOTH SIDES:

2l/2 = 92/2

SIMPLIFY IT:

l = 92/2

l = 46

Therefore, your answer should be:

l = 46

Good luck on your assignment & enjoy your day!

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Players no longer need commitment strategies to reach a mutually-beneficial cooperative equilibrium when games are repeated.

This is an exercise related to Game Theory.

The extended form is typically used to depict repeated games, commonly referred to as supergames, in game theory since they occur repeatedly across time.

The potential of collaborating means that we may choose to compromise in order to continue earning a payout over time, knowing that if we do not fulfill our part of the bargain, our adversary may decide not to either.

As contrast to one-shot games, recurring games provide a new set of incentives.

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Answer:

180-82-27= 71 degrees

Step-by-step explanation:

you just use the triangle sum theorem which states that the interior sum of angles is 180 degrees

The tangent linear function is:

y + 5.14 = (1/2)*(x - 1.18)

Two lines are parallel if the slope is the same one.

For the line:

x - 2y + 6 = 0

We can rewrite:

2y = x + 6

y = (1/2)*x + 3

The slope is (1/2).

Now, we want to find a line tangent to y = x⁴ - 6x

Parallel to the other one, so we need to differentiate and find the value of x such that the derivative is equal to 1/2

We need to solve:

1/2 = 4*x³ - 6

1/2 + 6 = 4x³

6.5/4 = x³

∛(6.5/4) = x

1.18 = x

Evaluating the function there, we will get:

f(1.18) = 1.18⁴ - 6*1.18 = -5.14

Then the linear function is:

y + 5.14 = (1/2)*(x - 1.18)

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Answer:

\(\boxed{\sf \ \ -15 \ \ }\)

Step-by-step explanation:

Hello

\(9\cdot\dfrac{12}{7}\cdot \dfrac{-35}{36}=-\dfrac{3*3*2*2*3*7*5}{7*3*2*3*2}=-15\)

as 9=3*3

12=4*3=2*2*3

35=7*5

36*6*6=2*3*2*3

hope this helps

Answer:

D is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

For the first question: You need to multiply 20 by 0.05 to find the sales tax amount in dollars, which gives you $1. The sales tax is equal to $1.

For the second question: To find the total cost, add $1 to $20 to get $21 as the total cost for the shirt.

Answer:

Proved

Step-by-step explanation:

Given

\(A = (-1,-1)\)

\(B = (-1,4)\)

\(C = (5,4)\)

\(D = (5,-1)\)

Required

Prove that PQRS is a rhombus

P = midpoint of AB

So:

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

\(P = \frac{1}{2}(-2,3)\)

\(P = (-1,\frac{3}{2})\)

Q = midpoint of BC

\(Q = \frac{1}{2}(-1+5,4+4)\)

\(Q = \frac{1}{2}(4,8)\)

\(Q = (2,4)\)

R = midpoint of CD

\(R =\frac{1}{2}(5+5,4-1)\)

\(R =\frac{1}{2}(10,3)\)

\(R = (5,\frac{3}{2})\)

S = midpoint of DA

\(S = \frac{1}{2}(5-1,-1-1)\)

\(S = \frac{1}{2}(4,-2)\)

\(S = (2,-1)\)

So, we have:

\(P = (-1,\frac{3}{2})\)

\(Q = (2,4)\)

\(R = (5,\frac{3}{2})\)

\(S = (2,-1)\)

To show that PQRS is a rhombus, the distance between PQ, QR, RS and SW must be equal.

Distance is calculated as:

\(D = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\)

For PQ

\(D_1 = \sqrt{(-1-2)^2 + (\frac{3}{2}-4)^2}\)

\(D_1 = \sqrt{(-3)^2 + (-\frac{5}{2})^2}\)

\(D_1 = \sqrt{9 + \frac{25}{4}}\)

\(D_1 = \sqrt{\frac{61}{4}}\)

For QR

\(D_2 = \sqrt{(2-5)^2 + (4-\frac{3}{2})^2}\)

\(D_2 = \sqrt{(-3)^2 + (\frac{5}{2})^2}\)

\(D_2 = \sqrt{9 + \frac{25}{4}}\)

\(D_2 = \sqrt{\frac{61}{4}}\)

For RS

\(D_3 = \sqrt{(5-2)^2 + (\frac{3}{2}-(-1))^2}\)

\(D_3 = \sqrt{(5-2)^2 + (\frac{3}{2}+1)^2}\)

\(D_3 = \sqrt{(3)^2 + (\frac{5}{2})^2}\)

\(D_3 = \sqrt{9 + \frac{25}{4}}\)

\(D_3 = \sqrt{\frac{61}{4}}\)

For SP

\(D_4 = \sqrt{(2-(-1))^2+(\frac{3}{2}-(-1))^2}\)

\(D_4 = \sqrt{(2+1))^2+(\frac{3}{2}+1)^2}\)

\(D_4 = \sqrt{(3)^2 + (\frac{5}{2})^2}\)

\(D_4 = \sqrt{9 + \frac{25}{4}}\)

\(D_4 = \sqrt{\frac{61}{4}}\)

From the calculations above:

\(D_1 =D_2 =D_3 =D_4 = \sqrt{\frac{61}{4}}\)

Hence: PQRS is a rhombus

The solution to the given inequality as represented in the task content are; z < - 1.00485413 OR z > 1.00485413.

It follows from the task content that the solution of the given inequality; ( 29 / 289z ) < ( 16 / 161 ) z is to be determined.

Since the given inequality is;

( 29 / 289z ) < ( 16 / 161 ) z

By cross multiplication; we have;

161 × 29 < ( 16z × 289z )

( 161 × 29 ) / ( 16 × 289 ) < z²

1.00973183 < z²

Therefore;

1.00485413 < z. OR. -1.00485413 > z.

Ultimately, z < - 1.00485413 OR z > 1.00485413.

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The function f can be implemented using a single 4-to-1 multiplexer and two inverters.

A 4-to-1 multiplexer is a digital logic component that selects one of four input signals based on the select lines. It has four data inputs (D0, D1, D2, D3), two select lines (S0, S1), and one output (Y). By properly connecting the inputs and select lines, we can realize the desired function f.

To implement the function f using a single 4-to-1 multiplexer and two inverters, we need to carefully assign the input signals and select lines to achieve the desired behavior. The truth table of the function f will guide us in determining the appropriate connections.

First, we can use the inverters to complement the required inputs if needed. Then, we can connect the complemented and uncomplemented inputs to the select lines of the multiplexer. The output of the multiplexer will be the result of the function f.

By carefully selecting the input assignments and connections, we can effectively implement the function f using a single 4-to-1 multiplexer and two inverters. This approach offers a compact and efficient solution for realizing the desired logic function.

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Cosine of ∠U is 28/53 in proper fraction, 28/53 in improper fraction, 0.52609 in whole number.

The cosine of an angle in a right triangle can be found using the ratio of the adjacent side to the hypotenuse. In this triangle, the adjacent side to ∠U is 28 and the hypotenuse is 53.

cos(∠U) = adjacent side ÷ hypotenuse = 28 ÷ 53 = 28/53

So, the cosine of ∠U is 28/53, written as a proper fraction.

Now let's convert cosine of ∠U is 28/53 in improper fraction:

The cosine of ∠U, which is 28/53, can be expressed as an improper fraction by dividing both the numerator and denominator by their greatest common factor.

gcd(28, 53) = 1, so the fraction cannot be further simplified.

Therefore, the cosine of ∠U, expressed as an improper fraction, is 28/53.

Now let's convert cosine of ∠U is 28/53 in whole number:

The cosine of ∠U, which is 28/53, can be expressed as a whole number by dividing the numerator by the denominator.

28 ÷ 53 = 0.526087

So, the cosine of ∠U expressed as a whole number is approximately 0.52609

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_____ The given question is not correct, so correct Question is:

Find the cosine of ∠U in Triangle UTV with side:

UV=28

VT=45

TU=53

Simplify your answer and write it as a proper fraction, improper fraction, or whole number.

Answer:

x = 2y + 6

Step-by-step explanation:

-x + 2y = -6

-x = -6 - 2y

x= 6 + 2y

x = 2y + 6

Therefore, the correct answer is (A).

To parameterize the portion of the plane

\(�+�+�=\)

4

x+y+z=4 that lies in the first octant, we need to find expressions for

\(�x, �y, and �\)

z in terms of parameters

\(�u and �v\)

that satisfy the given conditions.

In the first octant, all three coordinates,

\(�x, �y, and �z,\)

are positive.

Let's consider the parameterization options provided:

\((A) (�,�,4−�−�)(u,v,4−u−v), 0≤�≤10≤u≤1, 0≤�≤10≤v≤1\)

This parameterization satisfies the equation of the plane

\(�+�+�=4x+y+z=4, and the conditions �≥0x≥0, �≥0y≥0, �≥0z≥0\) for the first octant. So, option (A) is a valid parameterization.

To confirm, let's substitute the expressions for

\(�x, �y, and �\)

z into the equation of the plane:

\(�+�+�=�+�+4−�−�=4x+y+z=u+v+4−u−v=4\)

The equation holds true, so option (A) is a valid parameterization for the portion of the plane

\(�+�+�=4x+y+z=4\)that lies in the first octant.

Therefore, the correct answer is (A).

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It will take all three pumps, Working together, 1.56 minutes to fill the pool.

The given information, we can write three equations as follows:

1) (1/A + 1/B)*35 = C  ---(Equation 1)

2) (1/B + 1/C)*40 = C  ---(Equation 2)

3) (1/A + 1/C)*56 = C  ---(Equation 3)

We want  how many minutes it will take all three pumps, working together, to fill the pool, so let's represent the time taken by all three pumps working together as "t".

When all three pumps work together, they can fill the pool in one minute, so their combined rate is 1/C.

Using the rate formula, we can write the following equation:

1/A + 1/B + 1/C = 1/t   ---(Equation 4)

We have four unknowns (A, B, C, and t), so we need to solve for one of them to get the answer. Let's solve for "t".

First, we can simplify Equations 1, 2, and 3 as follows:

1) 1/A + 1/B = C/35

2) 1/B + 1/C = C/40

3) 1/A + 1/C = C/56

Next, we can substitute these equations into Equation 4 to get:

(C/35) + (C/40) + (C/56) = 1/t

Now, we can simplify and solve for "t":

LCD = 39200

1120C + 980C + 700C = 39200

2800C = 39200

C = 14

Substituting this value of "C" into any of the simplified equations, we can solve for "A" and "B". Let's use Equation 1:

1/A + 1/B = 14/35

5(A+B) = 98

A+B = 19.6

Now we can use A+B+C = 1/t to solve for "t":

t = 1 / (A+B+C) = 1 / (19.6 + 14) = 0.026 hours = 1.56 minutes

Therefore, it will take all three pumps, working together, 1.56 minutes to fill the pool.

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Answer:

The ship is approximately 100 km to the Port.

Step-by-step explanation:

The sketch to the question gives a triangle with two sides and an included angle. Let the distance from the Port to the stopping point of the ship be represented by c. It can be determined by the application of cosine rule. Cosine rule states that:

\(c^{2}\) = \(a^{2}\) + \(b^{2}\) -2ab Cos C

a = 50 km

b = 60 km

C = 51 + 80 = \(131^{o}\)

So that;

\(c^{2}\) = \(50^{2}\) + \(60^{2}\) -2(50 x 60) Cos \(131^{o}\)

   = 2500 + 3600 -6000 x -0.6561

   =  6100 + 3936.6

\(c^{2}\) = 10036.6

c = \(\sqrt{10036.6}\)

  = 100.183

c = 100.18 km

Thus, the ship is approximately 100 km to the Port.

There are 13.5 cubic meters of water in Mr. Johnson's pool.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

To find the volume of water in Mr. Johnson's pool, we need to multiply the length, width, and depth of the pool. The length is 2.5 meters, the width is 4.5 meters, and the depth of water is 1.2 meters.

So, the volume of water in Mr. Johnson's pool is:

2.5 meters x 4.5 meters x 1.2 meters = 13.5 cubic meters

Therefore, there are 13.5 cubic meters of water in Mr. Johnson's pool.

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Answer:

-3=b

Step-by-step explanation:

Hey there!

In order to find the value for b, we must first combine all like terms

-11-6b+3=16+2b

-8-6b=16+2b

-24=8b

Now we simplified the equation to a point where we can find the value of b in one step

-24/8 = 8b/8

-3=b

Answer:

-3

Step-by-step explanation:

Bring to the right of = the Number with b and to the left the other.

Remember to change sign of Number when you switch

So

\( - 11 + 3 - 16 = 2b + 6b\)

Do addition

\( - 24 = 8b\)

Find b

\(b = - 24 \div 8\)

b= -3

Given that the correlation between two variables is r=0.23. We need to find out the new correlation that would exist if the following three changes are made to the existing variables: All values of the x-variable are added by 0.14. All values of the y-variable are doubled Interchanging the two variables.  the correct option is B. 0.37.

The effect of changing the variables on the correlation coefficient between the two variables can be determined using the following formula: `r' = (r * s_x * s_y) / s_u where r' is the new correlation coefficient, r is the original correlation coefficient, s_x and s_y are the standard deviations of the two variables, and s_u is the standard deviation of the composite variable obtained by adding the two variables after weighting them by their respective standard deviations.

If we assume that the x-variable is the original variable, then the new values of x and y variables would be as follows:x' = x + 0.14 (since all values of the x-variable are added by 0.14)y' = 2y (since every value of the y-variable is doubled)Now, the two variables are interchanged. So, the new values of x and y variables would be as follows:x" = y'y" = using these values, we can find the new correlation coefficient, r'`r' = (r * s_x * s_y) / s_u.

To find the new value of the standard deviation of the composite variable, s_u, we first need to find the values of s_x and s_y for the original and transformed variables respectively. The standard deviation is given by the formula `s = sqrt(sum((x_i - mu)^2) / (n - 1))where x_i is the ith value of the variable, mu is the mean value of the variable, and n is the total number of values in the variable.

For the original variables, we have:r = 0.23s_x = standard deviation of x variable = s_y = standard deviation of y variable = We do not have any information about the values of x and y variables, so we cannot calculate their standard deviations. For the transformed variables, we have:x' = x + 0.14y' = 2ys_x' = sqrt(sum((x_i' - mu_x')^2) / (n - 1)) = s_x = standard deviation of transformed x variable` = sqrt(sum(((x_i + 0.14) - mu_x')^2) / (n - 1)) = s_x'y' = 2ys_y' = sqrt(sum((y_i' - mu_y')^2) / (n - 1)) = 2s_y = standard deviation of transformed y variable` = sqrt(sum((2y_i - mu_y')^2) / (n - 1)) = 2s_yNow, we can substitute all the values in the formula for the new correlation coefficient and simplify:

r' = (r * s_x * s_y) / s_ur' = (0.23 * s_x' * s_y') / sqrt(s_x'^2 + s_y'^2)r' = (0.23 * s_x * 2s_y) / sqrt((s_x^2 + 2 * 0.14 * s_x + 0.14^2) + (4 * s_y^2))r' = (0.46 * s_x * s_y) / sqrt(s_x^2 + 0.0396 + 4 * s_y^2)Now, we can substitute the value of s_x = s_y = in the above formula:r' = (0.46 * * ) / sqrt( + 0.0396 + 4 * )r' = (0.46 * ) / sqrt( + 0.1584 + )r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = r' = Therefore, the new correlation coefficient, r', would be approximately equal to.

Hence, the correct option is B. 0.37.

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Answer:

Step-by-step explanation:

12.6/4.2 = 3

Answer:-3

Step-by-step explanation:

Answer:

? ≈ 11.96

Step-by-step explanation:

using the Sine rule in the triangle

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\)

where a is the side opposite ∠ A and b the side opposite ∠ B

here a = 8, ∠ A = 40° , b = ? , ∠ B = 106° , then

\(\frac{8}{sin40}\) = \(\frac{?}{sin106}\) ( cross- multiply )

? × sin40° = 8 × sin106° ( divide both sides by sin40° )

? = \(\frac{8sin106}{sin40}\) ≈ 11.96 ( to the nearest hundredth )

Answer:

-1/9

Step-by-step explanation:

Answer:

Hi there your answer is -0.1 or -1/9

Step-by-step explanation:

You have to use pemdas so you start with parenthesis.

(-15/2)= -7.5.

Then, rewrite the equation so 5/6/-7.5.

5/6/-7.5= -0.1 or -1/9

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Answer:

The rule is "add 5, add 10, add 20" and the rule keeps doubling.

Answer:

P(7,4)= 840

Step-by-step explanation:

The distance from the top left corner of the foundation to the bottom right corner is 27 meters.

The distance between two points in space can be calculated using the Pythagorean theorem. In this case, we want to find the distance from the top left corner of the foundation to the bottom right corner.

To do this, we will use the length and width of the foundation, which are 20 meters and 18 meters respectively.

The Pythagorean theorem states that in a right triangle, the square of the distance (c) between the two points is equal to the sum of the squares of the other two sides (a and b). Mathematically, this can be represented as

=> c² = a² + b².

In our case, the two sides are the length (20m) and width (18m) of the foundation. To find the distance, we will first find the square of c by adding the squares of a and b. So,

=> c² = 20² + 18² = 400 + 324 = 724.

To find the distance, we will take the square root of c².

So,

c = √724 = 26.83

When we rounded to the nearest meter, c = 27m.

Complete Question:

The foundation of a building is in the shape of a rectangle, with a length of 20 meters(m) and a width of 18m. To the nearest meter, what is the distance from top left corner of the foundation to the bottom right corner.

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The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.

To define the supremum and infimum of the set A, we first need to determine the properties of the set.

The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.

To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.

Let's analyze the elements of A:

For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.

As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.

Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.

Again, analyzing the elements of A:

As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.

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