Divide. (25x^2 – 30x + 12) ÷ (5x – 4)

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:

2/6

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

∠ ABF + ∠ FBC = ∠ ABC , substitute values

7x + 20 + 2x - 5 = 159 , that is

9x + 15 = 159 ( subtract 15 from both sides )

9x = 144 ( divide both sides by 9 )

x = 16

Answer:

THe y intercept  is 30 and it represents the registration fee

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the diagonals of a parallelogram bisect each other , then

GX = XE , that is

3x - 5 = 2x ( subtract 2x from both sides )

x - 5 = 0 ( add 5 to both sides )

x = 5

Then

DF = 5x + 1 = 5(5) + 1 = 25 + 1 = 26 , so

XF = \(\frac{1}{2}\) DF = \(\frac{1}{2}\) × 26 = 13

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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Answer:

$1.89 per pound

Step-by-step explanation:

$7.56÷4

The inverse function f^(-1)(x) for f(x) = (8x + 3) / (5x + 3) is f^(-1)(x) = (3x - 3) / (8 - 5x). Hence, (3x - 3) / (8 - 5x) is the correct answer.

To find the inverse function f^(-1)(x) for f(x) = (8x + 3) / (5x + 3), we can switch the roles of x and f(x) and solve for f^(-1)(x).

Let y = f(x), then the equation becomes y = (8x + 3) / (5x + 3).

To find f^(-1)(x), we swap x and y and solve for x: x = (8y + 3) / (5y + 3).

Now, we rearrange the equation to isolate y: 5yx + 3x = 8y + 3.

Next, we solve for y: y(5x - 8) = 3 - 3x, giving y = (3 - 3x) / (5x - 8).

Therefore, the inverse function f^(-1)(x) is f^(-1)(x) = (3x - 3) / (8 - 5x).

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Answer:178176cm3

Step-by-step explanation:

to find the volume of a rectangular box(prism) use length times width times height or in this case 64x48x58 and because you are multiplying the cm as well its cubed.

The statement about systematic errors that is true is: They can occur when a selection bias is present.

Systematic errors can be defined as a type of error that affects the accuracy of the results of an experiment or study. It is mostly caused by the tools, materials, or a particular problem with the instrument used in the experiment. A systematic error can be of different types, including the following:

Scale Error: Scale errors occur due to calibration issues. They can occur due to a problem with the measuring instruments, which may not provide accurate readings during an experiment.

Selection Bias: It occurs when a researcher deliberately selects a certain group of individuals or data that are not representative of the general population. This can lead to inaccurate results for the study.

Resolution Error: This error is common when researchers do not choose the correct measurement tools to measure the variables of interest.

Therefore, option A is correct. This is because systematic errors can occur when a selection bias is present.

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Answer:

A

Step-by-step explanation:

   It would be A, because the two bisector lines that cut through this trapezoid  are the same length, so 5.9-4.1=1.8. So the length of RN would be 1.8. Hope this helps!

Answer:

1.8

Step-by-step explanation:

Answer:

THE ANDER IS EHE DUDUDUSU

Answer:

80 & 105

Step-by-step explanation:

The height of the next bounce which is on the third bounce will be 12.8 feet.

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

Then the common ratio is given as,

r = 80 / 200

r = 0.40

The height of the next bounce will be given as,

a₄ = 200 · (0.4)⁴⁻¹

a₄ = 200 · (0.4)³

a₄ = 200 · 0.064

a₄ = 12.8 feet

The height of the next bounce which is on the third bounce will be 12.8 feet.

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Answer:

25h + 12

Explanation:

21h -10h + 14h + 16 -9 +5  ( group term )

25h + 12                             ( simplified )

Answer:

\(25h+12\)

Step-by-step explanation:

To do this, we need to combine like terms:

\(21h-10h+14h+16-9+5\)

Combine terms that have "h" with each other.

\(11h+14h+16-9+5\)

\(25h+16-9+5\)

Now, combine the rest of the terms that don't have "h".

\(25h+7+5\)

\(25h+12\)

The sides of 15mm, 28mm and 11mm are the sides of a triangle.

To determine if three given lengths can form a triangle, we can apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

If we add the two shorter sides together, we get \(15 + 11 = 26\)  . This sum is greater than the longest side, which is \(28\) . Similarly, if we add the two smaller sides to the longest side, we get  \(11 + 28 = 39\) and  \(15 + 28 = 43\) , which are both greater than the remaining side.

Therefore, the three given lengths satisfy the Triangle Inequality Theorem and can form a triangle.

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Math SAT scores explain about 98.7% of the variation in the total SAT scores.

In statistics, correlation or dependence exists as any statistical relationship, whether causal or not, between two random variables or bivariate data.

A correlation exists as a statistical measure (expressed as a number) that defines the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable exists as the cause of the change in the values of the other variable.

Since r² exists = (0.9935)² = 0.9870, we interpret r² as 98.7% of the variation in the y variable exists explained by the x variable.

In context, math SAT score explains about 98.7% of the variation in total SAT score.

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The probability that the jury makes the correct decision is 0.9999

This is a binomial distribution problem where the event of interest is a juror making a correct decision (voting guilty) and the number of trials is 12 (the number of jurors).

The probability of a single juror making the correct decision is 0.80. Therefore, the probability of a single juror making the incorrect decision (voting not guilty) is 1 - 0.80 = 0.20.

To calculate the probability that at least 10 out of 12 jurors make the correct decision (voting guilty) if the defendant is guilty, we can use the binomial distribution formula:

P(X ≥ 10) = 1 - P(X < 10)

where X is the number of jurors who make the correct decision.

Since the probability of a single juror making the correct decision is 0.80, we can use the binomial probability formula to calculate the probability of X jurors making the correct decision

P(X = x) = (12 choose x) * 0.80^x * 0.20^(12-x)

where (12 choose x) is the number of ways to choose x jurors out of 12.

Using this formula, we can calculate the probability of fewer than 10 jurors making the correct decision:

P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)

We can use a calculator or software to calculate this probability:

P(X < 10) = 0.00000436

Therefore, the probability of at least 10 out of 12 jurors making the correct decision if the defendant is guilty is:

P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.00000436 = 0.99999564

Rounding to four decimal places, the probability is 0.9999.

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The correct answer is option B: Yes, because the function is continuous on the interval (-1,2] and differentiable on the interval (-1,2).

The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) where the instantaneous rate of change (the derivative) is equal to the average rate of change over the interval [a, b].

In this case, the function f(x) = -8 + x^2 is continuous on the closed interval [-1, 2] because it is a polynomial function, and polynomials are continuous everywhere. It is also differentiable on the open interval (-1, 2) because it is a differentiable function.

Therefore, by meeting the criteria of continuity on the closed interval and differentiability on the open interval, the Mean Value Theorem applies to the function f(x) = -8 + x^2 on the interval (-1, 2].

To find the point(s) guaranteed to exist by the Mean Value Theorem, we can determine the average rate of change of the function over the interval (-1, 2]. The average rate of change is given by (f(b) - f(a))/(b - a), where a and b are the endpoints of the interval.

Using the formula, we have:

Average rate of change = (f(2) - f(-1))/(2 - (-1)) = (-4 - (-7))/(2 + 1) = (-4 + 7)/3 = 1/3.

This means that there exists at least one point c in the interval (-1, 2) where the instantaneous rate of change (the derivative) of the function f(x) = -8 + x^2 is equal to 1/3.

In summary, the Mean Value Theorem applies to the function f(x) = -8 + x^2 on the interval (-1, 2]. It guarantees the existence of at least one point c in the open interval (-1, 2) where the instantaneous rate of change (the derivative) is equal to the average rate of change, which is 1/3.

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Recall that n factorial is equal to

Therefore, 3!

Answer:

-3/2

Step-by-step explanation:

You can do this using slope formula, y2-y1/x2-x1.

We first substitute in the numbers--> -2 - 13/ 6 - (-4)

Then we simplify to get--> -15/10 = -3/2

You could also graph the points and find the rise over run.

Hope this helps!

The value of interquartile range (IQR) of the data set which is plotted in the dot plot 1,2,3,3,4,4,4,6 is 1.5.

The interquartile range (IQR) of the data is the middle half of the data, which contains 2nd and 3rd quartiles.

Interquartile range is the difference of third quartile and first quartile.

IQR=Q₃-Q₁

In the dot plot below, the data is given as,

1,2,3,3,4,4,4,6

The first quartile is the medium of the lower half, while the third quartile is the medium of the upper half. For the above data,

Q_1=2.5

Q_3=4

Thus, Interquartile range is,

IQR=Q₃-Q₁

IQR=4-2.5

IQR=1.5

Hence, the value of interquartile range (IQR) of the data set which is plotted in the dot plot 1,2,3,3,4,4,4,6 is 1.5.

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The length of the two line segments together is 80 cm

Step 1: Convert 500mm into cm.

We know that the value of 1mm is equal to 0.1 cm.

Then,  500mm will be  500mm*0.1 = 50 cm.

Therefore, the second line segment is  50 cm long.

Step 2: Calculate total length.

Let the first line segment be L1= 30 cm long and the second line segment be L2= 50 cm long.

Now, the total length is

L = L1 + L2

Substitute the values L1= 30 cm and  L2= 50 cm in L = L1 + L2.

Hence, the length of the two line segments together is 80 cm

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Answer:

the solution points for the system of equations are (3, 25) and (-7/2, -7).

Step-by-step explanation:

We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:

Substitute y = 2x^2 + 5x - 10 into the second equation:

4x - (2x^2 + 5x - 10) = -11

Simplifying the left side of the equation:

4x - 2x^2 - 5x + 10 = -11

Rearranging the terms:

2x^2 - x + 21 = 0

Using the quadratic formula:

x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)

x = (1 ± sqrt(169)) / 4

x = (1 ± 13) / 4

Simplifying:

x = 3 or x = -7/2

Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:

For x = 3:

y = 2(3)^2 + 5(3) - 10 = 25

So one solution point is (3, 25).

For x = -7/2:

y = 4(-7/2) + 11 = -7

So the other solution point is (-7/2, -7).

Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).

Hence, the diameter of the shaft is 40 mm (rounded to one decimal place).

Given, The shaft is of mild steel, having an ultımate shearıng stress of 345MPa.

The line shaft running at 150r/m, transmitting 44.7 kW is subjected to torsion only.

Using a factor of safety of 6, calculate its diameter.

Mild steel has an ultimate shear strength of 345MPa.

Factor of Safety = 6Let the diameter of the shaft be d.

Torsion formula for hollow shafts:

Shearing stress, τ = 16T/πd³where,T is the torque on the shaft

d is the diameter of the shaft.

Length of the shaft, l = 1 meter

Power transmitted, P = 44.7 kW

= 44,700

Wattsspeed of rotation, N = 150 rpm

The torque on the shaft T = (60P)/(2πN)

= (60 × 44,700)/(2 × π × 150)

= 22,355 Nm

Shearing stress, τ = 16T/πd³τ

= (16 × 22,355)/(πd³) τ

= (356,880)/(πd³)

Let the allowable shear stress be τallτall = τ/FS345

= (356,880)/(πd³ × 6)

The diameter of the shaft, d = 0.04 meters = 40 mm

The diameter of the shaft is 40 mm.

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Hypotheses are always statements about the d. population parameters

Hypotheses are assertions or claims concerning population characteristics stated in statistics. An attribute or value of a population, such the population mean or percentage, is referred to as a population parameter. Based on sample data, hypothese are developed to draw conclusions or inferences about these population attributes.

The hypothesis can be expressed as comparisons of population metrics or as statements of equality or inequality. They serve as a basis for statistical studies and are used to examine certain assertions or research hypotheses. Finding pertinent solutions to the scientific inquiry is the main goal of the hypothesis. It is supported by a few evidences, and experimental methods are used to test the whole statement of the hypothesis.

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Complete Question:

Hypotheses are always statements about which of the following?  choose the correct answer below.

a. sample statistics

b. sample size

c. estimators

d. population parameters

Step-by-step explanation: