what number must be added to 1,575 to result in the sum of 8,625

Stokes' theorem is a fundamental theorem in vector calculus that relates the surface integral of a vector field over a closed surface to the line integral of the vector field around the boundary of that surface.

To evaluate the line integral ∫C F · dr using Stokes' theorem, we need to find the curl of the vector field F and calculate the surface integral of the curl over the surface enclosed by the curve C.

First, let's find the curl of the vector field F(x, y, z) = ⟨y^2, xy, xz⟩:

∇ × F =

| i j k |

| ∂/∂x ∂/∂y ∂/∂z |

| \(y^2\) xy xz |

Expanding the determinant, we have:

∇ × F = (z - y) i + 0 j + (x - 2y) k

Now, let's find the surface enclosed by the curve C, which is the intersection of the cylinder \(x^2 + (y - 1)^2 = 1\) with the plane y = z. This means we have:

\(x^2 + (y - 1)^2 = 1\)

y = z

Substituting y = z into the equation of the cylinder, we get:

\(x^2 + (z - 1)^2 = 1\)

This is the equation of a circle in the x-z plane centered at (0, 1) with a radius of 1.

Next, we need to calculate the surface integral of the curl over this surface. Since the surface is a circle lying in the x-z plane, we can parametrize it as:

r(u) = ⟨r cos(u), 1, r sin(u)⟩

where u is the parameter ranging from 0 to 2π, and r is the radius of the circle (in this case, r = 1).

Now, we can compute dr:

dr = ⟨-r sin(u), 0, r cos(u)⟩ du

Substituting the values into the curl, we have:

∇ × F = (r cos(u) - 1) i + 0 j + (r cos(u) - 2) k

Taking the dot product of F and dr, we get:

F · dr = (\(y^2\))(-r sin(u)) + (xy)(0) + (xz)(r cos(u))

= -r \(y^2\) sin(u) + 0 + r xz cos(u)

= -r(\(1^2\)) sin(u) + 0 + r(r cos(u))(r cos(u) - 2)

= -r sin(u) + \(r^3\)(\(cos^2\)(u) - 2cos(u))

Now, we can integrate this expression over the parameter u from 0 to 2π:

∫C F · dr = ∫₀²π [-r sin(u) + \(r^3\) (\(cos^2\)(u) - 2cos(u))] du

Integrating term by term, we get:

\(\int_C F \cdot dr &= \left[ -r(-\cos u) + \frac{r^3}{3} (\sin u - \sin(2u)) \right]_0^{2\pi} \\&= r(1 - \cos(2\pi)) + \frac{r^3}{3} (\sin(2\pi) - \sin(4\pi)) - \left[ r(1 - \cos(0)) + \frac{r^3}{3} (\sin(0) - \sin(0)) \right] \\&= r(1 + 0) + \frac{r^3}{3} (0 - 0) - \left[ r(1 + 0) + \frac{r^3}{3} (0 - 0) \right] \\&= 0\)

Therefore, the line integral ∫C F · dr evaluates to zero using Stokes' theorem.

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Answer:

450 kilo watt hour of electricity was used

Step-by-step explanation:

Here, we are interested in calculating the kilowatt-hour of electricity used.

From the question, we are told that the bill is $67.50 and the cost of 1 kilo watt hour is $0.15

So to know the amount of kilowatt hours of electricity used, we will simply divide the bill by the charge per 1 kwh

Mathematically that would be 67.5/0.15 = 450

Answer:

32

Step-by-step explanation:

12 * (3 + 2²) / 2 - 10

12(3 + 4) / 2 - 10

12(7) / 2 - 10

84 / 2 - 10

42 - 10

32

Best of Luck!

Answer:

Step-by-step explanation:

\(12\times (3+2^2)\div 2-10\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3+2^2\right)\:\\:\quad 7\\\\=12\times \:7\div \:2-10\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:12\times \:7\div \:2\:\\:\quad 42\\\\=42-10\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:42-10\:\\:\quad 32\)

(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/2

(B) Coordinates of Δ P"Q"R"

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (8,0),

Q(6,2)

R(-2,-4)

Coordinates of P'Q'R' are

P′(4, 0)

Q′(3, 1)

R′(−1, −2)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = \(D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

Where D = Distance between two points

from distance formula we can write that

PQ = \(\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}\)

Similarly

P'Q'= √2

PQ /P'Q' = 2

hence the scale factor of dilation is 1/2 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

(x,y) as (-x,y)

So the Coordinated of Δ P"Q"R" can be written as

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

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Answer:

3 roots.

Step-by-step explanation:

To determine how many roots a polynomial has, you have to look at the term with the highest exponent. That exponent is how many roots the polynomial will have.

Then, for:

Since this polynomial is factored already equalizing 0, we can see that there are three roots:

The main answer is that the infinite number of types of matter arises from the unique combinations of elements and their arrangements in terms of composition and geometry.

While the number of elements is limited, their combinations and arrangements allow for an infinite number of types of matter. Elements can combine in different ratios and configurations, forming various compounds and structures with distinct properties.

Additionally, the arrangement of atoms within a molecule or the spatial arrangement of molecules within a material can create different types of matter. These factors, along with the possibility of isotopes and different states of matter, contribute to the vast diversity and infinite types of matter despite the limited number of elements.

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Explanation:

We'll use the rule

x^y*x^z = x^(y+z)

This says that when we multiply exponential expressions with the same base, we add the exponents. In this case, the base is 2 so x = 2.

The exponents we're adding are -4 and 2

So,

2^(-4)*2^2 = 2^(-4+2) = 2^(-2)

This matches up with the a^b to show that a = 2 and b = -2

Furthermore, we'll use the rule that x^(-y) = 1/(x^y) to go from 2^(-2) to 1/(2^2) = 1/4 which is the value of c.

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer:

14

Step-by-step explanation:

You are told that the line segment MO has a total length of 20.

You are also told that point N is somewhere on that line between M and O.  They tell you that the distance from point N to point O is 6.  So to find the distance from point N to point M, you just subtract the length of N to O from the total length of the M to O segment.

                                                                           N to O = 6                                                

<-----M---------------------------------------------------N--------------------O------------------>

                                                    M to O = 20

So if M to O = 20 and you subtract the distance of N to O (6), you will get the distance from M to N.

Answer:

2

Step-by-step explanation:

The radical rule : \(\sqrt[3]{2^{3} }\) = 2  when the number inside is greater than or equal to 0

Answer:

60%

Step-by-step explanation:

Step-by-step explanation:

click the photo there is answer

Answer:

see explanation

Step-by-step explanation:

Substituting y = 3x - 4 into the equation gives

7x - 5(3x - 4) = 4 ← distribute and simplify left side

7x - 15x + 20 = 4

- 8x + 20 = 4 ( subtract 20 from both sides )

- 8x = - 16 ( divide both sides by - 8 )

x = 2

Substitute x = 2 into y = 3x - 4

y = 3(2) - 4 = 6 - 4 = 2

Answer:

hey here is ur answer

the perimeter of a square = 4* side

4*s=14

S = 14/4

s= 7/2 or 3.5

area = side * side

area = (7/2) sq

area = 12.25sq m

Step-by-step explanation:

Cyphon, this is the solution:

We have to multiply the following fractions:

7/12 * 4/3

7 * 4 / 12 * 3

28/36

Simplifying, we have:

7/9 (Dividing by 4 numerator and denominator)

We have to add the following fractions:

- 1/2 + 4/9

Let's find the lowest common denominator between 2 and 9, as follows:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

9, 18, 27, 36

The lowest common denominator is 18

The probability of making spaghetti for dinner tonight, given you already made chicken for dinner, is 0.67.

To find the probability of making spaghetti or chicken for dinner, we need to find the union of the two events.

P(Spaghetti or Chicken) = P(Spaghetti) + P(Chicken) - P(Spaghetti and Chicken)

P(Spaghetti or Chicken) = 0.43 + 0.54 - 0.36 = 0.61

b. To find the probability of making spaghetti for dinner tonight, given you already made chicken for dinner, we use conditional probability.

P(Spaghetti | Chicken) = P(Spaghetti and Chicken) / P(Chicken)

We know that P(Chicken) = 0.54 and P(Spaghetti and Chicken) = 0.36.

Therefore,

P(Spaghetti | Chicken) = 0.36 / 0.54 = 0.67

So the probability of making spaghetti for dinner tonight, given you already made chicken for dinner, is 0.67.

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If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.

In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.

The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.

If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.

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Answer:

0

Step-by-step explanation:

V-5V = -4V

-4V-5V = -9V

-9V+9V = 0

Answer:

AB is 5 + √2 or 6.41421356237

Step-by-step explanation:

triangle with the A is a

3, 4, 5 triangle

its hypotenuse is 5

triangle with the B is a

1, 1, √2 triangle

its hypotenuse is √2

AB is 5 + √2

Answer:

7/11 over 28/11

15/4 over 15

13/16 over 13/4

Step-by-step explanation:

Pythagoras' theorem is a basic relationship between the three sides of a right triangle. The length of the entire walkway to the nearest hundredth of a yard is 50.24 yds.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

In order to calculate the length of the walkway, we need to calculate the value of b first. Therefore,  the value of b using the Pythagoras theorem can be written as,

\(D^2=12^2+b^2\\15^2=12^2+b^2\\225=144+b^2\\b^2= 81\\b=9\)

As we  got the value of b, now the value of each of the four hypotenuses can be written as,

\(A = \sqrt{12^2+8^2} = \sqrt{208}=14.422\\\\B=\sqrt{6^2+8^2}=\sqrt{100} = 10\\\\C =\sqrt{6^2+9^2}=\sqrt{117} = 10.82\\\\D = 15\)

Adding the value of all the hypotenuse to get the length of the walkway, therefore, the length will be,

\(Sum = A+B+C+D = 14.422+10+10.82+15 = 50.24\)

Hence, the length of the entire walkway to the nearest hundredth of a yard is 50.24 yds.

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f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

The piecewise function for this problem is defined as follows:

A piece-wise function is a function that has different definitions, depending on the input of the function.

Between x = -3 and x = -1, the linear function has a slope of 1, with a x-intercept of -3, meaning that the parent function y = x was shifted left 3 units, hence it is given as follows:

f(x) = x + 3, -3 ≤ x < -1

Between x = -1 and x = 1, the function is constant at y = 5, hence it is given as follows:

f(x) = 5, -1 ≤ x ≤ 1.

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The statement is true that 95% of all possible sample means will fall above 76.71.

We know that the sample mean can be calculated using the formula;

\($\bar{X}=\frac{\sum X}{n}$\).

Given that the mean is 80 and the variance is 400 for the population and the sample size is 100. The standard deviation of the population is given by the formula;

σ = √400

= 20.

The standard error of the mean can be calculated using the formula;

SE = σ/√n

= 20/10

= 2

Substituting the values in the formula to get the sampling distribution of the mean;

\($Z=\frac{\bar{X}-\mu}{SE}$\)

where \($\bar{X}$\) is the sample mean, μ is the population mean, and SE is the standard error of the mean.

The sampling distribution of the mean will have the mean equal to the population mean and standard deviation equal to the standard error of the mean.

Therefore,

\(Z=\frac{76.71-80}{2}\\=-1.645$.\)

The probability of the Z-value being less than -1.645 is 0.05. Since the Z-value is less than 0.05, we can conclude that 95% of all possible sample means will fall above 76.71.

Conclusion: Therefore, the statement is true that 95% of all possible sample means will fall above 76.71.

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The function we have is:

The steps to find the inverse function are:

Step 1. Solve for x.

In this case, we solve for x by dividing both sides of the equation by 4:

Step 2. Change f(x) for x, and x for the inverse function f^-1(x):

If we call this inverse function h(x) we get the result:

Answer:

Step-by-step explanation:

As per definition the vertical angles are equal

Finding the value of x

Finding the angle measure

Answer:

12x² - 40

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

As a square has four sides of equal length, the perimeter of a square is four times the length of one side.

\(\begin{aligned}\textsf{Perimeter}&=4(3x^2-10)\\&=4 \cdot 3x^2+4 \cdot (-10)\\&=12x^2-40\end{aligned}\)

Answer:

Perimeter of square = 12x² - 40

Step-by-step explanation:

Perimeter of square formula,

→ P = 4 × Side

→ [ P = 4a ]

Now the perimeter of square is,

→ P = 4 × (3x² - 10)

→ P = 4(3x²) - 4(10)

→ P = (4 × 3)x² - 40

→ [ P = 12x² - 40 ]

Hence, perimeter is 12x² - 40.

Answer:

you have to take away you word they said how many