Prove that if A is a proper nonempty subset of a connected space X, then Bd(A) +0.

The function u(x, y) = xy is harmonic, and its harmonic conjugate is v(x, y) = (1/2)(x^2 - y^2).

(a) To show that u is harmonic, we need to demonstrate that it satisfies Laplace's equation, which states that the sum of the second partial derivatives of a function with respect to its variables is zero. For u(x, y) = xy, we have:

∂^2u/∂x^2 = 0, ∂^2u/∂y^2 = 0

Since both second partial derivatives are zero, u satisfies Laplace's equation, confirming that it is harmonic.

(b) To find the harmonic conjugate v(x, y) of u(x, y) = xy, we can apply the Cauchy-Riemann equations. According to these equations, for a function to have a harmonic conjugate, its partial derivatives must satisfy certain conditions. For u(x, y) = xy, the Cauchy-Riemann equations yield:

∂u/∂x = ∂v/∂y, ∂u/∂y = -∂v/∂x

Substituting u(x, y) = xy into the equations, we have:

y = ∂v/∂y, x = -∂v/∂x

Integrating the first equation with respect to y gives v(x, y) = (1/2)y^2 + g(x), where g(x) is an arbitrary function of x. Taking the derivative of v(x, y) with respect to x, we find:

∂v/∂x = g'(x)

Comparing this with x = -∂v/∂x, we see that g'(x) = -x. Integrating this equation gives g(x) = -(1/2)x^2 + c, where c is a constant. Therefore, the harmonic conjugate of u(x, y) = xy is v(x, y) = (1/2)(x^2 - y^2).

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Answer:

(5m-9n) (5m+9n)

Step-by-step explanation:

25m^2−81n^2

Rewriting each term

(5m)^2 - (9n)^2

This is the difference of squares

a^2 - b^2 = ( (a-b) (a+b)

(5m-9n) (5m+9n)

Answer:

(5m + 9n)(5m - 9n)

Step-by-step explanation:

we know a² - b² = (a + b)(a - b)

=>  Similarly, 25m² - 81n²

=> (5m + 9n)(5m - 9n)

Answer:

The answer is C

Step-by-step explanation:

At first glance, you'll notice that the line is going from left to right which tells us that the slope will be negative therefore the bottom option can be eliminated.

Knowing that the formula for slope is rise over run, you'll notice that the lines rises by -8 and runs by 3 which means that the slope would be -8/3.

This leaves us a final answer of  \(y=-\frac{8}{3}x-4\)

Answer:

A graph using y=mx+b would include a positive or negative line (slope) and a y-intercept. If there is a y-intercept between 1 & infinity then the line will not start on the origin. y=mx+b doesnt have to include a y-intercept though. It can include a y-intecept of 0. This would mean that the line would start on the origin. y=mx+b will ALWAYS be a straight line.

Step-by-step explanation:

Hope this helps :)

The equation used to represent the distance between two points A and B is AB  =  x Cos 28°

The equation can be defined as a mathematical statement made up of expressions. The length of the line that connects two points is known as the distance between the two points. A triangle is a closed shape with 3 sides, 3 angles and 3 vertices. Triangle is a 2- dimensional figure.

As per the given question,

Let the hypotenuse be x

The two points A and B are on the base of the triangle so,

Base - length = AB

The distance between the two points is

⇒   cos Θ   =   base / hypotenuse

where,      base = AB

                hypotenuse = x

⇒   cos Θ   =   AB / x

⇒   AB   =   x cos Θ      →   1

Substitute Θ  =  28 in 1,

⇒   AB = x cos 28°

Therefore, AB = x cos 28° is the equation used to represent the distance between two points A and B.

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The complete question is

When θ = 28° , which equation can be used to find the distance from point a to point b?

\( \large\color{lime}\boxed{\colorbox{black}{Answer : - }}\)

We know that, in ∆ABC,

∠A+∠B+∠C = 180°

But the triangle is right angled at C

ie., ∠C = 90°

Therefore, ∠A+∠B+ 90° = 180°

⇒ ∠A + ∠B = 90°

Therefore, cos(A + B) = cos 90º = 0

the parallel line is 2x+5y+15=0.

Step-by-step explanation:

ok I hope it will work

soo,

Solution

given,

given parallel line 2x+5y=15

which goes through the point (-10,1)

now,

let 2x+5y=15 be equation no.1

then the line which is parallel to the equation 1st

2 x+5y+k = 0 let it be equation no.2

now the equation no.2 passes through the point (-10,1)

or, 2x+5y+k =0

or, 2*-10+5*1+k= 0

or, -20+5+k= 0

or, -15+k= 0

or, k= 15

putting the value of k in equation no.2 we get,

or, 2x+5y+k=0

or, 2x+5y+15=0

which is a required line.

In any triangle, the greatest angle is opposite to the greatest side and the smallest angle is opposite to the smallest side.

Knowing that, first let's find the measure of the third angle, using the property that the sum of internal angles in any triangle is equal to 180°:

The smallest angle is C, so the smallest side is DE.

The greatest angle is E, so the greatest side is CD.

Therefore the order is:

DE < CE < CD

Answer:

10x=1/2(x+3)

Step-by-step explanation:

option b is the answer

Answer:

6

Step-by-step explanation:

Set up the equation to look like this:

6+7x=10x-12

then solve like normal

Answer:

240

Step-by-step explanation:

if she travels 1 mile per minute than she traveled 240. ! hour is 60 minutes so you would multiply 60 and 4 which gives you 240.

Answer: If you need a variable the answer is 4x

Step-by-step explanation:

Let x = the speed Shondra is going in mph.

4x= The miles Shondra drove

Answer:

I got c

Step-by-step explanation:

sorry if im wrong!

Answer:

I got C or B

Step-by-step explanation:

Not sure, Im not great at this stuff

Her mental age would be 8 yrs old.

IQ [ Intelligent Quotient ]  is a type of standard score that indicates how far above, or how far below, his/her peer group an individual stands in mental ability.

IQ of a person is given by the formula -

IQ = MA/CA * 100

IQ = Mental Age / Chronological Age * 100

According to the question, IQ = 100, CA = 8

⇒ 100 = MA / 8 *100

⇒1 = MA / 8

⇒ MA = 8 Yrs

Hence, the estimated mental age of susan is 8 yrs old.

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Answer:

y = 3x + 6

Step-by-step explanation:

Since the line is parallel, it has the same slope -- 3

y = 3x + b, sub point (1, 9)

9 = 3(1) + b

9 = 3 + b

b = 9 - 3

b = 6

y = 3x + b -- y = 3x + 6

Answer:

The area of the shaded region is 7π square centimeters.

Step-by-step explanation:

Note that Circle B has a radius of 3 cm, and the two smaller circles, Circles O and C, both have a radius of 1 cm.

The area of a circle is given by:

\(\displaystyle A = \pi r^2\)

Therefore, the area of Circle B, the entire circle, is:

\(\displaystyle \begin{aligned} A_B &= \pi (3)^2 \\ &= 9\pi \end{aligned}\)

The area of Circle O is:

\(\displaystyle \begin{aligned} A_O &= \pi (1)^2 \\ &= \pi \end{aligned}\)

And likewise, the area of Circle C is:

\(\displaystyle \begin{aligned} A_C &= \pi (1)^2 \\ &= \pi \end{aligned}\)

The area of the shaded area is the area of the Circle B subtracted by the area of Circles O and C. Hence:

\(\displaystyle A_\text{shaded} =A_B - \left(A_ O + A_ C\right)\)

Substitute and evaluate:

\(\displaystyle \begin{aligned} A_\text{shaded} &= (9\pi ) - (\pi + \pi) \\ &= 9\pi - 2\pi \\\ &= 7\pi \end{aligned}\)

The area of the shaded region is 7π square centimeters.

Answer:

x^4 +y+1

Step-by-step explanation:

The quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, -17) is \(-17(x-1)^{2}\).

The vertex form of a quadratic function is \(f(x) = a(x-h)^{2} + k\) where a, h, and k are constants and (h, k ) is the vertex of the graph of the function.

According to the given question we have

The graph has the vertex is (1, 0) and passes through (2, -17)

Since, the general form of a quadratic function in a vertex form  is

\(y = a(x-h)^{2}+ k\)

substitute, h = 1 and k = 0 in the above equation

⇒ \(y = a(x-1)^{2} +(0)^{2}...(i)\)

Also, the graph passes through the point (2, -17)

⇒ \(-17 = a(2-1)^{2}\)

⇒ -17 = a or a = -17

Substitute the value of a in equation (i).

⇒\(y = -17(x-1)^{2}\)

Therefore, the quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, -17) is \(-17(x-1)^{2}\).

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Answer:

ok number 9.) i believe its 7 if im wrong im so sorry

Step-by-step explanation:

Answer:

I will help with 10 i don't get 9 sorry so the answer is (a) F(5,4)

Step-by-step explanation:

So you have the midpoint and you put f(x, y) and D(-3,-8)

So

E=(x-3/2, y-8/2) =(1,-2) so

X-3/2 =1 , x-3=2 so x = 5

And y-8/2 = - 2. , so y-8 = - 4. , so y =4

So F =(5, 4)

The correct answer is option C. A sampling plan refers to a detailed strategy for obtaining a sample from a population for the purpose of data collection.

It describes the precise procedures needed to choose the sample, determine the members of the sample, and gather the data.

The sampling strategy should take into account the type of sampling design, sample size, sampling process, and the methods to be employed for data collecting.

The strategy for implementing sampling should be outlined in the plan, along with instructions on how to make sure the sample is representative of the population, how to prevent bias in the sampling process, and how to make sure the data gathered is of high quality.

A good sampling plan should provide a clear and consistent method for gathering data and be founded on basic statistical concepts.

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Answer:

Neither of them are right

Step-by-step explanation:

First, let's actually solve this equation:

8 ( x - 5 ) = 8x + 40

Distribute on the left:

8 ( x - 5 )

( 8 x X ) + ( 8 x ( -5 ) )

8x - 40

8x - 40 = 8x + 40

Add 40 to each side:

8x = 8x + 80

Subtract 8x from both sides:

0 = 80

0 ≠ 80

There are no solutions to the equation

Answer:

joe    

joe mama

++

Step-by-step explanation:

Answer:

16 + 104 = 120 square inches

Step-by-step explanation:

13 x 8 = 104

17 - 13 = 4

4 x 8 =32

32 divided by 2 is 16

so 16 +104 = 120

The model \(p = 200.3^d\) satisfies the statement, A population of cells starts at 200 and triples every day.

The formula for exponential growth is \(y = y_0.e^{(kt)}.\)

The formula for exponential decay is \(y = y_0.e^{(-kt)}.\)

Given, A population of cells starts at 200 and triples every day.

Where 'p' is the number of cells and 'd' is the number of days.

The situation is represented by \(p = 200.3^d\).

Now, Three times 200 is 600 and Nine times 200 is 1800.

At d = 1.

\(p = 200.3^1\).

\(p = 600\).

And,

At, d = 2.

\(p = 200.3^2\).

\(p = 1800\).

So, The model satisfies the statement and it is true.

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In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.

This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).

Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.

Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.

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Answer:

√5(√5 + √20)

= √5√5 + √5√20

= √25 + √100

= 5 + 10

= 15

The value of x is for the given polygons is 5.

In the given figure it is given that both the polygons are similar . They are just looking different. We can say that they are equivalent quadrilaterals.

From the figure , we can see that SR is equivalent to TW and PQ is equivalent to UV. Side PS is equivalent to TU and RQ is equivalent to WV.

So the the ration of the sides of length will also be equal.

∴ SR/PQ = TW/UV

⇒ x+1/ (10/3) = 9/5

⇒ x+1= 6

⇒x=5

Therefore, The value of x is for the given polygons is 5.

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The correct question is:

Find the value of x for the given polynomials. It is given that both polynomials are similar.

Answer:

C = 12.57 inches

Step-by-step explanation:

C=2πr

C=πd=π·4≈12.56637in

Answer:

for what you have you need to add one more $10 bill.

or make it total $120.25

good luck!!

The total amount each friend will get after split money equally is $120.25.

Given that;

The picture shows the $481 four friends worked together to earn.

And, They want to split this money equally.

Here, the total amount earn = $481

And, the number of friends = 4

Hence, the amount each friend will get,

$481/4 = $120.25

Therefore, the value of the amount is $120.25.

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When all samples are drawn from a single population, the mean of the distribution of differences should approximate 0.

When samples are drawn from a single population, the differences between pairs of samples should reflect the inherent variability within that population. If the population has a well-defined mean, the differences between pairs of samples will tend to cancel out, resulting in an average difference close to zero.

This is because the positive differences will be balanced by the negative differences, leading to an overall mean difference of approximately zero.

Therefore, option a, "0," is the correct answer. The mean of the distribution of differences should approach zero when all samples are drawn from a single population.

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