The Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).
What is Green's function?
Green's function is an important mathematical tool used to solve differential equations. It is defined as a solution to a homogeneous linear differential equation with a source, or delta, function as its input. Green's functions are also known as impulse response functions and can be used to describe the response of a system to an arbitrary input. Green's functions provide a way to solve differential equations without having to solve the entire equation all at once. They are particularly useful for solving equations with boundary conditions that are difficult to solve without the use of Green's functions. Green's functions can also be used to solve integral equations and provide a powerful tool for solving many physical problems.
The reflection method for finding a Green's function for a problem on a semicircular region can be used as follows. First, we solve the problem on the half-plane by finding a Green's function G(x, xo) that satisfies the boundary conditions given. Then, we reflect the solution across the boundary of the semicircle, namely T1 and T2, to obtain the Green's function on the entire semicircle.
The Green's function on the half-plane is given by G(x, xo) = მ (x-xo). Using this solution, we can reflect it across the boundary of the semicircle. For T1, the reflected solution is given by G(x, xo) = მ (x-xo)cos(θ), where θ is the angle between the normal vector to T1 and the vector from xo to x. For T2, the reflected solution is given by G(x, xo) = მ (x-xo)sin(θ), where θ is the angle between the normal vector to T2 and the vector from xo to x.
Therefore, the Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).
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Now select point D, and move it around. You will notice that moves with point D but remains parallel to . Check the box labeled Show Ratios of Intersected Segments to see the ratios AD : DB and AE : EC. What do you notice about the ratios as you move point D?
Answer: The ratios change as the position of D changes, but the two ratios remain equal to each other.
Step-by-step explanation:
Answer:
The ratios change as the position of D changes, but the two ratios remain equal to each other
Step-by-step explanation:
I need the solutions
Answer:
(-1, -2)
Step-by-step explanation:
The solution is the intersection, which is at (-1, -2)
Lucia has 48 markers and 64 stickers that she wants to give as favors for a party. She wants to put an equal number of markers and an equal number of stickers into each favor bag. She uses all the markers and stickers.
Use the drop-down menus to complete the statements below about the number of bags Lucia can make.
CLEARCHECK
The greatest number of bags Lucia can make is
. Each of these bags will have
markers and
stickers.
If she used more bags,
.
She could use
bags, but this is not the greatest number she could use.
The computation of the factors shows that the greatest number of bags that Lucia can make will be 16.
How to illustrate the factor?From the information given, Lucia has 48 markers and 64 stickers that she wants to give as favors for a party.
The computation of the factors shows that the greatest number of bags that Lucia can make will be calculated through then factors. This goes thus:
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
Factors of 64 = 1, 2, 4, 8, 16, 32, and 64.
Therefore, the highest common factor is 16.
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Answer:
16
Step-by-step explanation:
what is the area of the shaded region ?
Answer: The area is 8 it litterally tells you there
Step-by-step explanation:
The Venn diagram below shows information about the number of items in sets T and V.
An item is chosen at random.
Given that P(TIV) = j
The value of x from the venn diagram if P(T | V) = 1/5 is 16
How to determine the value of x
From the question, we have the following parameters that can be used in our computation:
The venn diagram
From the venn diagram, we have the following probability values
P(T | V) = (x - 4)/(3x + x - 4)
Evaluate the like terms
So, we have
P(T | V) = (x - 4)/(4x - 4)
From the question, we have
P(T | V) = 1/5
This means that
(x - 4)/(4x - 4) = 1/5
When evaluated, we have
x = 16
Hence, the value of x is 16
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Which set of three angles could represent the interior angles of a triangle?
O 19°, 70°, 91°
O 47°, 12°, 31°
O 50°, 20°, 20°
O 25°, 25°, 100°
Answer:
19 degrees, 70 degrees, and 91 degrees.
Step-by-step explanation:
The interior angles of a triangle sum to 180 degrees. 19 plus 91 is equal to 110, add 70 to 110 and you'll get 180. :)
∫(2x^3-x^2-2x+4)/(1+x^2)dx
Simplify the integrand as
\(\dfrac{2x^3 - x^2 - 2x + 4}{1 + x^2} = \dfrac{(2x^3 + 2x) - (x^2 + 1) - 4x + 5}{x^2 + 1} \\\\ = \dfrac{2x(x^2 + 1) - (x^2 + 1) - 4x + 5}{x^2 + 1} \\\\ = 2x - 1 - \dfrac{4x - 5}{x^2 + 1}\)
(in other words, compute the quotient and remainder)
We can further split up and prepare the remainder term for integration by rewriting it as
\(\dfrac{4x - 5}{x^2 + 1} = 2\times\dfrac{2x}{x^2 + 1} - \dfrac5{x^2 + 1}\)
Now we integrate:
\(\displaystyle \frac{2x^3 - x^2 - 2x + 4}{1 + x^2} \, dx = \int \left(2x - 1 - 2\times\frac{2x}{x^2+1} + \frac5{x^2+1}\right) \, dx\)
\(\displaystyle = x^2 - x - 2 \int \frac{2x}{x^2+1} \, dx + 5 \int \frac{dx}{x^2+1}\)
In the first remaining integral, substitute y = x² + 1 and dy = 2x dx. In the last integral, recall that d/dx [arctan(x)] = 1/(x² + 1).
\(\displaystyle = x^2 - x - 2 \int \frac{dy}y + 5 \int \frac{dx}{x^2+1}\)
\(\displaystyle = x^2 - x - 2 \ln|y| + 5 \arctan(x) + C\)
\(\displaystyle = \boxed{x^2 - x - 2 \ln(x^2+1) + 5 \arctan(x) + C}\)
what is the solution set for 4x + 12 ≤ 8?
Answer:x
≥
−
7
Step-by-step explanation:
Answer:
Inequality Form: x ≤ -1
Interval Notation: (−∞,−1]
First, determine if the three side lengths could form a triangle. (Recall from earlier, the sum of the two smaller sides must be greater than the third side). If yes, classify the triangle further as acute, right, or obtuse.17 ,1712 , Not a triangle
acute
right
obtuse
The triangle of given dimensions is isosceles and acute triangle.
Triangle is a shape with three sides and hence three angles. We know that triangles are classified according to the sides and angles. Based on angles, the classification of triangle is acute, obtuse and right triangle.
Based on sides, the classification of triangle is equilateral, isosceles and scalene triangle. Now, if the dimensions will form a triangle or not can be estimated through the formula -
side 1 + side 2> side 3
We see that 17 + 17 > 12
34 > 12
Thus, the triangle will form.
Moreover the two sides are equal hence it will be isosceles triangle. Since two sides are equal thus two angles will also be equal.
Now, if we square the sides and find their sum, it will be greater than square of third side. Hence, it is acute triangle.
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A box of chocolate contains 6 milk chocolates, 5 dark chocolates and
3 white chocolates. You randomly choose three chocolates to eat.
What is the probability of first pulling a milk chocolate, second pulling
a white chocolate, and then lastly choosing a milk chocolate?
Write your answer ar a percentage and round the the nearest tenth.
0 4.6%
04%
03.3%
04.1%
Answer:
i think is 3.3 but i dont know
Step-by-step explanation:
I WILL GIVE BRAINLIETS IF THESE ARE ALL RIGHT
This month the company reported an increase in profit of 25%. If the company made $45,000 last month, how much did they make this month?
A. $5,400
B. $5,625
C. $54,000
D. $56,250
Answer:
56,250
Step-by-step explanation:
First e turn the persentage into a decimal so we can multiply the 45,000 by it
45,000 x 0.25 = 11,250
Now we ad the total from last month to the amount we got in the last step to figure out how much the company earned this month
11,250 + 45,000 = 56,250
The company earned 56,250 this month :)
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try to find two values that sum to 76 if one value is 47 what is the other number?
The two values are 47 and 29
Here, we are trying to find two values that sum up to 76, but we already have one of the values.
Let us say the values are a and b
Since they sum uo to be 76, then we have an equation describing the sum as;
a + b = 76
But since we have one of the values already, say a= 47
Then 47 + b = 76
To get b, we simply bring the other value to the right hand side of the equation and this makes it negative;
Thus;
b = 76 - 47
We proceed to subtract;
b = 29
Here's a graph of a linear function. Write the
equation that describes that function.
xpress it in slope-intercept form.
Answer:
the slope intercept form is y = (1/2)x - 1
Step-by-step explanation:
The slope-intercept form is, y = mx + b
We see from looking at the graph that,
at x = 0, y = -1
So, from this we find that b = -1
at x = 2, y = 0,
now, we find the slope m,
using,
\(m = \frac{y_{2} -y_1}{x_2-x_1}\)
Using x_2 = 2, y_2 = 0,
x_1 = 0, y_1 = -1, we get,
m = (0-(-1))/(2-0)
m = 1/2
So, the slope intercept form is,
y = (1/2)x - 1
math math math math math math math
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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Written expression for (9x5)+(24-9)
Point C has a coordinate of (-4, -6) and point D has a coordinate of (1, -6), how far are they apart?
The distance between points C and D is given as follows:
5 units.
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The coordinates for this problem are given as follows:
(-4, -6) and (1, -6).
Hence the distance is given as follows:
\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)
D = 5 units.
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Select the correct answer. Which statement best describes the zeros of the function h(x) = (x – 6)(x2 + 8x + 16)? A. The function has two distinct real zeros. B. The function has three distinct real zeros. C. The function has one real zero and two complex zeros. D. The function has three complex zeros.
We can see here that the statement that best describes the zeros of the function h(x) = (x – 6)(x² + 8x + 16) is: C. The function has one real zero and two complex zeros.
What is a function?In mathematics, a function is a special type of relation. A relation is a set of ordered pairs, where each ordered pair consists of two elements.
To determine the zeros of the function h(x) = (x - 6)(x^2 + 8x + 16),
we can set the function equal to zero and solve for x.
Setting h(x) = 0, we have:
(x - 6)(x^2 + 8x + 16) = 0
Setting x - 6 = 0, we find:
x = 6
Setting x^2 + 8x + 16 = 0,
we can attempt to factor or use the quadratic formula.
Therefore, the function:
h(x) = (x - 6)(x^2 + 8x + 16) has one real zero (x = 6) and two complex zeros.
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(-37)+(-2) please tell quickly
Answer:-39
Step-by-step explanation:
The first thing is to open the bracket.
By doing that, the question becomes -37-2.
note that plus×minus=minus.
Hence,-39 as the final answer
The area of a square is 81cm2.Find the length and perimeter.
Answer:
Step-by-step explanation:area= s*s
so~ the side will be 9 as 9*9=81
n the perimeter = 4*9= 36
The length is 9 cm
The perimeter is 36 cm.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment.
how would i anwser this? help pls!
Answer:
Step-by-step explanation:
To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.
For example:
y=-2/3(-6)=7
-2/3x6=-4
-4+7=3
(-6,3)
You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.
To get the x value, you need to fill in the y in the equation y=-2/3x+7
for example:
5=-2/3x+7
-2=-2/3x
3=x
(3,5)
y=-2/3x+7
y=-2/3(15)+7
y=-10+7
y=-3
(15,-3)
y=-2/3x+7
15=-2/3x+7
8=-2/3x
-12=x
(-12,15)
3/8=4/7x what is x please help me omg
The value of the variable x = 21/32
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.
These expressions are also made up of certain arithmetic or mathematical operations.
These operations includes;
SubtractionDivisionAdditionMultiplicationBracketParenthesesFrom the information given, we have that;
3/8=4/7x
cross multiply the values, we have;
7x(3) = 8(4)
multiply the values and expand the brackets, we get the values;
21x = 32
Divide both sides by the coefficient of the variable x, we get;
x = 32/21
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Charlie ran the 200 meter dash in the all day competition one meter is approximately 3.28
Your welcome please give me brainiest also here's the explanation:
200*3.28=656
Hello, 3Coli Here!
Here is your answer:
200 times 3.28 = 656
You can multiply the two factors.
Please give Brainliest to xxtigrisloverxx, not me! She got her answers deleted by a mod, and her answers are correct.
Hopefully, this helps! :D
Ask your question below!
What is 2,443,802,280 rounded to the nearest ten million
Answer:2,440,000,000
Step-by-step explanation:
The average grade for an exam is 74, and the standard deviation is 7. The grades are curved to follow a normal distribution.
What is the probability that the grade of a randomly selected students score is more than 60?
Answer:
0.9772 = 97.72% probability that the grade of a randomly selected students score is more than 60.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average grade for an exam is 74, and the standard deviation is 7.
This means that \(\mu = 74, \sigma = 7\)
What is the probability that the grade of a randomly selected students score is more than 60?
This is 1 subtracted by the pvalue of Z when X = 60. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{60 - 74}{7}\)
\(Z = -2\)
\(Z = -2\) has a pvalue of 0.0228
1 - 0.0228 = 0.9772
0.9772 = 97.72% probability that the grade of a randomly selected students score is more than 60.
In a random sample of 80 people, 52 consider themselves as baseball fans. Compute a 95% confidence interval for the true proportion of people consider themselves as baseball fans and fill in the blanks appropriately. We are 95% confident that the true proportion of people consider themselves as
Answer:
(0.5455 ; 0.7545)
Step-by-step explanation:
Given that:
Sample size, n = 80
Baseball fans, x = 52
Proportion, p = x/n = 52 / 80 = 0.65
Using the relation :
Confidence interval :
p ± Zcrit√[(p(1 -p))/n]
Zcrit at 95% = 1.96
Lower boundary: p - Zcrit√[(p(1 -p))/n]
0.65 - 1.96√[(0.65(1 -0.65))/80]
0.65 - 1.96√[(0.65(0.35))/80]
0.65 - 1.96 * √0.00284375
0.65 - (1.96 * 0.0533268)
0.65 - 0.104520528
= 0.545479472
Upper boundary: p + Zcrit√[(p(1 -p))/n]
0.65 + 1.96√[(0.65(1 -0.65))/80]
0.65 + 1.96√[(0.65(0.35))/80]
0.65 + 1.96 * √0.00284375
0.65 + (1.96 * 0.0533268)
0.65 + 0.104520528
= 0.754520528
(0.5455 ; 0.7545)
lI need help please answer
Answer:
Look Below
Step-by-step explanation:
1) 81 = 729/9
2) 36 / 3 = 12
3) 4X = 20 (X = 5)
4) 34 = 176 ???
5) 1470/35 = 42
6) 1 = 2/2
7) 7X = 245 (X = 35)
8) 600X = 2400 (X = 4)
9) 936 = 78X (X = 12)
If you find any fault in my answers please let me know! About 4 I am not able to answer that because I don't see what the problem is asking. Sorry. I hope this helps! Have a good day!
If electricity is billed at a rate of $0.75 per KWH and you used on average 120 KWHs per month, what would you expect to pay each month?
You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.
How to find the expected monthly payTo calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.
Given:
Cost per KWH: $0.75
Average monthly usage: 120 KWHs
To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:
Monthly Cost = Cost per KWH * Average monthly usage
Plugging in the values, we have:
Monthly Cost = $0.75/KWH * 120 KWHs
Calculating the result:
Monthly Cost = $90
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What is equivalent to 0 = 2x2 - 16x – 18 when completing the
square?
Answer:
x = 1
x = -9
Step-by-step explanation:
(2x2 + 16x) - 18 = 0
2x2 + 16x - 18 = 2 • (x2 + 8x - 9)
x2 + 8x - 9
-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8
2 • (x + 9) • (x - 1) = 0
2 = 0
x+9 = 0
x = -9
x-1 = 0
x = 1
x2 + 8x - 9 = 0
x2+8x = 9
(x+4) • (x+4) =
(x+4)2
x2+8x+16 = 25 and
x2+8x+16 = (x+4)2
(x+4)2 = 25
x = -4 + √ 25
x2 + 8x - 9 = 0
has two solutions:
x = -4 + √ 25
or
x = -4 - √ 25
- B ± √ B2-4AC
x = ————————
2A
A = 1
B = 8
C = -9
B2 - 4AC =
64 - (-36) =
100
-8 ± √ 100
x = —————
2
x = ( -8 ± 10) / 2
x =(-8+√100)/2=-4+5= 1.000
or:
x =(-8-√100)/2=-4-5= -9.000
Answer: x = 1
x = -9
What is the volume, in cubic meters, of a rectangular prism with a height of 14 meters, a width of 17 meters, and a length of 13 meters?
Answer:
why is brainlys tutor system not free anymore I really need help from somebody, i used to use tutors so much but now i have none ro help me
factorize for me
y + 3y + 2-sin2x=0
Answer:
−(−4y−2+sin2(x))=0
Step-by-step explanation: