work out the area of a semi circle take pi to be 3.142 and five your answer to two decimal places

To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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Answer:

Any more information to the problem?

Step-by-step explanation:

In this cases, The two angles of elevation are 36° and 144°

To find the two angles of elevation for a projectile to reach a target 13 km downrange with an initial speed of 425 m/sec, we can use the projectile motion formula:

range (R) = (v² * sin(2 * angle)) / g

where v is the initial speed (425 m/sec), angle is the angle of elevation, and g is the acceleration due to gravity (approximately 9.81 m/s²).

We need to solve for angle.

First, convert the range to meters:

13 km = 13,000 m.

Next, plug the values into the formula:

13,000 = (425² * sin(2 * angle)) / 9.81

Now, solve for angle:

sin(2 * angle) = (13,000 * 9.81) / 425²

sin(2 * angle) ≈ 0.7387

Now, find the two angles using the arcsin function:

2 * angle = arcsin(0.7387)

angle = 0.5 * arcsin(0.7387)

There are two angles that will result in the same range:

angle_1 = 0.5 * arcsin(0.7387)

angle_2 = 180 - angle_1

Calculating the values:

angle_1 ≈ 36° angle_2 ≈ 144°

So, the two angles of elevation that will enable a projectile to reach a target 13 km downrange on the same level as the gun with an initial speed of 425 m/sec are approximately 36° and 144°.

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Answer:

12 pennies

4 dimes

3 nickels

2 quarters

Step-by-step explanation:

Let p = pennies

d = dimes

q = quarters

n - nickels

d + n + p + q = 21

p = 4n

d = n + 1

q = n - 1

Now just subsitute them in and add the terms

(n + 1) + n + (4n) + (n - 1) = 21

7n = 21

Divide both sides by 7

7n/7 = 21/7

n = 3

Now use the new n to plug in the rest of the equations

p = 4(3) = 12

d = 3 + 1 = 4

q = 3 - 1 = 2

Chad has a coin collection he has a total of 21 coins which include 12 number of pennies, 3 number of nickels, 4 number of dimes, 2 number of quarters.

Let's break down the information given in the problem step by step:

Chad has a total of 21 coins.

He has 4 times as many pennies as nickels.

He has 1 more dime than the number of nickels.

He has 1 less quarter than the number of nickels.

Let's use variables to represent the number of each type of coin:

Let P be the number of pennies.

Let N be the number of nickels.

Let D be the number of dimes.

Let Q be the number of quarters.

Now we can create a system of equations based on the information given:

P + N + D + Q = 21 (total number of coins)

P = 4N (four times as many pennies as nickels)

D = N + 1 (one more dime than the number of nickels)

Q = N - 1 (one less quarter than the number of nickels)

Now we can substitute the expressions for P, D, and Q from equations 2, 3, and 4 into equation 1:

4N + N + (N + 1) + (N - 1) = 21

Combine like terms:

7N = 21

Divide both sides by 7:

N = 3

Now that we know the number of nickels (N = 3), we can use this information to find the number of each type of coin:

Pennies (P) = 4N = 4 * 3 = 12

Dimes (D) = N + 1 = 3 + 1 = 4

Quarters (Q) = N - 1 = 3 - 1 = 2

So, Chad has:

12 pennies

3 nickels

4 dimes

2 quarters

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Answer:

Basic wage rate = $9.375 per hour

Step-by-step explanation:

Given :

Fortnight wage = $750

Basic week, hours worked per week = 40 hours

Weekly basic wage rate :

Fortnight = 2 weeks

Hence, weekly wage = fortnight wage / 2 = 750 /2 = $375

Weekly basic wage rate = $375 / Number of hours worked per week = $375 / 40 = $9.375 per hour

Firstly, we should understand that we have right triangles inside the rectangle

These are BDC and ADC

a) Side DC

What we have is a rectangle and parallel sides are equal in length

AB = DC = 36

Thus, DC = 36

b) DA

At the four edges of the rectangle, we have right angles, which are 90 degrees

So, we can use Pythagoras' here

The square of the diagonal equals the sum of the squares of the two other sides

So we have;

c) AC

Mathematically, the diagonals of a rectangle are congruent (equal in length) and they bisect each other

Thus, since BE is 19.5, BD is 2 * 19.5 = 39

AC = BD = 39

d) AE

AE is exactly same as BE which is 19.5

e) DE

DE is same as BE which is 19.5

f) Angle DAE

To get this, we consider triangle

g) Angle AEB

h) Angle ADC

This is part of the right angles; ADC is 90 degrees

i) BEC

Blender provides a visual interface that allows users to interactively mark seams and unwrap the UV coordinates for further adjustments and mapping onto the surface of the cube.

(a) In the simplest possible structure of a cube mesh, there are 8 vertices. Each corner of the cube represents a vertex.

(b) In the simplest possible structure of a cube mesh, there are 12 edges. Each edge connects two vertices of the cube.

(c) In the simplest possible structure of a cube mesh, there are 6 faces. Each face of the cube represents a face in the mesh.

(d) To mark seams in the mesh for the standard UV layout of a cube in Blender, you can select the edges that define the boundaries of each face. In the case of a cube, this means selecting all the edges that surround each face of the cube. By marking these edges as seams, Blender will unwrap the UVs in a way that corresponds to the standard layout of a cube.

(e) To create a different-looking UV layout, you can mark seams along different edges of the cube. For example, instead of marking the edges that define the boundaries of each face, you can mark seams along diagonals or other edges that result in a different division of the cube's surface. This will produce a UV layout that looks distinct from the standard layout.

Note: To actually perform these actions and see the results in Blender, you can open Blender and enter Edit Mode (press Tab), select the edges you want to mark as seams (press Ctrl+E and choose "Mark Seam"), and then unwrap the UVs (press U and choose the unwrapping method).

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The largest open interval where the function f(x) = 1/(x^2+1) is increasing is (-∞, 0) ∪ (0, ∞). On this interval, the function is increasing from negative infinity to zero and from zero to positive infinity.

Explanation:

To find where the function is increasing, we need to find where the first derivative of the function is positive. Taking the derivative of f(x), we get:

f'(x) = (-2x) / (x^2 + 1)^2

The denominator of this expression is always positive, so the sign of f'(x) is determined by the numerator. The numerator is negative for x < 0 and positive for x > 0. Therefore, f(x) is decreasing on (-∞, 0) and increasing on (0, ∞).

We also need to check the endpoints of these intervals to make sure that the function is increasing on the entire interval. As x approaches negative infinity, the function approaches 0, and as x approaches positive infinity, the function approaches 0. Therefore, the function is increasing on (-∞, 0) ∪ (0, ∞).

In summary, the largest open interval where the function f(x) = 1/(x^2+1) is increasing is (-∞, 0) ∪ (0, ∞). On this interval, the function is increasing from negative infinity to zero and from zero to positive infinity.

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Answer:

62.5%

Step-by-step explanation:

The number of states do not use nuclear: 20 + 12 = 32

The number of states that do not use nuclear and use coal: 20

so 20/32 = 5/8 = 62.5%

The values of x, y, and z in the given rhombus are: x = -31, y = 20, z = -87.

An equation is a mathematical statement saying that two amounts or values are the same, for example 6 x4=12x

We know that the side of a rhombus are equal in length.therefore we can solve the given equation

4y + 8 = -3x - 5 = -z + 1 = 88

Solving each equation for the variables, we get:

4y + 8 = 88

4y = 80

y = 20

-3x - 5 = 88

-3x = 93

x = -31

-z + 1 = 88

-z = 87

z = -87

Heance , the values of x, y, and z in the given rhombus are:

x = -31, y = 20, z = -87.

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Answer: one hundred + fourteen point six hundred + seventy four

Step-by-step explanation:

Answer:

One hundred and fourteen point six seven four

Answer:

It would be

y=2x/5 - 1

Answer:

y= 2 /5 x − 1

Step-by-step explanation:

Answer:

We have:

If:

Cos(θ) + Sin(θ) = √2*cos(θ)

We want to prove that:

Cos(θ) - Sin(θ) = √2*Sin(θ)

Well, let's start with the first relation:

Cos(θ) + Sin(θ) = √2*cos(θ)

Now we can subtract 2*Sin(θ) and we will get:

Cos(θ) + Sin(θ) - 2*Sin(θ) = √2*cos(θ) - 2*sin(θ)

Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)

Now, we also can rewrite the first equation as:

Cos(θ) + Sin(θ) = √2*cos(θ)

Cos(θ) - √2*cos(θ) = -  Sin(θ)

Cos(θ)*( 1 - √2) = -Sin(θ)

Cos(θ) = -Sin(θ)/( 1 - √2) = Sin(θ)/(- 1 + √2)

We can replace this in the right side of theequation:

Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)

Cos(θ) - Sin(θ) = √2* Sin(θ)/(- 1 + √2) - 2*sin(θ)

Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)

Now we have this:

√2/(- 1 + √2)) - 2 = a

if we multiply all by (-1  + √2) we get:

√2 - 2*(-1  + √2) = a*(-1  + √2)

√2  + 2 - 2*√2 =  a*(-1  + √2)

2 - √2 = a*(-1  + √2)

√2*(√2 - 1) = a*(-1  + √2)

√2*(√2 - 1)/(-1  + √2) = a

√2 = a

Then:

√2/(- 1 + √2)) - 2 = √2

If we replace this in the equation:

Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)

We get:

Cos(θ) - Sin(θ) = √2*Sin(θ)

Which is the thing we wanted to get.

Please find attached herewith the solution of your question.

If you have any query, feel free to ask.

The equation of the parabola passing through the given points is, y = (-1/4)x²  + 31/4.

To find the equation of a parabola passing through given points, we can use the standard form of a quadratic equation: y = ax² + bx + c.

Using the given points (-5, 6), (5, 6), and (9, -8), we can substitute the x and y values into the equation to form a system of three equations.

Plugging in the first point (-5, 6):
6 = a(-5)²  + b(-5) + c
Simplifying: 6 = 25a - 5b + c  --------(1)

Plugging in the second point (5, 6):
6 = a(5)²  + b(5) + c
Simplifying: 6 = 25a + 5b + c  --------(2)

Plugging in the third point (9, -8):
-8 = a(9)²  + b(9) + c
Simplifying: -8 = 81a + 9b + c  --------(3)

Now we have a system of three equations:
6 = 25a - 5b + c  
6 = 25a + 5b + c  
-8 = 81a + 9b + c

To solve this system, we can subtract equation (2) from equation (1) to eliminate the c term:
0 = 0 - 10b
Simplifying: b = 0

Substituting this value into equation (1):
6 = 25a + c

Substituting b = 0 into equation (3):
-8 = 81a + c

Now we have a system of two equations:
6 = 25a + c  
-8 = 81a + c  

By subtracting equation (1) from equation (3), we can eliminate the c term:
-14 = 56a
Simplifying: a = -1/4

Substituting this value back into equation (1):
6 = 25(-1/4) + c
Simplifying: 6 = -25/4 + c
Rearranging the equation: c = 31/4

Therefore, the equation of the parabola passing through the given points is:
y = (-1/4)x²  + 31/4

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The number  \(log_2^3\) is an irrational number.

For given question,

We need to prove \(log_2^3\) is an irrational number.

An irrational number is a real number x that cannot be written as the ratio of two integers.

Assume that \(log_2^3\) is rational.

⇒ \(log_2^3\) = a/b

where a and b are positive integers with no factor in common.

Then  3 = \(2^{(\frac{a}{b} )}\)

or

\(3^b=2^a\)

which is impossible since 3^(b) is odd and 2^(a) is even.

Hence \(log_2^3\) cannot be rational, that is it is irrational.

Therefore,  \(log_2^3\) is an irrational number.

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The structure of the coordinates associated with specific radian measurements on the unit circle follows a distinct pattern. The x and y coordinates represents the cosine and sine values of the angle, respectively.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a Cartesian coordinate system.

It is commonly used in trigonometry to relate angles to the coordinates on the circle.

When we measure an angle in radians on the unit circle, we can associate specific coordinates with that angle.

The x-coordinate of a point on the unit circle represents the cosine value of the angle, while the y-coordinate represents the sine value of the angle.

These coordinates follow a pattern based on the radian measurement.

For example, when the angle is 0 radians (or 0 degrees), the corresponding point on the unit circle is (1, 0), where the x-coordinate is 1 (cosine of 0) and the y-coordinate is 0 (sine of 0).

As the angle increases, the coordinates change accordingly. For instance, when the angle is π/2 radians (or 90 degrees), the point on the unit circle is (0, 1), where the x-coordinate is 0 (cosine of π/2) and the y-coordinate is 1 (sine of π/2).

This pattern continues as the angle increases or decreases, and the coordinates on the unit circle change accordingly.

By using trigonometric functions, we can determine the cosine and sine values of any given angle and associate them with the appropriate coordinates on the unit circle.

In summary, the structure of the coordinates associated with specific radian measurements on the unit circle follows a pattern where the x-coordinate represents the cosine value of the angle, and the y-coordinate represents the sine value of the angle.

Together, these coordinates create points on the unit circle that correspond to the given radian measurement.

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Option-A is correct that is has a mean of 0 and standard deviation of 1 is the standardized form of the normal distribution.

Given that,

We have to find what is the standardized form of the normal distribution.

We know that,

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

Therefore, Option-A is correct that is has a mean of 0 and standard deviation of 1 is the standardized form of the normal distribution.

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Part 2

The solution is described as p is less than or equal or equal to 14

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Answer:

42

Step-by-step explanation:

6x8 = 48 90 - 48 = 42

Answer:

12 cups, since .75*16=12

Step-by-step explanation:

The Excel function used when deciding to reject or fail to reject the null hypothesis is the T.TEST function.

This function is used to calculate the probability of obtaining the observed results or more extreme results, assuming that the null hypothesis is true. If the probability, also known as the p-value, is less than the significance level, typically 0.05, the null hypothesis is rejected, and it is concluded that there is sufficient evidence to support the alternative hypothesis.

Otherwise, if the p-value is greater than the significance level, the null hypothesis is not rejected, and it is concluded that there is not enough evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the level of significance (alpha) chosen for the test, typically 0.05 or 0.01, then the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the chosen alpha level, then the null hypothesis is not rejected.

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Answer: 19.26

Step-by-step explanation: 40% of 30 can be found like 30(0.40), which equals 12, since the game is 40% of they are getting $12 off. 30-12=18. The sales tax is 7% or 0.07 so you can find it by doing 18(0.07) which is 1.26, now you just add 1.26 and 18 which is 19.26.

Answer:

Yolanda bought 48 yards of ribbon, and spent 7.68 cents on it.

Step-by-step explanation:

First Step: Find out how much Yolanda spent

20.00 -12.32 = 7.68

Second Step: Divide Total Cost by Price of one Yard

7.68/0.16 = 48

Third Step: Double Check

48 x 0.16 = 7.68

I hope my answer helped you, good luck on your homework!

(a) The curve defined by the parametric equations x = t^2, y = -1/4t (t > 0) represents a parabolic trajectory, the point of intersection between the curve and the hyperbola is (4∛2, -1/(4∛2)).

To find the points on the curve where the tangent line is parallel to the line y = x, we need to determine when the slope of the tangent line is equal to 1.

The slope of the tangent line is given by dy/dx. Using the chain rule, we can calculate dy/dt and dx/dt as follows:

dy/dt = d/dt(-1/4t) = -1/4

dx/dt = d/dt(\(t^2\)) = 2t

To find when the slope is equal to 1, we equate dy/dt and dx/dt:

-1/4 = 2t

t = -1/8

However, since t > 0 in this case, there are no points on the curve where the tangent line is parallel to y = x.

(b) To determine the points on the curve where it intersects the hyperbola xy = 1, we can substitute the parametric equations into the equation of the hyperbola:

\((t^2)(-1/4t) = 1 \\-1/4t^3 = 1\\t^3 = -4\\\)

Taking the cube root of both sides, we find that t = -∛4. Substituting this value back into the parametric equations, we get:

x = (-∛4)^2 = 4∛2

y = -1/(4∛2)

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Answer:

f(x) = -x²

Step-by-step explanation:

Writing f(x) = -x² in vertex form gives f(x)=-(x-0)^2+0 which shows that the vertex (h,k) is at (0,0)

The other equations written in vertex form do not have (h,k) = (0,0)

Answer:

thats easy

Step-by-step explanation:

Answer:

Here is your answer

((7 * 1) ^ 9) ^ 9 =

(7 ^ 9) ^ 9 =

40353607 ^ 9 = 283753509180010707824461062763116716606126555757084586223347181136007

Step-by-step explanation: