P(a) = a17 + 16 How many terms does this Polynomial have?

To solve the 1-dimensional wave equation problem with c = 1, L = 2, initial velocity zero, and initial displacement f(x) = {x if 0 ≤ x ≤ 1, 2 - x if 1 ≤ x ≤ 2}, we need to find the solution u(x, t) that satisfies the equation:

∂²u/∂t² = c²∂²u/∂x²

subject to the initial conditions:

u(x, 0) = f(x)

∂u/∂t(x, 0) = 0

and the boundary conditions:

u(0, t) = 0

u(L, t) = 0

Using the method of separation of variables, we assume that the solution has the form:

u(x, t) = X(x)T(t)

Substituting this into the wave equation and rearranging, we get:

(X''(x)/X(x)) = (T''(t)/(c²T(t)))

Since the left-hand side depends only on x and the right-hand side depends only on t, both sides must be equal to a constant -λ, say, which we can choose to be positive:

X''(x)/X(x) = -λ

T''(t)/(c²T(t)) = -λ

The boundary conditions u(0, t) = u(L, t) = 0 imply that X(0) = X(L) = 0, which leads to the following eigenvalue equation:

X''(x)/X(x) = -λ, X(0) = X(L) = 0

The general solution of this equation is:

X(x) = sin(nπx/L), n = 1, 2, 3, ...

The corresponding eigenvalues are:

λ = (nπ/L)²

Using the initial condition u(x, 0) = f(x), we can express the solution u(x, t) as a series:

u(x, t) = ΣBn sin(nπx/L)sin(nπct/L)t

where the coefficients Bn are given by:

Bn = (2/L)∫f(x)sin(nπx/L)dx

We need to evaluate the integral ∫f(x)sin(nπx/L)dx for n = 1, 2, 3, ...

For n = 1:

B1 = (2/L)∫f(x)sin(πx/2)dx

= (4/π)∫xsin(πx/2)dx + (4/π)∫(2-x)sin(πx/2)dx

= (8/π)∫xsin(πx/2)dx

= -16/(π³) [x cos(πx/2) - 2/π sin(πx/2)] from 0 to 1

= -16/(π³) [cos(π/2) - 2/π sin(π/2) - 1]

= -16/(π³) (2/π - 1)

≈ -0.4373

For n = 2:

B2 = (2/L)∫f(x)sin(2πx/L)dx

= (4/π)∫xsin(πx)dx + (4/π)∫(2-x)sin(2πx/2)dx

= -8/(π³) [x cos(πx) + sin(πx)] from 0 to

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Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

To find an equation of a plane containing the three given points (5,0,5), (2,2,6), and (2,3,8) with a coefficient of x equal to 3, we can use the point-normal form of a plane equation. The equation of the plane is 3x + 2y - z = 7.

Let's consider the three given points as (x₁, y₁, z₁), (x₂, y₂, z₂), and (x₃, y₃, z₃). To find the equation of the plane, we need to determine its normal vector, which can be found using the cross product of two vectors in the plane.

We can choose two vectors from the given points, such as (5,0,5) - (2,2,6) = (3, -2, -1) and (5,0,5) - (2,3,8) = (3, -3, -3).

Calculating the cross product of these two vectors, we get (-6, -6, -6), which is the normal vector of the plane. Now, we can write the equation of the plane in point-normal form:

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0,

where A, B, and C are the components of the normal vector and (x₁, y₁, z₁) is one of the given points. Substituting the values, we have

-6(x - 5) - 6(y - 0) - 6(z - 5) = 0.

Simplifying the equation, we get -6x + 30 - 6y - 6z + 30 = 0, which can be rewritten as -6x - 6y - 6z + 60 = 0. Since we want the coefficient of x to be 3, we can multiply the entire equation by -1/2, resulting in 3x + 3y + 3z - 30 = 0. Finally, simplifying further, we obtain the equation of the plane as 3x + 2y - z = 7.

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Example of an undecidable problem is given by the problems in the system created by computer viruses.

According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.

A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.

whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.

If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.

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Answer:

ST = 7.1 in

Step-by-step explanation:

we can use SOH-CAH-TOA because we've got a right triangle

side ST would be 'adjacent'

side TU would be the 'hypotenuse'

so we use Cosine because that's used when you're dealing with  adjacent and hypotenuse:

cos 42° = ST/9.5

ST = cos 42° × 9.5

ST = 7.1

The 95% confidence interval for a population mean has a margin of error (E) of 41

The confidence interval for a population mean is given by:

Confidence interval = μ ± E = (μ - E, μ + E)

Where μ is the mean and E is the margin of error.

Since the confidence interval is (428, 510), hence:

μ - E = 428      (1)

μ + E =  510     (2)

Subtracting equation 1 from equation 2:

2E = 82

E = 41

μ - E = 428

μ -41 = 428

μ = 469

Hence the margin of error (E) is 41

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Answer:

6/7

Step-by-step explanation:

The constant rate of change is also know as the slope of the expression

Given

24x-28y=14

Write in standard form y = mx+c

m is the slope

24x-28y=14

-28y = -24x + 14

y = -24x/-28 + 14/-28

y = 6/7 x - 1/2

Compare

mx = 6/7 x

m = 6/7

Hence the  constant rate of change is 6/7

The range of the function is {-7, -3/2, -2, 2}.Hence, the correct option is the last option.

The range of the function is a set of all possible values of a function. It is the set of all output values of a function. In the given function, h(x) = 1/2x– 3 with a restricted domain of {-2,0, 2, 10}.Here is the solution;

As per the question, the given function is (x) = 1/2x– 3 with a restricted domain of {-2,0, 2, 10}.Now, let us find the range of the function; Let's find the value of the function at each of the domain points. x h(x)-2 h(-2) = -4-3 = -7 0 h(0) = -3/2 2 h(2) = -2 10 h(10) = 2

Therefore, the range of the function is {-7, -3/2, -2, 2}.Hence, the correct option is the last option.

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The sequence yn = √(n+1) - √n converges, and its limit can be found by simplifying the expression and applying the limit rules. The limit of yn as n approaches infinity is 0.

To find the limit of yn as n approaches infinity, we can simplify the expression. Let's start by rationalizing the numerator:

yn = (√(n+1) - √n) (√(n+1) + √n) / (√(n+1) + √n)

Simplifying the numerator, we get:

yn = [(n+1) - n] / (√(n+1) + √n)

= 1 / (√(n+1) + √n)

As n approaches infinity, both √(n+1) and √n also approach infinity. Therefore, the denominator (√(n+1) + √n) also approaches infinity. In the numerator, the constant 1 remains constant.

Using the limit rules, we can simplify the expression further:

lim(n→∞) yn = lim(n→∞) [1 / (√(n+1) + √n)]

= 1 / (∞ + ∞)

= 1 / ∞

= 0

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Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network.

Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network. This technique allows a user to take advantage of the computing power of multiple computers to render a scene. To do this, the user would divide the scene into several parts, assigning each part to a different computer. The computers would then render each part of the scene independently, and then the results are combined into a single image. This process can significantly reduce the time required to render a scene, as the workload is distributed over multiple computers. For example, if it would normally take a single computer 10 minutes to render a scene, net rendering could reduce that time to 2 minutes.

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Answer:

P<-18

multiply both sides by 3 3p/3<3(-6)

Simplify p<-18

Step-by-step explanation:

Answer:

(2,5)

Step-by-step explanation:

There isn’t only one right answer, the question is an ordered pair that doesn’t fit in the equation. So just pick two random numbers and then check to make sure it doesn’t fit. The picture shows my work.

y_y+z=

9_9+86+2=

0+86+2=

86+2=88

(a) The expression that represents the position of the fish relative to sea level after it rises 7.8 feet  is 13.52-7.8 = 5.72 , and

(b) The position of fish after rising 7.8 feet will be 5.72 feet below the sea level .

In the question ,

it is given that

fish swims 13.52 below  the sea level ,

original depth = 13.52 feet

fish rises by 7.8 feet relative to the sea level

Part(a)

Since the fish has risen 7.8 feet ,

so , the risen height 7.8 feet will be subtracted from original depth 13.52 feet

the expression becomes 13.52 - 7.8 = 5.72  .

Part(b)

The position of fish after it rises 7.8 feet is calculated using

= 13.52 - 7.8

Subtracting 7.8 from 13.52 we get

= 5.72

Therefore , (a) The expression that represents the position of the fish relative to sea level after it rises 7.8 feet  is 13.52-7.8 = 5.72 , and

(b) The position of fish after rising 7.8 feet will be 5.72 feet below the sea level .

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In the given scenario, we have to determine the value of c that minimizes f(c). The data points are x1, x2,....xn which are fixed and c is the only variable.Let's assume that f(c) = g(x1, x2,...,xn, c) is a function of one variable. In this case, we can find the minimum or maximum of the function by differentiating it with respect to c and equating it to zero.

Let's differentiate the function f(c) with respect to c: $f'(c) = \frac{df}{dc} = \frac{\partial g}{\partial c}$ (partial derivative of g with respect to c)Since we are interested in finding the minimum value of f(c), we have to check whether this critical point is a minimum or a maximum by analyzing the second derivative of f(c). So let's differentiate f'(c) with respect to c: $f''(c) = \frac{d^2f}{dc^2} = \frac{\partial^2g}{\partial c^2}$If $f''(c)>0$, then the critical point is a minimum, and if $f''(c)<0$, it is a maximum. If $f''(c) = 0$, then we can't say anything about the nature of the critical point.

If we are interested in finding the global minimum, we also have to check the endpoints of the interval on which c is defined.I hope that helps!

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Answer:

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.

\( \: first the formula of quadratic equation \: = - b ≠ \: \sqrt{ \frac{ \: {b }^{2} - 4ac}{ \: 2a} } \)

let's begin to solve this equation,,,

\(ax² + bx + c = 0 \\

ax² + bx + c =0 \\ {x}^{2} + \frac{b}{a} \: + \frac{ {b}^{2} }{2a} = \frac{b2}{a} - \frac{c}{a}

\\ x + \frac{ {b}^{2} }{2a} = - \frac{ {b}^{2} }{2a} - \frac{c}{a} \)

an equation having the maximum power of the variable equal to is called the quadratic equation the general form of quadratic equation is ax² + bx +c =0 where a,b,c are real numbers a ≠0 x is variable •

a quadratic equation can be solved by two method by factorization and by formula

by factorization a quadratic equation can be solved by factorization only when the product AC can be divided into two such part that it had the sum of the difference of the two part is equal to b

\(by the formula of quadratic equation can be solved by \ - } \)

\(x = \frac{ - b \sqrt{ {b}^{2} - 4ac } }{2a } \\ root \: of \: equation \: {ax}^{2} + bx + c = 0 \\ - b - \sqrt{ \frac{ {b}^{2} - 4ac}{2a} } \)

Answer:

3/8

Step-by-step explanation:

because 4/8 are red , 1/8 are white… (which is 5/8 now)

the remaining would be 3/8

If you check your work, the total would be 8/8

Since Tony is self-employed, he will have to pay all of the tax himself.

Take his adjusted earnings times the tax rate

58238.74 * 2.9%

58238.74 * .029

1688.92346

Rounding to the nearest cent

1688.92

Answer:

I think C is the current answer

Step-by-step explanation:

it makes sense to me because the $0.5 is depending on the $250

(a) To find the probability of correctly answering an individual question by blind guessing, the probability of guessing the correct answer for any given outcome is 1 out of 4, or 1/4 = 0.25.

(b) To calculate the expected number of questions a student will guess correctly on the exam (X), we multiply the probability of guessing a question correctly by the total number of questions.

Expected number of correct answers (X) = Probability of a correct guess * Total number of questions

X = 0.25 * 20 = 5

Therefore, the expected number of questions a student will guess correctly on this exam is 5. Since the student is blindly guessing, there is an average expectation of getting 5 correct answers out of the 20 questions.

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Answer:

it is 5 you don't add the 3 in it

Answer:

D

Step-by-step explanation:

lol this is a weird math question

jk

Hydrogen bonds occur only when hydrogen is covalently bonded to one of three elements: fluorine, oxygen, or nitrogen. Anything else isn't considered a hydrogen bond.

Answer:

its C; or their is a constat change in the output values and it is non linear

Step-by-step explanation:

this is because we can see that 0/0 match each other. There is a constamt chage in the imput valu.

Answer:

d) 5

Step-by-step explanation:

we can observe that the x-value 5 appears twice in the relation. However, in a function or a relation, each x-value should only have one corresponding y-value. Therefore, the repetition of (5, 1) and (5, 2) indicates an inconsistency or ambiguity in the relation. As a result, 5 is not a valid x-value in the domain.

Answer:

Step-by-step explanation:

Mary would have a rise of 12 and a run of 4, making her slope, or rate of change, $3 a day.

Julie would have a rise of 19 and a slope of 6, making her slope, or rate of change, $3.17 a day.

Since Julie is raising money at a faster rate, she would get to the goal of $1000 first.

Answer:

Mary would have a rise of 12 and a run of 4, making her slope, or rate of change, $3 a day. Julie would have a rise of 19 and a slope of 6, making her slope, or rate of change, $3.17 a day. Since Julie is raising money at a faster rate, she would get to the goal of $1000 first.

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The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

125 over 81

Step-by-step explanation:

x3= 125 over 27

Divide both sides by 3, you get:

x=125 over 81

Thats it lol

Answer:

Step-by-step explanation:

Answer:

\(2\sqrt{13}\)

Step-by-step explanation: