use series to evaluate the limit. lim x → 0 sin(3x) − 3x 9 2 x^3 x^5

Answer:

26 per week

Step-by-step explanation:

The solution of the second-order differential equation y'' - y' = 0 with the given initial conditions y(-1) = 2 and y'(-1) = -2 is y(x) = 2e^x - 4e^-x.

To find a solution to the second-order differential equation y'' - y' = 0, we first solve the characteristic equation by assuming a solution of the form y(x) = e^(rx). Plugging this into the differential equation, we get r^2e^(rx) - re^(rx) = 0. Factoring out e^(rx), we have e^(rx)(r^2 - r) = 0. This gives us two possible values for r: r = 0 and r = 1.

For r = 0, the corresponding solution is y₁(x) = c₁, where c₁ is a constant.

For r = 1, the corresponding solution is y₂(x) = c₂e^x, where c₂ is a constant.

To find the particular solution that satisfies the given initial conditions, we substitute the values of x = -1, y(-1) = 2, and y'(-1) = -2 into the general solution. This gives us the equations 2 = c₁ and -2 = c₂e^-1. Solving for c₁ and c₂, we find c₁ = 2 and c₂ = -2e.

Therefore, the solution to the second-order differential equation with the given initial conditions is y(x) = 2e^x - 4e^-x.

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Answer: 6

Step-by-step explanation:

Answer: y=6

Step-by-step explanation:

To test the given hypothesis, where the null hypothesis (H_ọ) states that the population mean (µ) is equal to 190, and the alternative hypothesis (H_A) states that µ is greater than 190, a one-tailed test should be performed.

Given that the sample mean (X) is 186, the sample standard deviation (s) is 22, and the sample size (n) is 14, we can use the t-test for a single sample to test the hypothesis.

Calculate the test statistic:

t = (X - µ) / (s / √n)

t = (186 - 190) / (22 / √14)

t ≈ -0.8182

Determine the critical value for the given significance level and degrees of freedom.

Since the alternative hypothesis is one-tailed (µ > 190), we need to find the critical value corresponding to the desired significance level (α). Let's assume a significance level of α = 0.05 and degrees of freedom (df) = n - 1 = 14 - 1 = 13. Using a t-distribution table or calculator, the critical value for a one-tailed test at α = 0.05 and df = 13 is approximately 1.771.

Compare the test statistic to the critical value:

If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Since -0.8182 is less than 1.771, we fail to reject the null hypothesis.

Therefore, based on the given sample, assuming a normal population, and performing a one-tailed test at α = 0.05, we fail to reject the null hypothesis (H_ọ: µ = 190) in favor of the alternative hypothesis (H_A: μ > 190).

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Answer:

1. If D= whole numbers then the answer is B.0 if it is integers the answer is A.-10

2. The answer is D. That number is an irrational number.

Step-by-step explanation:

Im pretty sure that #1 is B.0, but since there are no labels and i haven't done this in a while, I wasn't quite sure. Sorry.

Answer:

The angles are adjacent, and x=100

Step-by-step explanation:

The angles are adjacent because they share the same starting point. x=100 because x and the other angle are on a line, which has a measure of 180 degrees. We subtract 80 from 180 to get 100.

Hope this was helpful.

~cloud

Answer:

Alternate exterior angles

Step-by-step explanation:

If they shared a vertex, they would be vertical angles, but since they are on different lines, and alternate sides, the dark blue (alternate exterior angles) answer is correct.

Answer:

90[tex]\pi[/tex]

Step-by-step explanation:

if you want explanation say in comments

[tex]c_0 = 9, c_1 = 2(9^2), c_2 = 3(9^3), c_3 = 4(9^4)[/tex]and [tex]c_4 = 5(9^5)[/tex]. The radius of convergence R is infinity.

To find the coefficients of the power series representation of the function f(x) = 5/(1 - 9x)², we can expand the function using the geometric series formula. The formula states that for |x| < 1, we have:

1/(1 - 9x) = 1 + 9x + (9x)² + (9x)³ + ...

Now, let's differentiate both sides of the equation with respect to x:

d/dx [1/(1 - 9x)] = d/dx [1 + 9x + (9x)² + (9x)³ + ...]

To differentiate the left side, we can use the power rule:

d/dx [1/(1 - 9x)] = (1 - 9x)⁻²

To differentiate the right side, we differentiate each term individually. Since the derivative of x^n with respect to x is nxⁿ⁻¹, the terms with powers of x become:

d/dx [1 + 9x + (9x)² + (9x)³ + ...] = 0 + 9 + 2(9²)x + 3(9³)x² + ...

Equating the derivatives, we have:

(1 - 9x)⁻² = 9 + 2(9²)x + 3(9³)x² + ...

To obtain the coefficients of the power series representation, we compare the terms on both sides of the equation. Since the expression on the right side is already in the desired form, we can read off the coefficients as follows:

[tex]c_0 = 9\\c_1 = 2(9^2)\\c_2 = 3(9^3)\\c_3 = 4(9^4)\\c_4 = 5(9^5)[/tex]

Now, let's find the radius of convergence R of the series. The radius of convergence can be determined using the ratio test. The ratio test states that if the limit of |[tex]c_{n+1} / c_n[/tex]| as n approaches infinity is L, then the series converges if L < 1 and diverges if L > 1.

Applying the ratio test to our series, we have:

|[tex]c_{n+1} / c_n[/tex]| = |[(n+1)(9ⁿ⁺¹)] / [n(9ⁿ)]| = 9((n+1)/n)

Taking the limit as n approaches infinity, we get:

lim(n->∞) |[tex]c_{n+1}/ c_n[/tex]| = lim(n->∞) 9((n+1)/n) = 9

Since the limit is 9, which is less than 1, the series converges for all values of x within a radius of convergence R. Therefore, the radius of convergence R is infinity (R = ∞).

Therefore,[tex]c_0 = 9, c_1 = 2(9^2), c_2 = 3(9^3), c_3 = 4(9^4)[/tex]and [tex]c_4 = 5(9^5)[/tex]. The radius of convergence R is infinity.

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Answer: D, i am a hight school teacher names miss smell my butt, and i know that i am right

Answer:

i dont know im not that smart ask someone else dude

Step-by-step explanation:

There is a strong negative linear relationship between x and y, and almost all of the variation in y can be explained by the variation in x.

The correlation coefficient is -0.961 and the proportion of the variation in y that can be explained by the variation in the values of x is 92.3%.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient between x and y is -0.961, which indicates a strong negative linear relationship between the two variables.

The coefficient of determination (r²) measures the proportion of the variation in y that can be explained by the variation in the values of x. In this case, the value of r² is 0.923, or 92.3%. This means that 92.3% of the variability in y can be explained by the variability in x. Therefore, there is a strong negative linear relationship between x and y, and almost all of the variation in y can be explained by the variation in x.

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Answer:

horizontal

vertical

diagonal

Step-by-step explanation:

I guess I only know those.hope it helps you

Answer:

the transfer of energy from one organism to another

Step-by-step explanation:

Answer:  x = 10

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

(2x + 3) + (5x + 17) + 90 = 180

2x + 3 + 5x + 17 + 90 = 180

7x + 110 = 180

7x = 70

x = 10

The value of N₂(h), for the following data gives an approximation to the integral M = [tex]\int\limits^1_0 {f(x)} \, dx[/tex]  N₁(h)= 2.2341 N₁(h/2) = 2.0282 is 0.8754. So, none of the options are correct.

Given that N₁(h)= 2.2341 and N₁(h/2) = 2.0282.

Applying Richardson's extrapolation method, we can find the value of the definite integral M using the formula,

M = N₁(h) + k₂h² + k₄h⁴ + ...

Therefore, we have to find the value of N₂(h).

Here, h = 1 - 0 = 1.

N₂(h) can be obtained by the formula,

[tex]N_2(h) = \frac{(2^2 * N_1(h/2)) - N_1(h)}{2^2 - 1}[/tex] , Substituting the data values we get,

[tex]N_2(h) =\frac{(2^2 * 2.0282) - 2.2341}{2^2 - 1}[/tex]

[tex]N_2(h)= \frac{8.1128 - 2.2341}{3}[/tex]

[tex]N_2(h)=\frac{2.6263 }{3}[/tex]

[tex]N_2(h)=0.8754333 = 0.8754[/tex]

Therefore, none of the option is correct.

The question should be:

The following data gives an approximation to the integral M =  [tex]\int\limits^1_0 {f(x)} \, dx[/tex]  N₁(h)= 2.2341 N₁(h/2) = 2.0282. Assume M = N₁(h) + k₂h² + k₄h⁴ + ... then, N₂(h) =

a. 2.01333

b. 1.95956

c. 0.95957

d. 2.23405

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Answer:

20

Step-by-step explanation:

Answer:

226.19 inches

Step-by-step explanation:

The average amount Rebecca pays for electricity based on the given data is $124.60.

To calculate the average, we add up the amounts she paid in each month and then divide by the total number of months. In this case, the sum of her payments is $135 + $129 + $99 + $120 + $140 = $623. Dividing this sum by the total number of months (5), we get an average of $623 / 5 = $124.60. Calculating the average helps us determine the typical amount Rebecca pays for electricity based on the given data. It provides an overall picture of her average expenses in the specified period.

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The projection matrix P is [1/√11 -1/√337].

To find the projection matrix that projects vectors in ℝ³ onto the subspace W spanned by the vectors [3 1 1] and [15 11 -1], we can follow these steps:

Let's start by normalizing the basis vectors of W. Normalizing means dividing each vector by its magnitude to obtain unit vectors.

First basis vector:

u₁ = [3 1 1]

Normalize: v₁ = u₁ / ||u₁||

Compute the magnitude: ||u₁|| = √(3² + 1² + 1²) = √11

Normalize: v₁ = [3/√11, 1/√11, 1/√11]

Second basis vector:

u₂ = [15 11 -1]

Normalize: v₂ = u₂ / ||u₂||

Compute the magnitude: ||u₂|| = √(15² + 11² + (-1)²) = √337

Normalize: v₂ = [15/√337, 11/√337, -1/√337]

Next, we construct a matrix P using the normalized basis vectors as columns.

P = [v₁ v₂]

P = [3/√11 15/√337]

[1/√11 11/√337]

[1/√11 -1/√337]

Therefore, the projection matrix P that projects vectors in ℝ³ onto the subspace W spanned by the vectors [3 1 1] and [15 11 -1] is:

P = [3/√11 15/√337]

[1/√11 11/√337]

[1/√11 -1/√337]

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Answer:

7z

Step-by-step explanation:

Answer: 7z

Step-by-step explanation:

two negatives cancel into a positive, so -(-3z) is +3z. 4z + 3z = 7z

Answer: √113 or 10.63

Step-by-step explanation: the exact answer is √113, or 10.63 if you're looking for the decimal form

Step-by-step explanation:

Let the distance between two points A = (-4,7) and B = (4,0).

Here, x1 = -4 , y1 = 7

x2 = 4 , y2 = 0

Use the distance formula to find out the distance between two points are:

AB = √[(x2-x1)²+(y2-y1)²]

= √[{4-(-4)}²+(0-7)²]

= √[(4+4)²+(-7)²]

= √[(8)² + (-7)²]

= √[(8*8)+(-7*-7)]

= √[64+49]

= √[113] ⇛10.630 units approximately.

The posterior probability mass function of X is given below:0.4 * 0.0183 = 0.00732.0.6 * 0.0513 = 0.03078. Posterior Probability Mass Function of X: ____0.00732 if A = 1.0.____0.03078 if A = 1.5.

Explanation: The probability mass function for Poisson distribution is given by: P(X = x) = (e^-λ * λ^x) / x!Where,λ is the mean. The given prior probability mass function of A is P (A = 1.0) = 0.4P(A = 1.5) = 0.6.

Thus, the mean is either A = 1.0 or A = 1.5.

Now, let X be the number of defects on a roll of tape. Using the law of total probability, the probability mass function of X is P (X = x) = P (X = x, A = 1.0) + P (X = x, A = 1.5)

Using Bayes' theorem, the posterior probability mass function is given by: P (A = 1.0 | X = 4) = P (X = 4 | A = 1.0) * P (A = 1.0) / P (X = 4) P (A = 1.5 | X = 4) = P (X = 4 | A = 1.5) * P (A = 1.5) / P (X = 4)

Now, we need to calculate P (X = 4 | A = 1.0) and P (X = 4 | A = 1.5) using the Poisson distribution.

P (X = 4 | A = 1.0) = (e^-1 * 1^4) / 4! = 0.0183.P(X = 4 | A = 1.5) = (e^-1.5 * 1.5^4) / 4! = 0.0513.

Now, we need to calculate the value of the denominator,

P (X = 4). P (X = 4) = P (X = 4, A = 1.0) + P (X = 4, A = 1.5) = P (X = 4 | A = 1.0) * P (A = 1.0) + P (X = 4 | A = 1.5) * P (A = 1.5)

Put the values: P (X = 4) = (0.0183 * 0.4) + (0.0513 * 0.6) = 0.0342.

Put the values in the above posterior probability mass function equations,

we get: P (A = 1.0 | X = 4) = 0.00732 and P (A = 1.5 | X = 4) = 0.03078.

Therefore, the posterior probability mass function of X is:0.00732 if A = 1.0.0.03078 if A = 1.5.

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Answer:

600 cm²

Step-by-step explanation:

The shaded area (A) is calculated as

A = area of square - ( area of 3 unshaded triangles )

area of square = 40 × 40 = 1600 cm²

area of lower right triangle = [tex]\frac{1}{2}[/tex] × 20 × 40 = 10 × 40 = 400 cm²

area of upper left triangle = [tex]\frac{1}{2}[/tex] × 40 × 20 = 20 × 20 = 400 cm²

area of lower left triangle = [tex]\frac{1}{2}[/tex] × 20 × 20 = 10 × 20 = 200 cm²

Then

A = 1600 - (400 + 400 + 200 ) = 1600 - 1000 = 600 cm²

the correct answer is X= -3

Answer:

235.5 cubic feet

Step-by-step explanation:

The volume v of a circular cylinder whose base radius is r and height h is given as

v = πr^2h

where π is 22/7 or 3.14

Given that the radius is five feet and the height  is three feet

the volume v = 3.14 *5^2 * 3

= 235.5 cubic feet

The volume of the oblique circular cylinder is 235.5 cubic feet

Answer:

i think its c hope it helps

Step-by-step explanation: