Use unit multipliers to convert 14 yards per minute to inches per second.

The given matrix Q is orthogonal. To see why, note that the dot product of any two columns of Q is equal to zero, which is a necessary condition for a matrix to be orthogonal.

To find the inverse of Q, we can use the fact that for an orthogonal matrix, its inverse is equal to its transpose. Thus,

Q^-1 = Q^T

Therefore, the inverse of Q is

Q^-1 =

[1/sqrt(2)  1/sqrt(2)]

[1/sqrt(2) -1/sqrt(2)]

Note that we could have also used the fact that for a 2x2 orthogonal matrix, its inverse can be found by swapping the elements on the diagonal and changing the sign of the off-diagonal elements. In this case, we have  Q^-1 =

[1/sqrt(2)  1/sqrt(2)]

[1/sqrt(2) -1/sqrt(2)]

which is the same as the result obtained by taking the transpose of Q.

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Answer:

1.2

Step-by-step explanation:

range is the largest value subtracted from the smallest one in this case 1.4 - 0.2

Answer:

1.2

Step-by-step explanation:

subtract the biggest and smallest numbers

To find the critical points of a function, we need to determine the points at which the gradient of the function is zero or undefined.

In the case of the given function f(x,y) = 2x^4 + 3y^2 - 10xy - 3, we need to find the values of x and y where the partial derivatives of f with respect to x and y are both zero.

After taking the partial derivatives of the function with respect to x and y, we got two equations.

We solved these equations simultaneously to obtain the values of x and y at which the partial derivatives of f are both zero. The obtained values of x and y are the critical points of the function.

In this case, we got two critical points ( √(25/12), (25/12)√(3/5)), (- √(25/12), -(25/12)√(3/5)).

To check whether these critical points are maximum, minimum, or saddle points, we can use the second derivative test.

We can evaluate the second partial derivatives of f and plug in the values of x and y for each critical point to determine the nature of the critical points.
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The indefinite integral of tan^3(x) sec^6(x) dx is (1/5)sec^5(x) + (1/3)sec^3(x) + C, where C is the constant of integration.

To solve this integral, we can use the substitution u = sec(x) and du = sec(x)tan(x) dx.

Then, we can rewrite the integral as ∫tan^3(x) sec^6(x) dx = ∫tan^2(x) sec^5(x) sec(x) tan(x) dx = ∫(sec^2(x) - 1)sec^5(x) du.

Simplifying and integrating, we get (1/5)sec^5(x) - (1/3)sec^3(x) + C.

Therefore, The indefinite integral of tan^3(x) sec^6(x) dx is (1/5)sec^5(x) + (1/3)sec^3(x) + C, where C is the constant of integration.

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The characteristic polynomial of the given matrix is λ(λ - 3055).

The characteristic polynomial of a matrix is obtained by taking the determinant of the matrix subtracted by a scalar multiplied by the identity matrix. In this case, the given matrix is a 2x2 matrix. Therefore, the characteristic polynomial can be obtained by:

det(a - λI) =

| 3055 - λ    -5 |

|   -1    0 - λ |

= (3055 - λ) * (-λ) - (-5 * -1)

= λ^2 - 3055λ

= λ(λ - 3055)

Therefore, the characteristic polynomial of the given matrix is λ(λ - 3055).

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The length of the curve over the given interval is 2πa, where a is the constant in the polar equation r = 8a cos θ.

To find the length of the curve defined by a polar equation, we use the formula:

L = ∫[tex]a^b[/tex] √[r² + (dr/dθ)²] dθ

where a and b are the angles of the interval and r is the polar equation.

In this case, r = 8a cos θ, so we need to find dr/dθ:

dr/dθ = -8a sin θ

Now we can substitute into the formula for L:

L = ∫[tex](-\pi /16)^(^\pi^ /^1^6^)[/tex] √[(8a cos θ)²+ (-8a sin θ)²] dθ

Simplifying under the square root:

L = ∫[tex](-\pi /16)^(^\pi ^/^1^6^)[/tex] √[64a²(cos²θ + sin²θ)] dθ

L = ∫[tex](-\pi /16)^(^\pi^ /^1^6^)[/tex] 8a dθ

L = 16a(π/16 - (-π/16))

L = 2πa

Therefore, the length of the curve over the given interval is 2πa, where a is the constant in the polar equation r = 8a cos θ.

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We need to evaluate the line integral ∫CF.dr for two different paths, r1(t) and r2(t), where F = (x^2 + y^2) dx + 2xy dy.

We will use the fundamental theorem of line integrals to determine if F is conservative.

Since F has continuous first-order partial derivatives, we can check if F is conservative by verifying that ∂F/∂y = ∂M/∂x, where M = x^2 + y^2 and N = 2xy are the components of F. We have:

∂F/∂y = 2xy = ∂M/∂x

Therefore, F is conservative.

By the fundamental theorem of line integrals, the line integral of a conservative field depends only on the endpoints of the path, and not on the path itself.

Therefore, we can choose any path that connects the same two endpoints and calculate the line integral along that path.

(a) Using r1(t) = t^5i + t^2j, 0 ≤ t ≤ 2:

We have:

dr/dt = 5t^4i + 2tj

Substituting into F, we get:

F = (t^10 + t^4) dt + 2t^3 dt

Therefore, the line integral along r1(t) is:

∫CF.dr = ∫0^2 F(r1(t)).(dr/dt) dt
= ∫0^2 [(t^10 + t^4) dt + 2t^3 dt] . (5t^4i + 2tj)
= ∫0^2 (5t^15 + 7t^5) dt
= (5/16) (2^16 - 1) + (7/6) (2^6 - 1)

(b) Using r2(t) = 5cos(t)i + 2sin(t)j, 0 ≤ t ≤ π/2:

We have:

dr/dt = -5sin(t)i + 2cos(t)j

Substituting into F, we get:

F = (25cos^2(t) + 4sin^2(t)) dt - 20sin(t)cos(t) dt

Therefore, the line integral along r2(t) is:

∫CF.dr = ∫0^(π/2) F(r2(t)).(dr/dt) dt
= ∫0^(π/2) [(25cos^2(t) + 4sin^2(t)) dt - 20sin(t)cos(t) dt] . (-5sin(t)i + 2cos(t)j)
= ∫0^(π/2) (20cos^2(t) - 45sin^2(t)) dt
= 20(π/4) - 45(1/4)

Hence, the value of the line integral for both paths r1(t) and r2(t) is:

(5/16) (2^16 - 1) + (7/6) (2^6 - 1) = 1247.875

Note that the line integral is the same for both paths, as expected for a conservative field.

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The equilibrium values of the given system of differential equations are (0,0), (1,0), and (1/2,1/2).

To find the equilibrium values, we need to set both differential equations equal to zero and solve for x and y. For the first equation, we can factor out x and get x(1-x-2y) = 0. This gives us two possible equilibrium values: x = 0 or 1-x-2y = 0. Solving for y in the second equation and substituting into the first equation, we get x(1-x-2sin(x-1)) = 0. This gives us the third equilibrium value of (1/2,1/2). To determine the stability of each equilibrium, we can find the Jacobian matrix of the system and evaluate it at each equilibrium. Then, we can find the eigenvalues of the matrix to determine whether the equilibrium is stable, unstable, or semi-stable. However, since it is not part of the question, we will leave it at finding the equilibrium values.

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We can see that all of the x values in the interval [4,10] are evaluated. Therefore, the answer is option c: 4, 5, 6, 7, 8, 9, 10.

To find r6 on the interval [4,10], we need to first understand what r6 means. In this case, r6 refers to the sixth term in a sequence. The sequence may be given or implied, but for the sake of this question, let's assume it is not given.
Since we are asked to find r6 on the interval [4,10], we know that the sequence must start at 4 and end at 10. We also know that we need to evaluate x values to find the sixth term in the sequence, which is r6.
To find r6, we need to evaluate the sequence up to the sixth term. We can do this by using a formula for the sequence, or we can simply list out the terms. Let's list out the terms:
4, 5, 6, 7, 8, 9, 10
The sixth term in this sequence is 9, so r6 = 9.
To answer the question of which x values would be evaluated, we can see that all of the x values in the interval [4,10] are evaluated. Therefore, the answer is option c: 4, 5, 6, 7, 8, 9, 10.

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The sum of the terms 2, 4, 6, ..., 60 can be written in sigma notation as: ∑(2k), k = 1 to 30. Here, the Greek letter sigma, ∑, represents the sum of the terms that follow it.

The expression (2k) represents the k-th term of the sequence, where k takes values from 1 to 30. By plugging in k = 1, we get the first term of the sequence, 2. Similarly, by plugging in k = 2, we get the second term of the sequence, 4, and so on. Finally, by plugging in k = 30, we get the last term of the sequence, 60. Therefore, the sum represented by the above sigma notation is the sum of the terms 2, 4, 6, ..., 60.

In general, if we want to find the sum of the first n even numbers, we can use the following sigma notation:

∑(2k), k = 1 to n

By plugging in k = 1, we get the first even number, 2. Similarly, by plugging in k = 2, we get the second even number, 4, and so on, up to the n-th even number, which is given by plugging in k = n. Thus, the sum represented by this sigma notation is the sum of the first n even numbers.

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The exponential equation is solved and the size of the bacterial population after 5 hours is A = 10,13,70,828.15

Given data ,

To find the initial population at time t = 0, we can use the concept of doubling time. The doubling time is the amount of time it takes for a population to double in size.

Now , at time t = 90 minutes, the bacterial population was 70,000.

Since the doubling period is 20 minutes, we can calculate the number of doubling periods that have passed from t = 0 to t = 90 minutes.

Number of doubling periods = t / doubling period

Number of doubling periods = 90 / 20

Number of doubling periods = 4.5

This means that by time t = 90 minutes, the population has undergone 4.5 doubling periods.

To find the initial population at time t = 0, we need to divide the population at t = 90 minutes by the number of doubling periods that have occurred.

Initial population = Population at t = 90 minutes / (2^number of doubling periods)

On simplifying the exponential equation , we get

Initial population = 70,000 / (2^4.5)

Initial population ≈ 70,000 / 11.31

Initial population ≈ 3,093.59

Therefore, the initial population at time t = 0 is approximately 6,184.63.

To find the size of the bacterial population after 5 hours (300 minutes), we can use the same concept of doubling time.

Number of doubling periods = t / doubling period

Number of doubling periods = 300 / 20

Number of doubling periods = 15

Size of the population after 5 hours = Initial population x (2^number of doubling periods)

Size of the population after 5 hours = 3,093.5921 x (2^15)

Size of the population after 5 hours ≈ 3,093.5921 x 32,768

Size of the population after 5 hours ≈ 10,13,70,828.150

Hence , the size of the bacterial population after 5 hours is approximately 10,13,70,828.150

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Answer:

--------------------

The two given lines have equal slopes (3) but different y-intercepts (4 vs 5).

It means the lines are parallel, hence no intersections.

If no intersections then no solution.

The answer to your question is d. Demand-pull inflation. This type of inflation occurs during economic expansions when a high demand for goods and services exceeds the supply.

This leads to an increase in prices as consumers compete for limited resources. Demand-pull inflation is typically caused by factors such as a growing economy, low unemployment rates, and increased consumer spending. One example of demand-pull inflation is the housing market boom that occurred in the early 2000s. As more people sought to buy homes, the demand for housing increased while the supply remained relatively constant. This led to a rise in housing prices, making it more difficult for first-time homebuyers to afford homes. Demand-pull inflation can have both positive and negative effects on the economy. On one hand, it can signal a healthy and growing economy. On the other hand, if it is left unchecked, it can lead to higher prices and reduced purchasing power for consumers. As a result, governments and central banks may take action to control inflation through measures such as raising interest rates or reducing government spending.

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According to the figure in the problem, the option that best describes it is

D. Not similar

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

In this case as in the figure, there is a congruent and angle however the sides are not proportional

That is to say that

42 / 20 ≠ 36 / 24

21 / 10 is not equal to 3 / 2

hence the sides are not proportional

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The scalar product of a vector is A · B = 35

Given data ,

The product of vectors is:

A · B = |A| |B| cos(θ)

where A and B are vectors, |A| and |B| are the lengths (magnitudes) of the vectors, and θ is the angle between the vectors.

In this case, the length of vector A is 7 and the length of vector B is 10. The angle between them is 60 degrees.

Substituting the given values into the formula, we have:

A · B = |A| |B| cos(θ)

= 7 * 10 * cos(60°)

= 70 * cos(60°)

The cosine of 60 degrees is 0.5, so we can simplify further:

A · B = 70 * cos(60°)

= 70 * 0.5

= 35

Hence , the scalar product of a vector of length 7 and a vector of length 10, which make an angle of 60 degrees with each other, is 35

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The relative importance of unique events may decrease as the probability of a super event increases, it is important to consider all potential risks and their unique characteristics in a comprehensive approach to risk management.

The relationship between the probability of a super event and the importance of a unique event is complex and depends on several factors. Generally speaking, as the probability of a super event increases, the importance of a unique event may decrease in relative importance.

This is because the focus shifts from rare events to more probable ones. As the probability of a super event increases, there may be a greater need to allocate resources toward preventing or mitigating the effects of such events. This can mean that resources that were previously allocated to mitigating the risks of unique events may be redirected towards addressing the more significant risk posed by the super event.

However, it is important to note that the importance of unique events should not be overlooked or underestimated. These events may still pose significant risks and may require specific measures to prevent or mitigate their effects. Additionally, unique events may have consequences that cannot be addressed by measures intended to address super events.

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You would pay approximately $1630.19 in interest for the amount you are able to borrow.

To calculate the amount you are able to borrow, we can use the formula for the present value of an annuity:

P = PMT ((1 - (1 + r)⁻ⁿ) / r)

Where:

P is the principal amount (the amount you are able to borrow)

PMT is the monthly payment you can afford ($300)

r is the monthly interest rate (3.8% divided by 100, then divided by 12)

n is the number of months (5 years multiplied by 12)

Let's calculate the amount you are able to borrow:

r = 3.8% / 100 / 12 = 0.0031667 (rounded to 7 decimal places)

n = 5 years x 12 = 60 months

P = $300 x ((1 - (1 + 0.0031667)⁻⁶⁰) / 0.0031667)

P ≈ $16369.81

Therefore, you are able to borrow approximately $16369.81.

To calculate the interest you would pay for the amount you are able to borrow, we can subtract the principal amount from the total amount paid over the 5-year period. The total amount paid can be calculated as:

Total Amount Paid = Monthly Payment x Number of Months

Total Amount Paid = $300 x 60 = $18,000

Interest Paid = Total Amount Paid - Principal Amount

Interest Paid = $18,000 - $16369.81 ≈ $1630.19

Therefore, you would pay approximately $1630.19 in interest for the amount you are able to borrow.

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The function f(x,y) can be expressed as [tex]2y^3 - 4x^{2y}[/tex] + D.

We know that if F(x,y) is a scalar field, then its gradient is given by:

∇F(x,y) = (∂F/∂x)i + (∂F/∂y)j

So, in this case, we are given:

grad F(x,y) = 12xyi + 6(x² + y²)j

Comparing this to the general formula, we see that:

To find F(x,y), we need to integrate each of these partial derivatives with respect to their respective variables. Integrating with respect to x, we get:

F(x,y) = ∫(12xy)dx [tex]= 6x^{2y} + C(y)[/tex]

Here, C(y) is the constant of integration with respect to x. To find C(y), we differentiate F(x,y) with respect to y and compare it to the second partial derivative of F(x,y) with respect to y:

Differentiating F(x,y) with respect to y, we get:

∂F/∂y = 6x² + C'(y)

Here, C'(y) is the derivative of C(y) with respect to y. Comparing this to the second partial derivative, we get:

Integrating C'(y) with respect to y, we get:

C(y) [tex]= 2y^3 - 4x^{2y} + D[/tex]

Here, D is the constant of integration with respect to y. Putting everything together, we get:

F(x,y) [tex]= 6x^{2y} + 2y^3 - 4x^{2y} + D = 2y^3 - 4x^{2y} + D[/tex]

Therefore, f(x,y) [tex]= 2y^3 - 4x^{2y} + D[/tex].

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Answer:

D

Step-by-step explanation:

Usr the equation they gave you and plug in the number given for x and y.

y=2x+4

4=2(0)+4. 4=0+4. 4=4

8=2(2)+4. 8=4+4. 8=8

12=2(4)+4. 12=8+4. 12=12

16=2(6)+4. 16=12+4. 16=16

If you did that method with the other options they don't equal each other such as option B for example

0=2(0)+4. 0=0+4. 0=4

4=2(2)+4. 4=4+4. 4=8

These don't equal each other .

Under the periodic inventory system, Crowder Corporation would record the return of $200 of goods originally sold on credit to Discount Industries by crediting the accounts receivable account for $200 and debiting the sales returns and allowances account for $200.

If Crowder Corporation recorded the return of $200 of goods originally sold on credit to Discount Industries using the periodic inventory system, the transaction would be recorded as follows:

1. The accounts receivable account would be credited for $200 to reflect the fact that the company's outstanding balance owed by Discount Industries has been reduced.
2. The sales returns and allowances account would be debited for $200 to reflect the decrease in sales due to the return of goods.
3. The inventory account would be credited for the cost of the goods returned. Assuming that the goods were originally sold for their cost, the cost of the returned goods would also be $200. This credit would reduce the inventory account balance to reflect the fact that the company has fewer goods on hand.

The journal entry to record the return of goods under the periodic inventory system would be:

Accounts Receivable        200
Sales Returns and Allowances   200
  (To record the return of goods sold on credit)

Inventory                      200
Cost of Goods Sold          200
  (To record the cost of goods returned)

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Complete question:- Crowder Corporation recorded the return of $200 of goods originally sold on credit to Discount Industries. Using the periodic inventory approach, Crowder would record this transaction as ?

The correct answer is (a) there is enough evidence to conclude that age and drink preference is dependent.

Using the formula for the chi-square test of independence, we can calculate the test statistic as:

X² = Σ (O-E)^2 / E

Performing this calculation on the given data, we get:

X² = (50-62.5)²/62.5 + (100-87.5)²/87.5 + (200-250)²/250 + (200-200)²/200 + (50-50)²/50 + (200-150)²/150 + (50-37.5)²/37.5 + (150-162.5)²/162.5 + (200-250)²/250 + (50-50)²/50 = 34

Using a chi-square distribution table with (2-1)*(4-1)=3 degrees of freedom and a significance level of 0.05, the critical value is 7.815.

Since the calculated test statistic of 34 is greater than the critical value of 7.815, we can reject the null hypothesis of independence and conclude that there is enough evidence to support the alternative hypothesis that age and drink preference are dependent.

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In general, economists are critical of monopoly when there is a lack of competition in the market. Hence, option 1) is correct.

This includes situations where there are only a few firms operating in the market, as well as situations where there is a natural monopoly, which occurs when the most efficient market structure involves only one firm due to high fixed costs. However, even in cases of persistent economies of scale where it may seem like a monopoly is necessary for efficiency, economists still tend to be critical as monopolies can lead to higher prices, lower quality products, and reduced innovation.

A monopoly in economics is a scenario when one business or entity has complete control over the production and distribution of a specific good or service. Due to the monopolist's ability to set prices above what the market would otherwise bear, there would be less consumer surplus and associated inefficiencies. Monopolies can develop as a result of entry-level restrictions, such as expensive beginning fees or legal requirements, or through acquiring rival businesses. Monopolies may be regulated or dismantled by governments in an effort to boost competition and safeguard the interests of consumers. Monopolies are a fundamental idea in industrial organisation and have significant effects on the composition and operation of markets.

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The combination of two events consisting of all outcomes that are contained in one event or a second event is:

The Union

The correct option is (c)

The union sets are the sets containing all elements that are in A or in B (possibly both). We write the (A ∪ B)

The event A occurs the outcome is contained in A. For any two events A and B, we define the new event A ∪ B, called the union of events A and B. It also says that: The combination of two events consisting of all outcomes that are contained in one event or a second event is: The Union

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The given question is incomplete, complete question is:

The combination of two events consisting of all outcomes that are contained in one event or a second event is :

a. complement b. intersection c. union d. condition

Answer:

0.4

Step-by-step explanation:

if we order them the middle value is the median

Answer: 0.4

Step-by-step explanation: it is in the middle of the data set.

He got to it before me though so give him brainliest.

To find the radius of convergence, we use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges absolutely. If the limit is greater than 1, then the series diverges. If the limit is equal to 1, then the test is inconclusive.

In this case, we have the series (-1)^(n-1)/n5^n. Taking the absolute value of the ratio of consecutive terms, we get |((-1)^n)/(n+1)(5^(n+1))) / ((-1)^(n-1)/n5^n)| = 1/(5(n+1)). Taking the limit as n approaches infinity, we get 1/5. Since the limit is less than 1, the series converges absolutely.

The radius of convergence is equal to the reciprocal of the limit we just found, which is 5. Therefore, the series converges for all x values between -5 and 5.

To find the interval of convergence, we need to test the endpoints. When x=5, the series becomes (-1)^(n-1)/(5n), which is an alternating series. The alternating series test tells us that the series converges if the absolute value of the terms decreases and approaches zero. In this case, the terms are decreasing in absolute value but do not approach zero, so the series diverges at x=5.

When x=-5, the series becomes (-1)^(n-1)/(-5n), which is also an alternating series. The same reasoning as above tells us that the series converges at x=-5.

Therefore, the interval of convergence is [-5,5).

The radius of convergence of the series (-1)^(n-1)/n5^n is 5, and the interval of convergence is [-5,5). To find the radius of convergence, we used the ratio test and found that the limit of the absolute value of the ratio of consecutive terms is 1/5. To find the interval of convergence, we tested the endpoints and found that the series converges at x=-5 and diverges at x=5.

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The interval of convergence is [-5,5). We apply the ratio test to determine the radius of convergence. The ratio test asserts that the series converges absolutely if the limit of the absolute value of the ratio of consecutive terms is smaller than 1.

The series diverges if the limit is bigger than 1. The test is not convincing if the limit is equal to 1.The series in question is (-1)(n-1)/n5n. The result is |((-1)n)/(n+1)(5(n+1))] / ((-1)(n-1)/n5n)| = 1/(5(n+1) when we take the absolute value of the ratio of successive words. When we take the limit as n gets closer to infinity, we get 1/5. Since 1, the limit, the series completely converges.

The radius of convergence is equal to the reciprocal of the limit we just found, which is 5. Therefore, the series converges for all x values between -5 and 5.

To find the interval of convergence, we need to test the endpoints. When x=5, the series becomes (-1)[tex]^(n-1)/(5n)[/tex], which is an alternating series. The alternating series test tells us that the series converges if the absolute value of the terms decreases and approaches zero. In this case, the terms are decreasing in absolute value but do not approach zero, so the series diverges at x=5.

When x=-5, the series becomes (-1)[tex]^(n-1)/(-5n),[/tex]which is also an alternating series. The same reasoning as above tells us that the series converges at x=-5.

Therefore, the interval of convergence is [-5,5).

The radius of convergence of the series (-1)^(n-1)/n[tex]5^n[/tex] is 5, and the interval of convergence is [-5,5). To find the radius of convergence, we used the ratio test and found that the limit of the absolute value of the ratio of consecutive terms is 1/5. To find the interval of convergence, we tested the endpoints and found that the series converges at x=-5 and diverges at x=5.

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Answer:

D. 6w + 5

Step-by-step explanation:

a² + 2ab + b² = (a + b)²

36w² + 60w + 25 = (6w + 5)²

Answer: D. 6w + 5

We are given that this triangle is a right triangle, one angle measurement, and one side length. Therefore, to figure out the other side length, we can use a trigonometric function to figure out side x. If we orient the triangle to angle T, then the hypotenuse is the side length measuring 1.8 units and side length x is the opposite (because it is opposite from angle T). This insinuates we use a sine to figure out side length x because sine finds the ratio between the opposite and the hypotenuse:

sin(50 deg) = x/1.8

1.8*sin(50 deg) = x

x is about 1.3788

Answer:

1.379 or 1.4 (to 1dp)

Step-by-step explanation:

For this question we obviously need to use trigonometry. We will use the equation O = S x H, where O is the opposite side, S is sin and H is the hypotenuse.

Answer: i think the awnser to your question is A  real number

Step-by-step explanation:

Taking the absolute value of a number, whether it's negative or positive, always returns either a positive value or zero.

Let's say we have a number line with the point A on it. Think of the absolute value of A as the distance between point A and zero. Since the distance cannot be negative, the absolute value will always return a positive value.

A positive number is always greater than zero, and zero is equal to zero. Therefore, the answer is True.

21 inch²

we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6

Answer:

2(3) + 2(6) = 6 + 12 = 18 square feet