(b) estimate the errors in the approximations t8 and m8 in part (a). (use the fact that the range of the sine and cosine functions is bounded by ±1 to estimate the maximum error. round your answer to seven decimal places.) |et| ≤ |em| ≤

The inverse Laplace transform of the given function using the convolution theorem is t⁵/12.

To find the inverse Laplace transform of the given function using the convolution theorem, we need to first factorize the denominator. This gives us:
F(s) = 1/s⁴(s²+1) = 1/s⁴ * 1/(s²+1)

Now, we can use partial fraction decomposition to express F(s) as a sum of simpler fractions. This gives us:
F(s) = A/s + B/s² + C/s³ + D/s⁴ + E/(s²+1)

Where A, B, C, D, and E are constants that we need to solve for. Multiplying both sides by s⁴(s²+1), we get:
1 = As³(s²+1) + Bs²(s²+1) + Cs(s²+1) + D(s²+1) + Es⁴

Setting s=0, we get:
1 = D

Setting s=±i, we get:
0 = E

Using the other equations, we can solve for A, B, and C. This gives us:
A = 0, B = 0, C = -1/2

Therefore, the partial fraction decomposition of F(s) is:
F(s) = -1/(2s³) + 1/(s⁴)

Now, we can use the convolution theorem to find the inverse Laplace transform of F(s). The convolution theorem states that the inverse Laplace transform of the product of two functions is equal to the convolution of their inverse Laplace transforms. That is:

L-¹{F(s)}(t) = L-¹{-1/(2s³)} * L-¹{1/(s⁴)}

Using a table of Laplace transforms, we can find that:

L-¹{-1/(2s³)} = t²/2

L-¹{1/(s⁴)} = t³/6

Therefore, the inverse Laplace transform of F(s) is:
L-¹{F(s)}(t) = t²/2 * t³/6 = t⁵/12

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Answer:

d. All of the above are true

Step-by-step explanation:

All of the following statements,

a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.

b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.

C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.

are true

If we were to denote the counterclockwise rotation by θ, then the angle would be measured around the origin, starting from the positive x-axis and proceeding in a counterclockwise direction.

In 2D space, angles are measured around the origin and are referred to as the angle of rotation. This is measured in degrees or radians and can be calculated using trigonometry.

In 2D space, angles are measured about the origin. In other words, the point (0,0) is used as a reference point. In addition, the standard position of an angle is a unit vector along the positive x-axis that has been rotated counterclockwise by the angle in question.

If we were to denote the counterclockwise rotation by θ, then the angle would be measured around the origin, starting from the positive x-axis and proceeding in a counterclockwise direction.

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Answer:

y-187.50= 1.50(x-125)

this is in point slope, but in slope intercept it would be y=1.50x+0

Step-by-step explanation:

Answer:

\(y-187.50=1.50(x-125)\)

Step-by-step explanation:

Slope = $1.50

\(x=125\)

\(y=$187.50\)

Answer:

2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2. Now we collect the factors, so our final answer is 60 = 5 x 3 x 22.

Step-by-step explanation:

Answer:

51t^3

Step-by-step explanation:

64+3=67

67 +(-16)=51

t^2 +t= t^3

now you just add them up but they cant be combined because one is a number and the other a variable w an exponent so we just get 51t^3

\(\huge\bold{ANSWER:}\)

\(✠===============✠\)

\( \small\sf\to\green{solution:}\)

\(t = \frac{distance}{speed} \)

\(t = \frac{1.25}{10} \)

\( = 0.125\)

\(0.125 hr \times \frac{60min}{1hr} = 7.5min\)

\(7.5min = 7min + 0.5min\)

\(0.5min \times \frac{60s}{1min} = 30s \)

\(combining: 00 : 07 : 30\)

or

0 hours, 7 minutes, 30 seconds

therefore,the answer is 00:07:30

\(✠===============✠\)

Answer:

The answer is C.

Step-by-step explanation:

First divide both sides by -6.

48/-6 > x/-6

Remember, you switch the signs if you are dividing by a negative number.

The final answer will be x<-8.

Hope this helps!

Answer:

81000000

Step-by-step explanation:

bracket one

3^2 = 9

9^2 = 81

bracket two

10^3 = 1000

1000^2 = 1000000

81 × 1000000 = 81,000,000

im not very good at explaining but ive tried to break it into parts just to make it a bit simpler to understand :)

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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The inequality that describes the number of songs that can be on the disc is given as follows:

n < 20.

The graph, composed by the numbers to the left of n = 20, is given by the image presented at the end of the answer.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

A rewritable compact disc must have less than 20 songs on it, hence the inequality is given as follows:

n < 20.

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Answer:

Step-by-step explanation:

to make 3255 a perfect square subtract 6 from 3255

3255 - 6 = 3249

3249 is a perfect square

Answer:

1 I think

Step-by-step explanation:

To determine the optimal order quantity for Rocky Mountain Tire Center, you must consider ordering costs, storage costs, and the purchase price of the tires. The order quantity should minimize the total cost including both ordering cost and storage cost.

The EOQ formula is given by: EOQ = √((2DS) / H)

Where: D = Annual demand (7,000 go-cart tires)

S = Ordering cost per order ($40) H = Holding cost - percentage of the purchase price (40% of the purchase price)

we need to determine the purchase price per tire based on the quantity ordered.

EOQ = √((2 * 7,000 * 40) / (0.4 * 15))

=118 tires

they should order approximately 118 tires.

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The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

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To find the LCM:

1. List the multiples of each number:

Multiples of 14:

Multiples of 28:

2. The LCM is the smallest number that appears in the two lists above.

Answer:

x = 0.357143

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-1.6 - 2x = 5x + 0.9

Step 2: Solve for x

None of the options given in the question is correct.

To find when the object is at rest, we need to determine the values of t for which the velocity of the object is zero.

In other words, we need to find the values of t for which the derivative of the position function s(t) with respect to t is equal to zero.

Given the position function s(t) = ln(t^3 - 8t), we can find the velocity function v(t) by taking the derivative of s(t) with respect to t:

v(t) = d/dt ln(t^3 - 8t).

To find when the object is at rest, we need to solve the equation v(t) = 0.

v(t) = 0 implies that the derivative of ln(t^3 - 8t) with respect to t is zero. Taking the derivative:

v(t) = 1 / (t^3 - 8t) * (3t^2 - 8) = 0.

Setting the numerator equal to zero:

3t^2 - 8 = 0.

Solving this quadratic equation, we find:

t^2 = 8/3,

t = ± √(8/3).

Since the problem asks for the time when the object is at rest, we are only interested in the positive value of t. Therefore, the object is at rest when t = √(8/3).

The answer is not among the options provided (t=0 and t=1, t=1 and t=4, t=4 only, t=1 only). Hence, none of the options given in the question is correct.

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Answer:

£75

Step-by-step explanation:

Current value= 80

previous value= 100

current value 1

previous value = 100/80

current value-  £60

previous value 100x60/80

=6000/80

= £75

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Given:

Principal value = $5823.00

Rate of interest = 2.25%

Time = 4 years

To find:

The amount in the account after 4 years.

Solution:

The formula for amount is

\(A=P\left(1+\dfrac{r}{100}\right)^t\)

where, P is principal, r is rate of interest and t is time period.

Putting P=5823, r=2.25 and t=4 in the above formula.

\(A=5823\left(1+\dfrac{2.25}{100}\right)^4\)

\(A=5823\left(1+0.0225\right)^4\)

\(A=5823\left(1.0225\right)^4\)

\(A=5823(1.0930833)\)

\(A=6365.0240559\)

\(A\approx 6365.024\)

Therefore, the amount in the according after 4 years is about $6365.024.

Answer:

\(a_{n}\) = - 5n - 2

Step-by-step explanation:

there is a common difference between consecutive terms , that is

a₂ - a₁ = - 12 - (- 7) = - 12 + 7 = - 5

a₃ - a₂ = - 17 - (- 12) = - 17 + 12 = - 5

a₄ - a₃ = - 22 - (- 17) = - 22 + 17 = - 5

a₅ - a₄ = - 27 - (- 22) = - 27 + 22 = - 5

this indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + d(n - 1)

a₁ is the first term and d the common difference

here a₁ = - 7 and d = - 5 , then

\(a_{n}\) = - 7 - 5(n - 1) = - 7 - 5n + 5 = - 5n - 2

Answer:

5

Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

Slope = (28 - 18) / (4 - 2)

Slope = 10 / 2 = 5

Answer:

5

Step-by-step explanation:

5 is your answer because if you plot these on a graph you would know how many points there are in between them and there are 5

i hope this helps :)

Holy will take 13/5 or 2.6 hours to finish the bookcase.

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Time taken by Fritz to build a bookcase =  8 hours

So, Bookcase build by Fritz in 1 hour = 1/8

Similarly,

Time taken by Holly to build a bookcase =  10 hours

So, Bookcase build by Holly in 1 hour = 1/10

So, bookcase build in 3 hours

Fritz = 3/8

Holly = 3/10

Total bookcase build in 3 hours =  3/8 + 3/10 =  27/40

So. remaining work =  1 - 27/40 =  13/40

Thus, Time taken by Fritz to complete the bookcase =  8 * (13/40) hours

                                                                                         =  13/5 or 2.6 hours

Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.

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Answer:

x+2

hope this helps ;)

and cute pfp

Answer:

Step-by-step explanation:

x-1, because 3 fits the criteria, x>=1

Answer:

27.44

Step-by-step explanation:

area of the half sircle = 12.56

area of the rectangle = 40

area of the shaded protion = 40 -12.56

=27.44 square yards

Answer:

Step-by-step explanation:

Rap music is generally more popular with young blacks than young whites, during the 80s-90s when rap was becoming more popular with artists such as 2pac, BIG, Dr. Dre, etc they were more popular among young blacks than whites

Answer:D

Step-by-step explanation: the average of the 30 stocks in the Dow Jones increased

The correct statement is "Since the data is variable and available, the given question is a statistical question." Therefore, option B is correct.

The question "How many times do Jack Nursing Home residents search the Internet each day?" is a statistical question because it is a variable that varies from person to person and from day to day. The purpose of the question was to collect data on Internet searches, indicating an interest in understanding the distribution and patterns of residents' search behavior.

Additionally, in the question he states that web search data is available. This means there is an opportunity to collect and analyze data to generate meaningful insights. This question is therefore a statistical question that takes into account the variability and availability of the data. 

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Answer:

4.41 x 10^3 hope this helps

Answer:

32000 is your answer its not to hard all you got to do is type it into the calculator and press enter