the area in square units , between the curve and the x-axis on the interval
[-3,4] is closest to:

(a) Inverse Laplace transform of F(s) = 4s/(s² - 81) is

[tex]f(t) = 2e^{(9t)} + 2e^{(-9t).[/tex]

We can rewrite F(s) as F(s) = 4s/[(s - 9)(s + 9)].

Using partial fraction decomposition, we can express F(s) as F(s) = A/(s - 9) + B/(s + 9), where A and B are constants.

Multiplying both sides by (s - 9)(s + 9), we get 4s = A(s + 9) + B(s - 9).

Expanding and equating coefficients, we have 4s = (A + B)s + 9A - 9B.

Equating coefficients of s on both sides, we get A + B = 4.

Equating constants on both sides, we get 9A - 9B = 0, which gives A = B.

From A + B = 4, we have 2A = 4, so A = B = 2.

Therefore, F(s) can be written as F(s) = 2/(s - 9) + 2/(s + 9).

Now, using the inverse Laplace transform formulas:

[tex]L{e^{at}} = 1/(s - a),\\L{e^{(-at)}} = 1/(s + a),[/tex]

we can find the inverse Laplace transform of F(s):

[tex]f(t) = L^{(-1)}{F(s)} = 2L^{(-1)}{1/(s - 9)} + 2L^{(-1)}{1/(s + 9)}\\= 2e^{(9t) }+ 2e^{(-9t).[/tex]

Therefore, the inverse Laplace transform of F(s) = 4s/(s² - 81) is f(t) = 2e^(9t) + 2e^(-9t).

(b) Inverse Laplace transform of F(s) = (7s + 52)/(s² + s - 1):

We can rewrite F(s) as F(s) = (7s + 52)/[(s - 1)(s + 1)].

Using partial fraction decomposition, we can express F(s) as F(s) = A/(s - 1) + B/(s + 1), where A and B are constants.

Multiplying both sides by (s - 1)(s + 1), we get (7s + 52) = A(s + 1) + B(s - 1).

Expanding and equating coefficients, we have 7s + 52 = (A + B)s + (A - B).

Equating coefficients of s on both sides, we get A + B = 7.

Equating constants on both sides, we get A - B = 52.

Solving these equations, we find A = 29 and B = -22.

Therefore, F(s) can be written as F(s) = 29/(s - 1) - 22/(s + 1).

Using the inverse Laplace transform formulas:

[tex]L{e^{at} = 1/(s - a),\\L{e^{(-at)} = 1/(s + a),[/tex]

we can find the inverse Laplace transform of F(s):

[tex]f(t) = L^{(-1)}{F(s)} = 29L^{(-1)}{1/(s - 1)} - 22L^{(-1)}{1/(s + 1)}\\= 29e^t - 22e[/tex]

To know more about Inverse Laplace transform refer here:

https://brainly.com/question/30404106

#SPJ11

Answer:

3

Step-by-step explanation:

Since it's at the same time of the day, the ratio between the height of the person and the shadow they cast will stay the same. So the man's height to shadow ratio is 6:8 = 3:4. The son's height to shadow ratio would be the same so x:4 = 3:4 therefore his height is 3 feet.

Answer:

Step-by-step explanation:

I will try my best to help you with algebra what is the question

Answer:

.305

Step-by-step explanation:

Step-by-step explanation:

2/33=6/x

x=99

since there are 11 rest stops and you are trying to find the space in the middle of the two rest stops.

99/11 rest stops

9 miles in between rest stops

9/y=30/1

9/30=y

3/10=y

.3 inches=y

Hope that helps :)

Answer:

Yes, it will fit snugly in a 90º corner

Step-by-step explanation:

To do this, we simply need to check if the given sides of the shelf is right-angled.

So, we have:

[tex]Hypotenuse = \sqrt{242[/tex]

[tex]Side\ 1 = Side\ 2 = 11[/tex]

To check for right-angle triangle, we make use of:

[tex]Side\ 1^2 + Side\ 2^2 = Hypotenuse^2[/tex]

This gives:

[tex]11^2 + 11^2 = \sqrt{242}^2[/tex]

[tex]121 + 121 = \sqrt{242}^2[/tex]

[tex]242 = \sqrt{242}^2[/tex]

[tex]242 = 242[/tex]

This shows that the given sides of the shelf is a right-angled triangle.

Hence, it will fit the wall

Answer:

A

Step-by-step explanation:

Answer:

201.1 square feet

Step-by-step explanation:

The radius (r) of the patio is 16/2 = 8

Area of a circle is π[tex]r^{2}[/tex] so [tex]8^{2}[/tex]π = 201.0619298 or 64π

Answer:

It will take 113.10 ft² of tiles to cover the patio.

Step-by-step explanation:

area of a circle formula: A = πr²

The diameter is twice the length of the radius. To find the radius, divide the diameter by 2:

16/2 = 8

To find the area of the circular patio, apply the radius to the formula A = πr²:

A = π6²

A = 113.10 ft²

If the sample size decreases while the significance level remains the same, the length of the confidence interval is expected to increase. It is important to note that the exact change in length will depend on the specific data and sample characteristics.

If the sample size decreases but the significance level (alpha) remains the same, the length of the confidence interval will typically increase.

In general, the length of a confidence interval is influenced by two main factors: the variability of the data (measured by the standard deviation or standard error) and the sample size. A larger sample size provides more information and reduces the variability, resulting in a shorter confidence interval.

When the sample size decreases, the amount of information available to estimate the population parameter decreases as well. This can lead to increased variability and uncertainty in the estimation process. As a result, the confidence interval tends to widen to account for the increased uncertainty and potential sampling error.

Therefore, if the sample size decreases while the significance level remains the same, the length of the confidence interval is expected to increase. It is important to note that the exact change in length will depend on the specific data and sample characteristics.

Know more about Potential  here:

https://brainly.com/question/28300184

#SPJ11

Answer:

(5.1×10^15)×(8.1×10^5

Answer:

c the right tail is longer than the left

Step-by-step explanation:

Answer:

See solutions below

Step-by-step explanation:

From the given diagram;

AC = opposite

AB = 7 = hypotenuse

Angle of elevation = 70 degrees

Using SOH CAH TOA

Sin theta = opp/hyp

Sin theta = AC/AB

Sin 70 = AC/7

AC = 7sin70

AC = 7(0.9397)

AC = 6.58

Similarly

tan 70 = AC/BC

tan 70 = 6.58/BC

BC = 6.58/tan70

BC = 6.58/2.7475

BC = 2.39

tan m<A = BC/AC

tanm<A = 2.39/6.58

tan m<A = 0.3632

m<A = 19.96degrees

Answer:

100.571inches

Step-by-step explanation:

Perimeter. =2πr

Perimeter. =2×22÷7×16

Perimeter. =704÷7

Perimeter. =100.571inches

PLEASE GIVE BRAINLIEST

Step-by-step explanation:

try to do 180 - 135 organise a 45-degree that is the first answer of a and b you're taking 180 - 144 you got the answer also 28 degrees

Answer:

The distribution with the larger median is test scores after football.

The distribution with larger mean is test scores after half day.

Step-by-step explanation:

Answer:

There were a total of 72 Easter eggs.

Step-by-step explanation:

Since five students participated in an Easter egg hunt, where Ally snatched up one quarter of all of the eggs, Brett only managed to get half of what Ally found, Lee snagged six more than Brett, Jen ended up with half of Lee's take, While Lisa snagged three times that, to determine how many eggs were there in total, the following calculation must be performed:

Ally: 0.25X

Brett: 0.125X

Read: 0.125X + 6

Jen: 0.0625X + 3

Smooth: 0.1875X + 9

X - 0.25X - 0.125X - 0.125X - 0.0625X - 0.1875X = 0.25

0.25X = 6 + 3 + 9

0.25X = 18

Ally: 18

Brett: 9

Read: 15

Jen: 7.5

Smooth: 22.5

18 + 9 + 15 + 7.5 + 22.5 = X

72 = X

Thus, there were a total of 72 Easter eggs.

To estimate the distance traveled between t=0 and t=8 using the average of the left and right sums with 4 subdivisions, we can approximate the area under the velocity curve.

The average of the left and right sums is a numerical integration technique used to estimate the area under a curve. In this case, we want to estimate the distance traveled, which corresponds to the area under the velocity curve.

Given that the velocity function is v(t) = t^2 - 8, we can divide the interval [0, 8] into 4 equal subdivisions. Using the left and right sums, we evaluate the velocity at the left and right endpoints of each subdivision and multiply it by the width of each subdivision.

Calculating the estimates for each subdivision and summing them will give us an approximation of the total distance traveled between t=0 and t=8.

To perform the calculation, we evaluate the velocity at the left endpoints of each subdivision (0, 2, 4, 6) and the right endpoints (2, 4, 6, 8). Then, we multiply each velocity value by the width of the subdivision (2 units). Finally, we sum these estimated distances to obtain the approximation of the total distance traveled.

The detailed calculations would involve substituting the values into the velocity function, multiplying by the width, and summing the results.

Therefore, by using the average of the left and right sums with 4 subdivisions, we can estimate the distance traveled between t=0 and t=8 for the given velocity function.

To learn more about numerical integration click here :

brainly.com/question/31678362

#SPJ11

Answer:

it's 75 feet above sea level

Answer:

75 feet

take 125

minus

50

which give you 75.

Answer:

It goes up

Step-by-step explanation:

(a) The function f(x) = |x − 2| + 1 is a one-to-one function and onto, but not a bijection. (b) The function f(x) = −3x + 2 is a one-to-one function but not onto and not a bijection. (c) The function f(x) = x² − 2x + 1 is a one-to-one function, onto, and a bijection.

Let's evaluate each given expression to determine if it is a function and, if so, determine its characteristics:

(a) Given f: Z → Z+, f(x) = |x − 2| + 1.

This expression represents a function. A function is a relation between two sets where each input value (x) maps to a unique output value (f(x)). In this case, for any integer input x, the function f(x) returns the absolute value of the difference between x and 2, plus 1. Since each input has a unique corresponding output, this function is one-to-one.

To determine if the function is onto or a bijection, we need to examine the range of the function. The range of f(x) is the set of all possible output values. In this case, the function returns only positive integers (Z+). Therefore, the function is onto since it covers the entire range of positive integers. However, it is not a bijection since the domain (Z) and the codomain (Z+) have different cardinalities.

(b) Given f: Z → Z+, f(x) = −3x + 2.

This expression also represents a function. It is a linear function that takes an integer input x and returns the value obtained by multiplying x by -3 and then adding 2. Since each input value maps to a unique output value, the function is one-to-one.

To determine if the function is onto or a bijection, we examine the range of f(x). The function f(x) returns positive integers (Z+). However, it does not cover the entire range of positive integers. Specifically, it only produces negative or zero values when x is positive. Therefore, the function is not onto, and it is not a bijection.

(c) Given f: R → R, f(x) = x² − 2x + 1.

This expression represents a function. It is a quadratic function that takes a real number input x and returns the value obtained by substituting x into the equation x² - 2x + 1. Since each input value maps to a unique output value, the function is one-to-one.

To determine if the function is onto or a bijection, we again examine the range of f(x). The quadratic function f(x) is a parabola opening upward, and its vertex is located at (1, 0). This indicates that the lowest point on the graph is at y = 0, and the range of f(x) includes all real numbers greater than or equal to 0. Therefore, the function is onto, and it is a bijection.

In summary:

(a) The function f(x) = |x − 2| + 1 is a one-to-one function and onto, but not a bijection.

(b) The function f(x) = −3x + 2 is a one-to-one function but not onto and not a bijection.

(c) The function f(x) = x² − 2x + 1 is a one-to-one function, onto, and a bijection.

Learn more about bijection here

https://brainly.com/question/32691273

#SPJ11

The inverse Laplace transform of [tex]X(s) = (s+1)/(s^2 + 4s + 4)[/tex] is [tex]x(t) = e^-^t * (t + 1)[/tex]. The poles are located at s = -2, and the region of convergence (ROC) includes all values of s to the right of -2 on the real axis. This means that the Laplace transform is valid for all values of s greater than -2.

To find the inverse Laplace transform, we can use partial fraction decomposition. The denominator of X(s) factors as [tex](s + 2)^2[/tex], indicating a repeated pole at s = -2. The numerator is (s + 1), which is a first-order polynomial.

Applying partial fraction decomposition, we can express X(s) as [tex](A/(s + 2)) + (B/(s + 2)^2)[/tex]. Solving for A and B, we find A = 1 and B = -1.

Now, we can take the inverse Laplace transform of each term. The inverse Laplace transform of A/(s + 2) is [tex]e^-^2^t[/tex], and the inverse Laplace transform of [tex]B/(s + 2)^2[/tex] is [tex]t * e^-^2^t[/tex].

Thus, the inverse Laplace transform of X(s) is [tex]x(t) = e^-^t * (t + 1)[/tex].

The poles of X(s) are located at s = -2. The region of convergence (ROC) can be determined by examining the values of s for which X(s) converges. In this case, since the poles are at s = -2, the ROC includes all values of s to the right of -2 on the real axis.

In summary, the inverse Laplace transform of X(s) = [tex](s+1)/(s^2 + 4s + 4)[/tex] is [tex]x(t) = e^-^t * (t + 1)[/tex]. The poles are located at s = -2, and the ROC includes all values of s to the right of -2 on the real axis.

To learn more about Inverse Laplace transform, visit:

https://brainly.com/question/13138631

#SPJ11

Answer:

1. y = 2x + 5

2. (-5) + 3 + (-8) = 3 - 5 - 8 = 3 - 13 = -10

3. given: 1/2, 3/4, 7/8, 0.55, 0.1

1/2, 3/4, 7/8 = 4/8, 6/8, 7/8

4/8 < 6/8 < 7/8

1/2 < 3/4 < 7/8

0.55 = 55/100 = 11/20

0.1 = 1/10 = 2/20

2/20 < 11/20

0.1 < 0.55

1/2 = 10/20

2/20 < 10/20 < 11/20

0.1 < 1/2 < 0.55

3/4 = 15/20

11/20 < 15/20

0.55 < 3/4

thus

0.1 < 1/2 < 0.55 < 3/4 < 7/8

The given set of vectors in R with the defined addition and scalar multiplication operations does not satisfy the closure properties, violating the vector space axioms.

In the first part, the set of vectors with the given operations does not satisfy all of the vector space axioms.

In the second part, let's examine the vector space axioms to determine which ones are not satisfied.

Closure under addition: The axiom states that for any vectors u and v in the set, the sum u + v must also be in the set. If we consider the vectors (1, 0) and (0, 1), their sum is (1, 1), which is not in the given set. Therefore, closure under addition is not satisfied.

Closure under scalar multiplication: The axiom states that for any scalar c and vector u in the set, the scalar multiple c * u must be in the set. If we consider the vector (1, 1) from the previous example, multiplying it by a scalar c will result in the vector (c, c). However, for certain values of c, such as c = 2, the resulting vector (2, 2) is not in the given set. Hence, closure under scalar multiplication is not satisfied.

Since the set does not satisfy closure under addition and closure under scalar multiplication, it does not satisfy the vector space axioms.

Learn more about scalar multiplication here:

https://brainly.com/question/30221358

#SPJ11

A number system is a system for the presentation of numbers into groups or categories

The true statement is the option;

C. All irrational numbers are real numbers

Reason:

The number system is composed of two types of numbers, which are;

Imaginary Numbers;

The imaginary numbers are the numbers that have the value √(-1), within them

Real Numbers:

There are two types of real numbers which are;

Rational numbers; Numbers that can be written in the form [tex]\dfrac{a}{b}[/tex], where a, and b, are integers

Irrational numbers; Numbers that cannot be expressed in the form [tex]\dfrac{a}{b}[/tex], such as π, √2, e

Therefore;

All irrational numbers are real numbers

Learn more here:

https://brainly.com/question/9842110

Answer:

3a-12c

Step-by-step explanation:

(5a-7c)-(2a+5c)

5a-7c-2a-5c

(5a-2a)+(-7c-5c)

3a-12c

Answer:

3a - 12c

Step-by-step explanation:

The required answer is  [61.77, 69.23].

Given: Mean height of all 9th grade students at one high school is estimated as ≈65.5 Population standard deviation is σ = 3 inches. Number of samples n = 6Margin of error at 99% confidence level = 1.23Margin of error = E = z(σ/√n)Now, z = inv Norm(0.995) (as it is 99% confidence interval, α=0.01 and 1-α=0.99)⇒ inv Norm(0.995) = 2.58∴ E = 2.58(3/√6) = 3.73∴ The margin of error at the 99% confidence level is 3.73 inches .

Confidence interval = [sample mean - E, sample mean + E]=[65.5 - 3.73, 65.5 + 3.73] = [61.77, 69.23]

∴ The 99% confidence interval for the population mean height of all 9th-grade students at that high school is [61.77, 69.23].

Know more about confidence interval  here:

https://brainly.com/question/32546207

#SPJ11

Step-by-step explanation:

a a reflex angle is more than 180° but less than 360° so in this case the reference angle of 95 degrees we are going to take 360° - 95 degrees to get255°

Answer:

D

Step-by-step explanation: