What is the value of x? i will give brainliest please help

(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]

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Answer:

C

90

Step-by-step explanation:

B is likely the center, I think. You can't do it otherwise.

The tangent and a radius of a circle meet at 90o

therefore the answer is 90.

All of this could be confirmed with a diagram.

Answer:

100.571inches

Step-by-step explanation:

Perimeter. =2πr

Perimeter. =2×22÷7×16

Perimeter. =704÷7

Perimeter. =100.571inches

PLEASE GIVE BRAINLIEST

The five-number summary for the given data is as follows: Minimum = 40, First Quartile = 51.5, Median = 69, Third Quartile = 86, Maximum = 95.

To obtain the five-number summary, we consider the minimum, first quartile, median, third quartile, and maximum values of the dataset.

Minimum: The smallest value in the dataset is 40.

First Quartile: The first quartile (Q1) is the median of the lower half of the dataset. To find Q1, we arrange the data in ascending order: 40, 46, 50, 55, 58, 61, 64, 69, 74, 79, 85, 86, 90, 94, 95. Since there are 15 data points, the median is the 8th value (69), which becomes the first quartile.

Median: The median is the middle value of the dataset. In this case, since we have an odd number of data points, the median is the 8th value (69).

Third Quartile: The third quartile (Q3) is the median of the upper half of the dataset. Again, using the ordered data, we find Q3 as the median of the values above the median (69). This gives us the third quartile of 86.

Maximum: The largest value in the dataset is 95.

Thus, the five-number summary for the given data is Minimum = 40, Q1 = 51.5, Median = 69, Q3 = 86, and Maximum = 95.

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Answer:

Gavin has 3 parts left.

Step-by-step explanation:

8-3-2=3. The time was not important.

Answer:

Step-by-step explanation:

Yes

Answer:

yes because for every pound it is $3

Step-by-step explanation:

i know this because 1 times 3 is 3 and 3 times 3 is 9 and 7 times 3 is 21 and 10 times 3 is 30

Answer:

15 students.  30%

Step-by-step explanation:

Using trigonometric identity, sin(α + β) = -28/85.

To compute sin(α + β), we can use the trigonometric identity:

sin(α + β) = sin α cos β + cos α sin β

Given the values:

sin α = 15/17 (π/2 < α < 3π/2)

sin β = -4/5 (π < β < 3π/2)

To find sin α, we can use the Pythagorean identity:

cos α = ±√(1 - sin² α)

Since α is in the range π/2 < α < 3π/2, sin α is positive, so cos α will be negative.

sin α = 15/17

cos α = -√(1 - (15/17)²)

      = -√(1 - 225/289)

      = -√(64/289)

      = -8/17

Now, we can substitute the values into the formula for sin(α + β):

sin(α + β) = (sin α cos β) + (cos α sin β)

          = (15/17) * (-4/5) + (-8/17) * (-4/5)

          = -60/85 + 32/85

          = -28/85

Therefore, sin(α + β) = -28/85.

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The partial sums will cease to change when the terms of the series become smaller than the smallest representable number in the floating-point system.

In floating-point arithmetic, there is a finite range of representable numbers and a limited precision for calculations. When dealing with infinite series, the terms are added or subtracted sequentially, but due to the limitations of numerical precision, there is a point at which the terms become too small to affect the sum significantly.

For the series 1/n, as n increases, the terms approach zero but never actually reach zero. Eventually, the terms become smaller than the smallest representable number in the floating-point system, and at this point, they essentially contribute zero to the sum. As a result, the partial sums of the series will cease to change beyond this point.

It's important to note that although the sum of the series may appear to be finite in floating-point arithmetic, mathematically, the series diverges and does not have a finite sum. The convergence to a finite value in floating-point arithmetic is a result of the limitations of numerical representation and precision. A divergent infinite series, such as the sum of 1/n from n=1 to infinity, can have a finite sum in floating-point arithmetic due to the limitations of numerical precision.

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Answer:

6283 in³

Step-by-step explanation:

The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.

Since the cardboard box is in the shape of a cube, its volume V = L³

So, L = ∛V

Since V = 12000 in³,

L = ∛(12000 in³)

L= 22.89 in

So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2

So, V = 4π(L/2)³/3

= 4πL³/8 × 3

= πL³/2 × 3

= πL³/6

= πV/6

= π12000/6

= 2000π

= 6283.19 in³

≅ 6283.2 in³

= 6283 in³ to the nearest whole cubic inch

Answer:

2/3

Step-by-step explanation:

the ratio of base1 ABCD to base 1 of WXYZ is        

                      8                 to      12

     8/12    = 2/3      

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

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Answer:

it's 75 feet above sea level

Answer:

75 feet

take 125

minus

50

which give you 75.

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:

slope = 9  

Step-by-step explanation:

To find the slope of a line that passes through a pair of points, use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of (-7,-2) and (-6,7) into the formula and simplify:

[tex]m = \frac{(7)-(-2)}{(-6)-(-7)} \\m = \frac{7+2}{-6+7} \\m = \frac{9}{1} \\m = 9[/tex]

So, the slope is 9.

Answer:

12m

Step-by-step explanation:

1m = 1000mm

12m to mm

12 × 1000

= 12000mm

1200mm to m

1200 ÷ 1000

= 1.2m

Answer:

62.80

Step-by-step explanation:

I hope this helped you out!!

Answer:

62.8

Step-by-step explanation:

Circumference is 2pi*radius. 2*pi*10 = 20 * 3.14 = 62.8

Answer:

43

Step-by-step explanation:

A is the answer

Answer:

Ima steal your points

Step-by-step explanation:

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:

Answer:

B, [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

Diagonals of a square are congruent so AC= 4

using pythagorean theorem we can then do [tex]x^{2} +x^{2}[/tex]=[tex]4^{2}[/tex]

[tex]2x^{2} = 16\\x^{2} =8\\x=\sqrt{8} \\x=2\sqrt{2}[/tex]

Then for perimeter we times the [tex]2\sqrt{2}[/tex] by 4 and get

[tex]8\sqrt{2}[/tex]

Hope this helps and please mark brainliest!!

(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.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Origibal data set

8, 11, 15, 22, 6

Rearranging The value :

x : 6, 8, 11, 15,22

Mean = Σx / n

n = sample size =5

Mean = (6+8+11+15+22) = 62

Mean = 62 / 5 = 12.4

Median = 1/2(n+1)th term

Median = 1/2(6)th term = 6/2 = 3rd term = 11

A.)

X = 4, 5, 15, 23, 19

MEAN = (4 +5 + 15 + 23 + 19) / 5 = 13.2

B.)

X = 2, 6, 5, 23, 34

Mean = (2+6+5+23+24) / 5

Mean = 60 / 2 = 12

C.)

X = 3, 7, 12, 21, 13

X = 3, 7, 12, 13, 21

Mean = (3+7+12+13+21) /5 = 11.2

Median = 1/2(6)th term = 6/2 = 3rd term = 12

Answer:

80

Step-by-step explanation:

200/2.50=80

Answer:

8km

Step-by-step explanation:

there are 4 unit between Gabe's house and the library so distance is 4×2=8km

Answer:

D. 23

Step-by-step explanation:

m-12-(11)=0

m-23 = 0

m = 23

Answer:

(5.1×10^15)×(8.1×10^5

Answer:

C

Step-by-step explanation:

trust me if you really need this done

Answer:

Angelo needs to use the formula V = [tex]\frac{4}{3} \pi (8.5)^3[/tex].

Step-by-step explanation:

The formula for finding the volume of a sphere is [tex]V=\frac{4}{3} \pi r^3[/tex], wherein the variable, r, is the radius. Diameter is one half of the radius; thus, it would be 17/2 = 8.5. Substitute the values into the equation (i.e. V = [tex]\frac{4}{3} \pi (8.5)^3[/tex]).

The probability of the weight loss falling between 8 pounds and 11 pounds is 1/2

Variation of weight = Between 6 to 12.

It is required to ascertain the percentage of the overall range that corresponds to that interval in order to calculate the chance that the weight reduction will fall between 8 pounds and 11 pounds.

Calculating the total range of weight -

Range = Higher weight - Lower weight

= 12 - 6

= 6

Similarly, calculating the total range of weight for 8 pounds and 11 pounds

Range = Higher weight - Lower weight

= 11 - 8

Calculating the probability -

Probability = Range of interest / Total range

= 3 / 6

= 1/2.

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Complete Question:

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost between 8 pounds and 11 pounds

a. 1/2

b. 1/4

c. 2/3

d. 1/3