Consider a system given by -20 + x = 10 X + 0 u 0 y=[-1 2] a) Find the equilibrium solution xe b) Determine which equilibria a asymptotical stable c) Determine the equilibrium solutions are Lyapunov stable d) Determine if the system is BIBO stable.

Answer:

a.  70°

Step-by-step explanation:

m∠BDC + m∠CDA = m∠BDA

-3x + 34 - 2x + 56 = 150

-5x + 90 = 150

-5x = 60

x = -12

m∠BDC = -3x + 34 = -3(-12) + 34

              = 36 + 34 = 70°

Answer:

B. all of these are true

Step-by-step explanation:

The Square is a rhombus because all the sides of a square are equal in length. Even, the diagonals of both square and rhombus are perpendicular to each other and bisect the opposite angles. Therefore, we can say the square is a rhombus.

Hope this helped!!

Step-by-step explanation:

area of rhombus =1/2×d1×d2

area of rhombus =1/2×9cm×5cm

area of rhombus =22.5cm²

area of rhombus = 1/2×d1×d2

area of rhombus =1/2×8in×17in

area of rhombus= 68in²

Answer:  8 pupils are absent

Step-by-step explanation:

20 percent * 40 =

(20* 40)/100 =

(800)100 =

 =8

Answer:

Solution x=16

Step-by-step explanation:

Answer:

The volume of the rectangular prism is 336

The volume of the triangular prism is 24.875

Add them together, 360.875. You can round if you want

Answer:

arc XY = 46°

Step-by-step explanation:

The inscribed angle XZY is half the measure of its intercepted arc , then

arc XY = 2 × 23° = 46°

Answer:

0.000173611 miles is 11 inches

15.22359 miles is 24.5km

Step-by-step explanation:

Answer:

50.3

Step-by-step explanation:

area for circle formula=πr^2

r=4

π4^2 which is 50.3 rounded

Answer:

50.3

Step-by-step explanation:

A=πr^2

π·4^2≈50.3

Answer:

5 hours or 300 mins

Step-by-step explanation:

Answer:

C: 108 cans

Step-by-step explanation:

just trust me bro

Answer:

-Se plantarán 50.000 arboles.

-Si se planta un árbol cada 50 m, se plantarán 25.000 arboles.

Step-by-step explanation:

Para encontrar cuántos arboles se plantarán, tienes que dividir la longitud el paseo entre la distancia que habrá entre los árboles:

1250/0,025=50.000

Ahora, para encontrar cuántos arboles se plantarán si se planta uno cada 50m, primero tienes que encontrar cuántos kilómetros hay en 50 m considerando que 1 km es igual a 1000 metros. Para esto, puedes utilizar una regla de tres:

1 km → 1000 m

  x   ←   50 m

x=(50*1)/1000

x= 0,05 km

Ahora puedes dividir la longitud del paseo entre 0,05 para encontrar el número de arboles que se plantarán:

1250/0.05=25.000

De acuerdo a esto, la respuesta es que se plantarán 50.000 arboles.

Si se planta un árbol cada 50 m, se plantarán 25.000 arboles.

Answer:

75 times.

Step-by-step explanation:

Well there are 12 months and 3 of them start with the letter J, so theoretically, 25% of the months chosen will start with the letter J because [tex]\frac{3}{12}=\frac{1}{4}[/tex], which is 25%. 25% of 300 (or [tex]\frac{300}{4}[/tex], for those who like fractions) is 75, so theoretically, we can expect a month that starts with the letter J 75 times.

Hope this helps!

P.S: Please mark me as brainliest!

a) We have the function given by; y = 8x + 3We need to find the arclength of the curve between the limits of x = 2 and x = 8.The arclength L of the curve is given by; L = ∫(2,8) sqrt(1 + f'(x)²)dx Here, f(x) = 8x + 3 Differentiate f(x) with respect to x;f'(x) = 8Now, substitute f'(x) in the above equation; L = ∫(2,8) sqrt(1 + 8²)dx L = ∫(2,8) sqrt(65)dxL = sqrt(65)∫(2,8)dxL = sqrt(65) [x]₂⁸L = sqrt(65) [8 - 2]L = 6sqrt(65)Therefore, the arclength L of this curve is 6sqrt(65).

b) We are given the function y = 8x + 3We need to rotate this curve by 2π radians about the x-axis to get the required surface of revolution. The formula for the surface area of the surface of revolution generated by revolving the curve y = f(x) between x = a and x = b about the x-axis is given by;A = ∫(a,b) 2πf(x) sqrt(1 + f'(x)²)dx Here, f(x) = 8x + 3f'(x) = 8We know that the limits of integration are from x = 2 to x = 8.

Substitute the values in the above equation; A = ∫(2,8) 2π(8x + 3) sqrt(1 + 8²)dxA = 16π ∫(2,8) (8x + 3) sqrt(65)dxA = 16π [∫(2,8) (8x sqrt(65))dx + ∫(2,8) (3 sqrt(65))dx]A = 16π [2/3(8sqrt(65))² - 2/3(2sqrt(65))² + 3sqrt(65)(8 - 2)]A = 16π [2/3(8sqrt(65))² - 2/3(2sqrt(65))² + 3sqrt(65)(6)]A = 192πsqrt(65)

Therefore, the area of the surface of revolution, A that is obtained when the curve is rotated by 2π radians about the x-axis is 192πsqrt(65) square units.

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Answer:

16 2/3 yards

Step-by-step explanation:

Hope this helps and have a wonderful day!!!!

Answer:

V=pi x (r)^2 x h

V-volume r-radius h-height

V= pi x (3)^2 x 9

V= pi x 9 x 9

V= pi x 81

V= 254.47 (rounded)

The correct answer is option B. 0.6 mL which is the powder volume in the vial.

To determine that 0.6 mL of powder volume in the vial, we need to subtract the volume of the sterile water used for reconstitution from the final volume.

The vial states that it needs to be reconstituted with 3.4 mL of sterile water for a final volume of 4 mL. This means that 3.4 mL of sterile water will be added to the vial to make a total volume of 4 mL.

To find the powder volume, we subtract the volume of the sterile water (3.4 mL) from the final volume (4 mL):

Powder volume = Final volume - Volume of sterile water

Powder volume = 4 mL - 3.4 mL

Powder volume = 0.6 mL

Therefore, the powder volume in the vial is 0.6 mL.

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Answer:

5

Step-by-step explanation:

2-5=5. Subscribe Single-3 FF on yt

The sample space of all possible pairs of marbles that can be drawn is:

{BB, BR, RB, RR, RR, RR}

It is the total number of possible outcomes from a given set.

We have,

The sample space is the set of all possible outcomes of the experiment.

In this case, we are drawing two marbles from a bag containing 2 blue and 5 red marbles, without replacement (meaning that we do not put the first marble back into the bag before drawing the second one).

The sample space consists of all possible pairs of marbles that can be drawn:

{BB, BR, RB, RR, RR, RR}

where BB means both marbles are blue, BR means the first marble is blue and the second is red, RB means the first marble is red and the second is blue, and RR means both marbles are red.

Note that there are two outcomes corresponding to drawing two red marbles because there are 5 red marbles in the bag.

Thus,

The sample space of all possible pairs of marbles that can be drawn is:

{BB, BR, RB, RR, RR, RR}

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The  complete question:

In an experiment, a bag contains 2 blue marbles and 5 red marbles. Two marbles are drawn from the bag.

List the sample space.

The degree of precision of the quadrature formula with an error term of 24 f‴() is 2.

To know more about the degree of precision of a quadrature formula, refer here:

The degree of precision of a quadrature formula represents the highest power of x that the formula can integrate exactly. In this case, the error term of the formula is given as 24 f‴(), where f‴() denotes the third derivative of the function f(x). The degree of precision is determined by the highest power of x that appears in the error term.

In a quadrature formula, the error term typically has the form K * h^p, where K is a constant, h is the step size, and p is the degree of precision. In this case, the error term is 24 f‴(). We can see that there is no dependence on the step size h, which implies that h^p = h^0 = 1. Therefore, the highest power of x in the error term is determined by the highest power of x that appears in f‴().

Since the error term is 24 f‴(), it indicates that the highest power of x in f‴() is 1. Thus, the degree of precision of the quadrature formula is 2, as the highest power of x in the error term is two degrees less than the highest power of x that the formula can integrate exactly.

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option A is the correct statement regarding the exponential distribution.

What is Exponential Distribution?

The exponential distribution is a continuous probability distribution that models the time between events occurring at a constant average rate. It is often used to describe situations where events happen randomly and independently over time, such as the time between phone calls received at a call center or the time between arrivals of customers at a service counter.

The correct answer is:

[tex]\textbf{A. The exponential distribution has the property that its mean equals its variance.}[/tex]

The exponential distribution is characterized by the property that its mean is equal to its variance. This means that the average value of the distribution and the spread of the distribution are the same. In other words, the measure of central tendency and the measure of dispersion are equal in the exponential distribution.

This property holds true for all exponential distributions, regardless of the specific rate parameter or scale parameter. It is a fundamental characteristic of this distribution.

Therefore, option A is the correct statement regarding the exponential distribution.

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The velocity of the stream is approximately 2.13 feet per second.

To calculate the velocity of the stream, we can use the formula:

Velocity = Distance / Time

Given that the drop of food coloring travels 32 feet in 15 seconds, we can plug in these values into the formula:

Velocity = 32 feet / 15 seconds

To find the velocity, we divide 32 by 15:

Velocity ≈ 2.13 feet per second

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Answer:

x=22

Step-by-step explanation:

Rule states diagonals = same so 6x-36 = 96 in which x=22 cause 6(22)=132

132-36 = 96

Answer:

259 students

Step-by-step explanation:

First, find how many will check out science fiction books

350(0.14)

= 49

Find how many will check out sports books

350(0.12)

= 42

Subtract these amounts from 350

350 - 49 - 42

= 259

So, she should expect 259 students not to check out science fiction and sports books

The journal entry that Amy Company will make to record the collection of cash from Tory Turnbull, who paid within the discount period, would include a credit to Cash for $160. Therefore, option d is the correct answer.

This is because Tory Turnbull will pay $8,000 - $160 (2% of $8,000) to avail the discount. The Sales Discount account is not involved in the journal entry as the discount was taken by the customer, not given by Amy Company.

Therefore, the correct answer is d. Credit to Cash of $160. This entry reflects the cash received by Amy Company and the reduction in the Accounts Receivable balance for the amount paid by the customer.

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Answer:

c

Step-by-step explanation:

For n e N let an be the number of strings of 0's and l's,

(a) i. a₁ = 2, ii. a₂ = 1, iii. a₃ = 2, iv. a₄ = 3, v. a₅ = 5.

(b) The values of aₙ represent the nth term in the Fibonacci sequence.

(c) The set of strings of length n can be built by appending "1" or "01" to strings of length n-1 and n-2.

(d) The conjecture that the values of aₙ represent the nth term in the Fibonacci sequence is proven using mathematical induction.

(a) To find the values of aₙ, we'll calculate them one by one:

i. a₁: We have two possible strings of length 1 that satisfy the condition: "1" and "0". So a₁ = 2.

ii. a₂: For a string of length 2, the only valid option is "10". So a₂ = 1.

iii. a₃: Now, let's consider strings of length 3. We can build them by appending either "1" or "01" to valid strings of length 2. From the previous step, we know that a₂ = 1. Thus, we have two options: "101" and "100". So a₃ = 2.

iv. a₄: Similarly, for strings of length 4, we can append either "1" or "01" to valid strings of length 3. From the previous step, we know that a₃ = 2. Thus, we have three options: "1010", "1001", and "1000". So a₄ = 3.

v. a₅: Continuing the same pattern, we can append either "1" or "01" to valid strings of length 4. From the previous step, we know that a₄ = 3. Thus, we have five options: "10101", "10100", "10010", "10001", and "10000". So a₅ = 5.

(b) If we look closely at the values of aₙ that we calculated, we notice that they form the Fibonacci sequence: 2, 1, 2, 3, 5, ...

Conjecture: The values of aₙ represent the nth term in the Fibonacci sequence.

(c) To build the set of strings of length n from the sets of strings of length n-1 and n-2, we can append either "1" or "01" to the strings of length n-1 and n-2.

For example, to obtain a string of length 4, we can append "1" or "01" to the strings of length 3. Similarly, to obtain a string of length 5, we can append "1" or "01" to the strings of length 4.

(d) To prove our conjecture that the values of aₙ represent the nth term in the Fibonacci sequence, we can use mathematical induction. We would need to show that a₁ = F₁, a₂ = F₂, and assume that aₖ = Fₖ and aₖ₋₁ = Fₖ₋₁ hold for some k ≥ 2 and prove that aₖ₊₁ = Fₖ₊₁.

Since a₁ = 2 = F₁ and a₂ = 1 = F₂, the base cases hold.

Next, assume that aₖ = Fₖ and aₖ₋₁ = Fₖ₋₁ hold for some k ≥ 2.

From the construction in part (c), we know that to obtain a string of length k+1, we append "1" to a string of length k and append "01" to a string of length k-1.

So, aₖ₊₁ = aₖ + aₖ₋₁ = Fₖ + Fₖ₋₁.

Using the property of the Fibonacci sequence that Fₖ + Fₖ₋₁ = Fₖ₊₁, we can conclude that aₖ₊₁ = Fₖ₊₁.

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To calculate the required sample size in Excel for estimating the true proportion of satisfied customers within a 3% margin of error with 99% confidence,

In Excel, you can use the NORM.S.INV function to find the critical value corresponding to the desired confidence level. In this case, we use 1 - (1-0.99)/2 to find the z-score for 99% confidence level.

We square this z-score and multiply it by (0.50.5)/(0.030.03), which represents the maximum variance under worst-case scenario and the desired margin of error. The CEILING function is used to round up the result to the nearest whole number since the sample size should be an integer.

you can use the formula =CEILING(MROUND((NORM.S.INV(1-(1-0.99)/2,0)^2)(0.50.5)/(0.03*0.03),1),1). The result will give you the minimum sample size needed for the desired confidence level and margin of error.

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Answer:

A insects and plants

Step-by-step explanation:

the decaying things are used as fertilizer for plants to grow and insects to eat

Given the set { 1 , 1 , 1 , 1 , 2 , 3 } . Picking a number at random.The probability of choosing a "1" is 2 / 3 . False

In the given set {1, 1, 1, 1, 2, 3}, there are four occurrences of the number "1" and a total of six elements in the set.

To calculate the probability of choosing a "1", we need to divide the number of favorable outcomes (the occurrences of "1") by the total number of possible outcomes (the total number of elements in the set).

The number of favorable outcomes is 4 (the occurrences of "1"), and the total number of possible outcomes is 6 (the total number of elements in the set).

So, the probability of choosing a "1" is 4/6, which simplifies to 2/3.

Therefore, the statement is true: the probability of choosing a "1" from the given set is 2/3.

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