A continuous time system can behave roughly throughout a variety of periods using a discretized state matrix. A continuous time condition matrix should be used in its place if these requirements are not satisfied since a discretized state matrix might not adequately depict the performance of a continuous time system.
A continuous time condition matrix is a matrix that is used to indicate the state of a system at any moment, as opposed to a discretized state matrix, which is used to describe the status of a system at discrete time intervals. Under the following conditions, a discrete-time state matrix is identical to a time series state matrix:
The system may be regarded as being in stable equilibrium at each time point since the time gaps between every discretization are short enough. This indicates that the behavior of the system does not drastically vary from one-time point to the next.
Over the time frames between each discretization, a linear model accurately predicts the behavior of the system. This means that the behavior of the system can be precisely predicted by a linear equation of the type "Ax = Bu," where A as well as B are matrices and x as well as u are vectors that, respectively, represent the system's state and input.
Over the intervals between each discretization, the system's input remains constant. This indicates that the system's input does not drastically vary from one-time point to the next.
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PLEASE HELP!!!!! 90 POINTS!!!!!
Graph the following system of equations.
2x + 4y = 8
2x + 6y = 18
What is the solution to the system?
There is no solution.
There is one unique solution, (−6, 5).
There is one unique solution, (−4, 4).
There are infinitely many solutions.
Answer:
There is one unique solution, (−6, 5).
Step-by-step explanation:
2x + 4y = 8
2x + 6y = 18
2x + 4y = 8 ==> solve for 2x
2x + 4y - 4y = 8 - 4y
2x = 8 - 4y
2x + 6y = 18 ==> solve for 2x
2x + 6y - 6y = 18 - 6y
2x = 18 - 6y
8 - 4y = 18 - 6y ==> 2x = 8 - 4y and 2x = 18 - 6y
8 - 4y + 6y = 18 - 6y + 6y ==> solve for y by first adding 6y on both sides to
remove negative y
8 + 2y = 18 ==> simplify
8 - 8 + 2y = 18 - 8 ==> isolate y
2y = 10
y = 5
2x + 4(5) = 8 ==> substitute 5 for y in 2x + 4y = 8
2x + 20 = 8
2x - 20 + 20 = 8 - 20 ==> subtract 20 on both sides to isolate 2x
2x = -12
x = -6
x = -6, y = 5 ==> (6, 5)
Answer: There is one unique solution, (−6, 5).
The tatue i 4. 6 meter high. The angle of elevation from the oppoite corner of the courtyard to the top of the tatue i 8
The statue is 4. 6 meter high. The angle of elevation from the opposite corner of the courtyard to the top of the statue is 8,Tan 8 = 4.6/opposite and opposite = 4.6/tan 8 = 5.8 meters
First, we calculate the opposite side of the triangle using the tangent function. To do this, we need to use the angle of elevation (8 degrees) and the height of the statue (4.6 meters). We use the tangent function to calculate this, which is written as:
tan 8 = 4.6/opposite
Solving for the opposite, we get:
opposite = 4.6/tan 8 = 5.8 meters
This means that the opposite corner of the courtyard to the top of the statue is 5.8 meters away.
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Each year the value of a car decreases by 12% of its value at the beginning of that year. The original value of the car is $20000. Calculate the value of the car at the end of 3 years
Answer:
The value of the car at the end of 3 years will be $13707.
Step-by-step explanation:
If the original value of the car is $20000, then after the first year, the value of the car will be $20000 - (12/100)*$20000 = $17600.
After the second year, the value of the car will be $17600 - (12/100)*$17600 = $15552.
After the third year, the value of the car will be $15552 - (12/100)*$15552 = $13707.
Therefore, the value of the car at the end of 3 years will be $13707.
Help asp thank you show your work if you want
Answer:
[tex]y=-\frac{2}{3}x+1[/tex]
Step-by-step explanation:
Parallel means same slope.
[tex]y=-\frac{2}{3}x+b[/tex]
[tex]5=-\frac{2}{3} (-6)+b[/tex]
5 = 4 + b
b = 1
[tex]y=-\frac{2}{3}x+1[/tex]
f(x)=2x^2
g(x)=x+1
prove fg(x)=gf(x)
Answer:
here is the answer with proper steps.
(x + 2)(x+4)²
———————
(x+4)
Answer:
(x + 2)(x + 4)
Step-by-step explanation:
for the denominator we have (x + 2)(x + 4)(x + 4).
divide the denominator by (x + 4), you would be left with (x + 2)(x + 4).
FILL IN THE BLANK. the _______ _______ is a statement we are trying to find evidence to support.
Answer:
Alternative Hypothesis
You just signed a 2 years lease for a one bedroom apartment in Brooklyn. The rent is $2,657 per month pulse $200 security deposit. Thinking long-term, you are wondering if it is better to rent or own a property. How will the total amount of rent you pay change over time?
After the end of the lease period the pay, the rent would increase to $3030.83 approx.
What is a Lease agreement?A lease is a legal agreement by which the owner of a building, a piece of land, or something such as a car allows someone else to use it for a period of time in return for money.
Given here, a 2-year lease is - $2,657 per month plus a $200 security deposit. Now, the average increase in the rate in the U.S is 14.07%
thus, at the end of the two-year lease period, the new rent would be
= (1+14.07/100) × $2,657
= $3030.83
Hence, the new rent with a security deposit is $3030.83 + security deposit.
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In a board of directors composed of 14 people, how many different ways can one chief
executive officer, one director, and one treasurer be selected?
Answer:
2184
Step-by-step explanation:
This question involves permutations. We can solve it using the formula
[tex]\frac{n!}{(n-r)!}[/tex]
where n=14 (because we are choosing from 14 people)
and r=3 (because we are choosing 3 people)
and we are using the permutation formula because the order or placement in which these 3 people are choosing matters (having a person 1 being a director is different from having person 1 being a chief executive officer)
14!/(14-3)!
= 14!/11!
= 14 x 13 x 12
= 2184
(3x)°
(6x-12)
(2x+13)° find the value of x
Answer:
x = 25
Step-by-step explanation:
The two interior angles equal the exterior angle.
6x - 12 = 3x + 2x + 13 Combine like terms
6x - 12 = 5x + 13 Subtract 5x from both sides of the equation
6x -5x - 12= 5x - 5x + 13
x - 12 = 13 Add 12 to both sides of the equation
x - 12 + 12 = 13 + 12
x = 25
thanks for helping me!
Answer:
<E=180-60=120
t=60 degrees
u=8
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suppose you want to encrypt the message 10101111 by encrypting the decimal number that corresponds to the message. what is the decimal number
To find the decimal number that corresponds to the message "10101111", you can convert the binary number to decimal.
By using the following formula:
decimal = [tex]sum(binary[i] X 2^{(n-i-1)})[/tex]
binary = converting binary number
i = index of the current digit in the binary number
n = total number of digits in the binary number
[tex]2^{(n-i-1)}[/tex] is the corresponding power of 2
use the following steps to convert the binary number "10101111"
Calculate the decimal value for each digit in the binary number:
binary[0] = 1, [tex]2^{(8-0-1)}[/tex] = [tex]2^7[/tex] = 128
binary[1] = 0, [tex]2^{(8-1-1)}[/tex] = [tex]2^6[/tex] = 64
binary[2] = 1, [tex]2^{(8-2-1)}[/tex] = [tex]2^5[/tex] = 32
binary[3] = 0, [tex]2^{(8-3-1)}[/tex] = [tex]2^4[/tex] = 16
binary[4] = 1, [tex]2^{(8-4-1)}[/tex] = [tex]2^3[/tex] = 8
binary[5] = 1, [tex]2^{(8-5-1)}[/tex] = [tex]2^2[/tex] = 4
binary[6] = 1, [tex]2^{(8-6-1)}[/tex] = [tex]2^1[/tex] = 2
binary[7] = 1, [tex]2^{(8-7-1)}[/tex] = [tex]2^0[/tex] = 1
Adding decimal values for each digit
Total decimal value = 1128 + 064 + 132 + 016 + 18 + 14 + 12 + 11
= 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1
= 175
Hence, the decimal number that corresponds to the binary number "10101111" is 175.
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solve each equation by completing the square
[tex]x^{2} -34x+289=0[/tex]
After completing the square, the equation is ____ and the solution is _________
WHOEVER ANSWERS CORRECTLY WILL BE MARKED BRAINLIEST
Answer:
x = 17------------------------------------------------
Complete the square as follows:
x² - 34x + 289 = 0x² - 2*17*x + 17² = 0 Identity (a ± b)² = a² ± 2ab + b²(x - 17)² = 0x - 17 = 0 Square root both sidesx = 17Angles 2 and 8 are what type of angles?
A. Same side interior angles
B. Alternate exterior angles
C. Alternate interior angles
D. Corresponding angles
Help!!!
Answer:
B. Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are angles that are outside two lines intersected by the transversal and are located on opposite sides of the transversal. Also, they have the same degree! So, the answer is B.
What is the first quartile of the given data set?
The value of first quartile of the given data set is 2.5
What is first quartile?The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.
Given is a data set,
According to the data,
The lower quartile is between 0 and 2.5, which under 25% of the data.
Hence, The value of first quartile of the given data set is 2.5
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Which sentence does NOT contain an error in pronoun-antecedent agreement?
a. A large herd of buffalo thundered across the plain and left a cloud of dust in their wake.
b. When the crowd reached the center of town, the mayor was surprised by their size.
c.Our gymnastics team proved their skills during the individual floor exercises.
Answer:
a
Step-by-step explanation:
pls help having trouble!
Answer:
a is 30 degrees.
Step-by-step explanation:
The degree of a triangle is 180, which means that all the degrees in any triangle will always add up to 180. Since CB and DB are congruent, the angles C and D will be the same. This means that to get the answer, just subtract the value we already have from 180 and divide the sum by 2.
[tex]\frac{180-120}{2} = \frac{60}{2} = 30[/tex]
At a school there are six lessons in a day.
In total, the six lessons last for 4 hours.
a) Assume that each lesson lasts the same amount of time.
How many minutes long is the final lesson?
Optional working
Answer:
40mins
Step-by-step explanation:
4hrsx60
=240mins
240mins/6 lessons
=40mins per lesson
Subtract the expressions.
(7.43n − 2.2) − (6 + 10.5n)
−30.70n − 4.5
−3.07n − 8.2
9.63n − 4.5
17.93n + (−8.2)
The solution to the expression is (b) -3.07n - 8.2
How to subtract the expressions?From the question, we have the following parameters that can be used in our computation:
(7.43n − 2.2) − (6 + 10.5n)
Remove the brackets
So, we have
(7.43n − 2.2) − (6 + 10.5n) = 7.43n − 2.2 − 6 - 10.5n
Evaluate the like terms
(7.43n − 2.2) − (6 + 10.5n) = -3.07n - 8.2
Hence, the solution is (b) -3.07n - 8.2
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g you would like to obtain a 90% confidence interval with margin of error 0.02, what is the minimum sample size you need?
I would like to construct a 95% confidence interval with a 4% margin of error. We don't have an estimate for the percentage, so we use a conservative estimate.
This is the minimum sample size, so we need to round up to 601. The larger the sample, the more confident the responses truly represent the population.
This shows that for a given confidence level, the confidence interval gets smaller as the sample size increases. At least 1450 samples from each group are required.
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HELP QUICK!!
An item on sale costs 35% of the original price. If the original price was $60, what is the sale price?
PLEASE HELP I AM SO BEHIND ON SCHOOL WORK !!!
Which equation represents the same line as the points in the table?
y=−3x+2y is equal to negative 3 x plus 2
y=−34x+83y is equal to negative 3 fourths x plus 8 thirds
y=2x−34y is equal to 2 x minus 3 fourths
y=−34x+2
Answer:
Use this site, it will help you in the long run.
Help me quickly please! (I will mark brainliest)
The graphs in this problem that show continuous data are given as follows:
Top right.Bottom left.What are continuous and discrete graphs?Continuous and discrete graphs have different formats to show the data, which are presented as follows:
For a continuous data, the data shown is all the real numbers in an interval, hence a continuous graph is represented by solid lines. This means that the second and third graphs in this problem, that is, the top right and the bottom left graphs represent continuous data.
For discrete data, only certain values are represented in an interval, hence the graph of discrete data is composed only by dots, which is the case for the first and last graphs in this problem, that is, the top left graph and the bottom right graph.
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here is a famous problem: nn guests arrive at a party. each person is wearing a hat. we collect all hats and then randomly redistribute the hats, giving each person one of the nn hats randomly. what is the probability that at least one person receives his/her own hat?hint: use the inclusion-exclusion principle.
The probability that at least one person receives his/her own hat is 1 - (1/n)^n, using the inclusion-exclusion principle.
The inclusion-exclusion principle states that the probability of event A or B occurring is equal to the probability of event A plus the probability of event B minus the probability of event A and B occurring. In this case, the probability of at least one person receiving his/her own hat is the probability of one person receiving his/her own hat plus the probability of two people receiving their own hats minus the probability of three people receiving their own hats, and so on. This can be expressed mathematically as 1 - (1/n)^n, where n is the number of guests. This formula can be applied to any situation where a random event is being repeated multiple times with the same set of outcomes.1 - (1/10)^10 = 0.99.
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Moussa is younger than Sophia. Their ages are consecutive even integers. Find Moussa's age if the product of their ages is 24.
Moussa's age if the product of their ages is 24 is 4 years.
How to calculate their age?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Moussa is younger than Sophia. Their ages are consecutive even integers.
Let the ages be x and x + 2.
This will be illustrated as:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
x² + 6x - 4x - 24 = 0
x(x + 6) -4(x + 6) = 0
x - 4 = 0
x = 4
x + 2 = 4 + 2 = 6
The ages are 4 and 6 years.
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If the product of Sophia age and Moussa age is 24, the age of Moussa is 4 years.
How to find the Moussa's age?Moussa is younger than Sophia. Their ages are consecutive even integers.
The product of there ages is 24. Moussa's age can be found as follows:
Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.
Hence,
Let
x = age of Moussa
x + 2 = age of Sophia
Hence, the product of their age will be as follows:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
lets factorise the quadratic equation. The numbers one can multiply to get -24 and add to get 2 are -4 and 6. Therefore,
x² - 4x + 6x - 24 = 0
x(x - 4) + 6(x - 4) = 0
(x + 6)(x - 4) = 0
Therefore,
x = - 6 and x = 4
We can only use positive numbers.
Therefore, the age of Moussa is 4 years
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Factorize:
x^4 - (x-z)^4
=(2x2 −2xz+z ^2 )(2x−z)(z)
Store A sells a dozen donuts in packages as a BOGO, with the regular price of dozen at $6.35. Store B offers a dozen donuts without a special for $3.35. Store C offers a dozen and a half at a price of $6.50. Store D gives you a 25% discount if you buy 2 at a price of $3.70 each. Which is the better buy?
Store D provides the best value, with the lowest price per donut at $0.24.
To determine which store has the best deal, you should compare the price per donut at each store.
At Store A, the BOGO offer means that you can buy one dozen donuts for the regular price of $6.35 and get a second dozen for free. This means that you are paying $6.35 for 2 dozen donuts, or $0.27 per donut.
At Store B, a dozen donuts cost $3.35, or $0.28 per donut.
At Store C, a dozen and a half donuts cost $6.50, or $0.26 per donut.
At Store D, if you buy 2 dozen donuts at $3.70 each and receive a 25% discount, you will pay $3.70 × 2 × (1 - 0.25) = $5.77 for 2 dozen donuts, or $0.24 per donut.
Thus, based on these prices, Store D is the best deal, as it has the lowest price per donut at $0.24.
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use the graphs of f and g to graph h(x) = (f + g)(x). (graph segments with closed endpoints.)
Different x values must be taken into account in order to graph h (x). So the graph of the h(x) is given below.
In the given question, we use the graphs of f and g to graph h(x) = (f + g)(x).
A diagram that compares the fluctuation of one variable to that of one or more other variables, such as a collection of points, lines, line segments, curves, or regions.
The graph is given below:
h (x) = (f + g) (x)
The function h(x) can be written as
h (x) = f (x) + g (x)
Different x values must be taken into account in order to graph h (x).
h (0) = f (0) + g (0) = 2 - 1 = 1
h (1) = f (1) + g (1) = 3 + 0 = 3
h (2) = f (2) + g (2) = 1 + 0.5 = 1.5
h (3) = f (3) + g (3) = 2 + 0 = 2
So the graph of the h(x) is given below:
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What is the equation of the linear function in point-slope form that passes through (6, 5) and has a slope of?
y-5=(x-6)
x-6=1/(x-5)
Answer:
y – 5 = m(x – 6)
Step-by-step explanation:
using y =mx +c as our guide line
Step 1 : identification of coordinates
(6,5) ;x1= 6,y1 = 5
step 2 : applying the formula
y – y1 = m(x – x1)
y – 5 = m(x – 6)
Elie built a large rectangular vegetable garden that i 9 meter long and ha an area of 72 quare meter. What i the perimeter of Elie’ vegetable garden
Answer:
The perimeter of Elie's vegetable garden is 34 meters.
Step-by-step explanation:
The formula for area is: a=w*l.
A = area
W = width
L = length
If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.
72=w*9
You can divide both sides by 9 to get the width, which is 8 meters.
To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:
2(9)+2(8)=34
The perimeter of Elie's vegetable garden is 34 meters.