Problem 3 Determine the real expression of sequence x[n] whose z-transform is X(z) = 1 + 2z-2 1+ z-2
Answers
The real expression of sequence x[n] is:
x[n] = 3 δ[n] - (-1)^n
To find the real expression of sequence x[n] from its z-transform X(z) = (1 + 2z^-2)/(1 + z^-2), we can use partial fraction decomposition to write:
X(z) = (1 + 2z^-2)/(1 + z^-2) = 1 + z^-2 + 1/(1 + z^-2)
Then, we can use the inverse z-transform formula to obtain:
x[n] = (1/2πj) ∮ X(z)z^n-1 dz
where the contour of integration encloses the region of convergence of X(z). In this case, the region of convergence is the annulus 1 < |z| < ∞, so we can choose a contour that encloses this region and apply the residue theorem to evaluate the integral. The only singularity of X(z) inside the contour is a pole of order 2 at z = -1, so we need to compute the residues at this pole. We have:
Res[X(z), z = -1] = lim(z+1)^2 X(z)
= lim(z+1)^2 (1 + 2z^-2)/(1 + z^-2)
= lim(z+1)^2 [(1 + 2/z^2)/(1 + 1/z^2)]
= 3
Therefore, the inverse z-transform is:
x[n] = (1/2πj) ∮ X(z)z^n-1 dz = 3 δ[n] - (1/2πj) ∮ (1 + z^-2)/(1 + z^-2) z^n-1 dz
The integral in the second term can be evaluated by applying the residue theorem. The only singularity inside the contour is a simple pole at z = -1 with residue 1, so we have:
(1/2πj) ∮ (1 + z^-2)/(1 + z^-2) z^n-1 dz = -Res[(1 + z^-2)/(1 + z^-2) z^n-1, z = -1]
= -lim(z+1) (1 + z^-2) z^n-1
= (-1)^n
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Related Questions
Please help with this
Answers
Answer:
\(f(x) = 100(1.05)^t\)
A particular bacteria double in area on a petri dish every day. If on the first day the bacteria covers 3 mm^2, how much area should the bacteria cover by the 10th day?
Answers
When a bacteria gets double in area per day then the area that will cover by the bacteria in the 10tn day will be 1536 mm^2.
Geometric progression:
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
The Geometric progression for this question will be 3,6,12,24..............
Here,
The first term a=3
Common ratio r=2
Number of days n=10
Formula:
Nth term = a\(r^{n-1}\)
So,
10th term = a\(r^{10-1}\)
=3×\(2^{9}\)
=3×512
=1536
Therefore the bacteria will cover an area of 1536 mm^2 by the 10th day , when it get doubled in every day.
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Can someone please help me with this math problem, I'm confused and I need someone to please answer this by 11:59 it's currently 10:46 where I am located! I will also mark you brainiest!
Answers
Step-by-step explanation:
You make a T-chart of x and y and graph it, like this:
If x = 1, y = 5
x | y
0 | 4
1 | 5
2 | 6
3 | 7
4 | 8
on and on it goes. . .
The diffusion equation can be written as R2=4Dt where R is the average displacement, D is the diffusion constant, and t is the time. What can you say about the relationship between average displacement squared (R2) and time (t)? (Is it linear, exponential, etc.?)
Question 10
For the analysis, we will include a trendline on our R2 vs. t graph. The trendline equation has the form y=mx+b. Which variable from the diffusion equation corresponds to y in the trendline equation? Which variable from the diffusion equation corresponds to x in the trendline equaton?
Question 11
Given your answer to question 10, how could you solve for the diffusion constant in terms of the slope and a constant?
Question 12
Suppose your trendline equation is y=1.24x+5.63 Solve for the diffusion constant.
Answers
The fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:
D = 1.24/4 = 0.31
What is a Diffusiοn?Diffusiοn is the prοcess by which particles οf a substance mοve frοm an area οf high cοncentratiοn tο an area οf lοwer cοncentratiοn, resulting in a net mοvement οf particles dοwn their cοncentratiοn gradient.
This οccurs due tο the randοm mοtiοn οf individual particles, which leads tο a tendency fοr particles tο spread οut and becοme evenly distributed οver time.
Answer tο Questiοn 9:
The relatiοnship between average displacement squared (R²) and time (t) is linear.
Answer tο Questiοn 10:
The variable 'R2' in the diffusiοn equatiοn cοrrespοnds tο 'y' in the trendline equatiοn, and the variable 't' in the diffusiοn equatiοn cοrrespοnds tο 'x' in the trendline equatiοn.
Answer tο Questiοn 11:
We can sοlve fοr the diffusiοn cοnstant 'D' in terms οf the slοpe 'm' and a cοnstant 'c' by equating the diffusiοn equatiοn and the trendline equatiοn.
The diffusiοn equatiοn: R2 = 4Dt
The trendline equatiοn: y = mx + b
Substituting the cοrrespοnding variables, we get:
R2 = y, D = cοnstant, t = x, m = slοpe, b = cοnstant
Sο, we have:
R2 = 4Dt
y = mx + b
Equating the twο equatiοns, we get:
y = 4Dx + 0 (since b = 0)
Cοmparing this with the trendline equatiοn y = mx + b, we can see that:
m = 4D
Therefοre, we can sοlve fοr 'D' as:
D = m/4
Answer tο Questiοn 12:
Given the trendline equatiοn y = 1.24x + 5.63, we can see that the slοpe 'm' is 1.24.
Using the fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:
D = 1.24/4 = 0.31
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A line is graphed on a coordinate plane with a slope of (-2/3) and passes through the point (-6,1). What is the y-intercept of the graph?
Answers
The y-intercept of the graph is -3.
To find the y-intercept of the graph, we need to determine the point where the line intersects the y-axis. The y-intercept represents the value of y when x is equal to zero.
Given that the slope of the line is -2/3, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Plugging in the known values, we have 1 = (-2/3)(-6) + b. We substitute the x-coordinate of the given point (-6) into the equation and the y-coordinate (1) as well.
Simplifying the equation, we have 1 = 4 + b. To isolate b, we subtract 4 from both sides, yielding b = 1 - 4 = -3.
Therefore, the y-intercept of the graph is -3. This means that the line intersects the y-axis at the point (0, -3).
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which choice is equivalent to the expression below 2^7 times 19
Answers
The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432
4.32x+1=17.8929 Sole for x
Answers
Answer:
x = 3.91039
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
4.32x + 1 = 17.8929
Step 2: Subtract 1 on both sides
4.32x = 16.8929
Step 3: Divide both sides by 4.32
x = 3.91039
This is due at the end of the day please help
Answers
Answer:
Step-by-step explanation:
the answer is 8
8 shipping cost
8 + X = Y
What is the percentage difference between 1982802.91786170.42
Answers
Given:
Two numbers are given as
\(\begin{gathered} 1982802.9 \\ 1786170.42 \end{gathered}\)Required:
We need to find the percentage difference between both numbers
Explanation:
Consider
\(\begin{gathered} a=1982802.9 \\ b=1786170.42 \end{gathered}\)The formula to find the percentage difference is
\(100*\frac{\text{ la-bl}}{\frac{(a+b)}{2}}\)put the values
\(\)Question 10 of 10
Sample A and sample B are from the same population. If the sample
proportion for sample A is 0.53, the sample proportion for sample B has to be
0.53
A. True
B. False
Answer is false
Answers
Answer:
It’s false
Step-by-step explanation:
It doesn’t need to be the same
The length of a rectangle exceeds its width by
11 inches, and the area is 26 square inches.
What are the length and width of the
rectangle?
Separate the answers with a comma.
Enter the correct answer.
Answers
Answer:
width = 2 in
length = 13 in
Step-by-step explanation:
x(11+x) = 26
x² + 11x - 26 = 0
(x + 13)(x - 2) = 0
x = 2
What is the next term of the arithmetic sequence? 7,11,15,19,7,11,15,19
Answers
Answer:
7
Step-by-step explanation:
4 times at an addition of 4, then a subtraction of 12
. Quantas senhas com 4 algarismos diferentes podemos escrever com os algarismos 1, 2, 3, 4, 5, 6?
Answers
Answer:
We can write 360 distinct passwords using the numbers 1, 2, 3, 4, 5, and 6.
Step-by-step explanation:
We have to find how many passwords with 4 different digits can we write with the numbers 1, 2, 3, 4, 5, and 6.
Firstly, it must be known here that to calculate the above situation we have to use Permutation and not combination because here the order of the numbers in a password matter.
Since we are given six numbers (1, 2, 3, 4, 5, and 6) and have to make 4 different digits passwords.
Now, for first digit of the password, we have 6 possibilities (numbers from 1 to 6).Similarly, for second digit of the password, we have 5 possibilities (because one number from 1 to 6 has been used above and it can't be repeated).Similarly, for the third digit of the password, we have 4 possibilities (because two numbers from 1 to 6 have been used above and they can't be repeated).Similarly, for the fourth digit of the password, we have 3 possibilities (because three numbers from 1 to 6 have been used above and they can't be repeated).So, the number of passwords with 4 different digits we can write = \(6 \times 5 \times 4 \times 3\) = 360 possibilities.
Hence, we can write 360 distinct passwords using the numbers 1, 2, 3, 4, 5, and 6.
a packaging box is filled 4/5 of the way with packing peanuts what decimal represents the fraction of the box filled with pack penauts
Answers
Answer:
0.8
Step-by-step explanation:
4/5, you divide 5 from 4 and get 0.8
HELP PLEASE THANK YOU
Answers
Solve the following equation.
-2(n+7)=15
Answers
suppose that it is reported that 75% of workers aged 18 and over drive to work. find the probability that more than 3 of the 10 workers chosen drive to work alone.
Answers
On solving the provided question, we can say that Probability 8 drive to work\(= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123 = > 1 - 0.1236 = 0.8764\)
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
x = number that drive to work alone
Likelihood that exactly eight people drive alone to work is equal to the probability that no more than seven people drive alone.
\(P(x < = 7) = 1 - P(x > 7) = 1- P(x = 8)\)
That probability
Probability 8 drive to work
\(= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123\\=1 - 0.1236 = 0.8764\)
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A group of friends wants to go to the amusement park. They have no more than $280 to spend on parking and admission. Parking is $19.50, and tickets cost $33.75 per person, including tax. Which inequality can be used to determine semanticsp, the maximum number of people who can go to the amusement park?
Answers
The number of people who can go to the amusement park is 8.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given: the group of friends had $280.
For parking= $19.50
Remaining will be,
=$(280-19.50)
= $ 260.5
Cost of ticket per person = $33.75
Thus, number of tickets they can buy
=260.5 / 33.75
=7.718 = 8 peoples
Hence, number of people who can go to the amusement park is 8.
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Joe has 2/10 of a dollar. Ashley has 20/100 of a dollar. Billy has 3/100 of a dollar. Together, what fraction of a dollar do they have?
Answers
Answer:
they have 43/100 or 43% out of 100
Step-by-step explanation:
Because joe has 2/10| 2/10=20% or 2
Joe=20
Ashley also has the same thing as joe so 20.
Ashley=20
Billy has 3/100 that = 3 so what's 20+20+3=43 and there's your answer.
Have a great day:)
The electric potential in a volume of space is given by V(x,y,z)=x
2
+xy
2
+yz Determine the electric field in this region at the coordinate (−7,1,−3). (Enter the components of the field vector, separated by a commas. The potential function above is assumed to be in units of Volts, the coordinates are assumed to be in units of meters, and your answer is assumed to be in units of V/m. In other words: only enter the numbers, but no units. ). T
Answers
The electric field in this region at the coordinate (-7, 1, -3) is 13 V/m in the x-direction, 14 V/m in the y-direction, and -1 V/m in the z-direction.
To determine the electric field in the given region, we need to take the negative gradient of the electric potential function V(x, y, z). The electric field is defined as the negative gradient of the potential:
E = -∇V
The gradient of a scalar function in Cartesian coordinates is given by:
∇V = (∂V/∂x, ∂V/∂y, ∂V/∂z)
To find the electric field at the coordinates (-7, 1, -3), we need to calculate the partial derivatives of V(x, y, z) with respect to x, y, and z.
∂V/∂x = 2x + y^2
∂V/∂y = 2xy
∂V/∂z = y
Now, substitute the coordinates (-7, 1, -3) into these partial derivatives:
∂V/∂x = 2(-7) + (1)^2 = -14 + 1 = -13
∂V/∂y = 2(-7)(1) = -14
∂V/∂z = (1) = 1
the components of the electric field vector at (-7, 1, -3) are (-∂V/∂x, -∂V/∂y, -∂V/∂z):
E = (-(-13), -(-14), -(1)) = (13, 14, -1)
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Psl I need the answer I am in test
Answers
Answer:
lolololololololololololololololol
Find the domain and range of the following rational function. Use any notation. f(x)=(3)/(x-1) f(x)=(2x)/(x-4) f(x)=(x+3)/(5x-5) f(x)=(2+x)/(2x) f(x)=((x^(2)+4x+3))/(x^(2)-9)
Answers
Domain and Range of the given rational functions are:Given rational function f(x) = 3/(x-1)The denominator of f(x) cannot be zero.x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}
The range of f(x) is all real numbers except zero.Given rational function f(x) = (2x)/(x-4)The denominator of f(x) cannot be zero.x ≠ 4 Therefore the domain of f(x) is {x | x ≠ 4}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x+3)/(5x-5)The denominator of f(x) cannot be zero.5x - 5 ≠ 0x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}The range of f(x) is all real numbers except 1/5.Given rational function f(x) = (2+x)/(2x)The denominator of f(x) cannot be zero.x ≠ 0 Therefore the domain of f(x) is {x | x ≠ 0}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x^2+4x+3)/(x^2-9)For the denominator of f(x) to exist,x ≠ 3, -3
Therefore the domain of f(x) is {x | x ≠ 3, x ≠ -3}The range of f(x) is all real numbers except 1, -1. Function Domain Rangef(x) = 3/(x-1) {x | x ≠ 1} All real numbers except zerof(x) = (2x)/(x-4) {x | x ≠ 4} All real numbers except zerof(x) = (x+3)/(5x-5) {x | x ≠ 1} All real numbers except 1/5f(x) = (2+x)/(2x) {x | x ≠ 0} All real numbers except zerof(x) = (x^2+4x+3)/(x^2-9) {x | x ≠ 3, x ≠ -3} All real numbers except 1, -1
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The unit costs of 10 different kinds of cereal are shown. $0.12, $0.15, $0.18, $0.29, $0.12, $0.55, $0.20, $0.24, $0.28, $0.17 a. Find the mean, median, and mode(s) of the data.
Answers
The mean, median and mode of the data sets are 0.23, 0.19 and 0.12 respectively.
How to find mean, median and mode?Mean, median and mode are measure of central tendency.
The mean is the average of the numbers.
The median is the middle number in a sorted, ascending or descending list of numbers.
The mode is the number that occurs the highest number of times.
Therefore, let's arrange the data in ascending order.
$0.12, $0.12, $0.15, $0.17 , $0.18, $0.20, $0.24, $0.28, $0.29, $0.55
Hence,
mean = sum of the numbers / 10
mean = 0.12 + 0.12 + 0.15 + 0.17 + 0.18 + 0.20 + 0.24 + 0.28 + 0.29 + 0.55 / 10
mean = 2.3 / 10
mean = 0.23
median = 0.18 + 0.20 / 2
median = 0.38 / 2
median = 0.19
mode = 0.12
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Answer:
Step-by-step explanation:
Mean is 0.23, since you add all the numbers up, then divide by all the numbers there are.
For example, there are 10 numbers, and if you add all of the numbers together, you get 2.3.
2.3 divided by 10 is 0.23
I will get the median and modes later.
Terrell arranges x roses at $3.50 each with 10 carnations at $2.25 each. He makes a bouquet of flowers that averages $3.00 per flower. Choose an equation to model the situation.
A. 3.50x + 2.25(10) = 3(x + 10)
B. 3.50x + 2.25 = 0.75x
C. 3.50x + 3 = 22.5(x + 10)
D. 3.50x + 2.50 = 0.75(x + 10)
Answers
Answer:
c
Step-by-step explanation:
Equation to model the situation is ( 3.5x + 22.5 ) = 3(x+10), Option A.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Given data are :
The number of roses = x,
Price of each rose = $ 3.50,
So, the total price of roses = 3.5x dollars.
Now, the number of carnations = 10,
The cost of each carnation = $2.25,
So, the total cost of all carnations = 10 × 2.25 = $ 22.5,
Thus, the total cost of a bouquet of flowers = ( 3.5x + 22.5 ) dollars,
Also, the total numbers of flower = x + 10.
Hence, the average cost of flowers = Total cost / total flowers
average cost flowers = ( 3.5x + 22.5 ) / (x+10)
According to the question,
The average cost of flowers = $ 3.00
( 3.5x + 22.5 ) / (x+10) = 3
or,
( 3.5x + 22.5 ) = 3(x+10)
Therefore, equation to model the situation is ( 3.5x + 22.5 ) = 3(x+10).
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LOL Can someone help me with this LOL?!!
Please simplify that!!!
Answers
Step-by-step explanation:
You should study the exponential laws. Remember that (a/b) to the exponent of m is the same as a to the exponent of m over b to the exponent of m.
Therefore, 2 to the exponent of 5×4 over 3 to the exponent of 2×4 equals to 1048576/6561.
Answer:
2 to the exponent of 5×4 over 3 to the exponent of 2×4 equals to 1048576/6561.
Step-by-step explanation:
By randomly assigning subjects to treatment conditions, many extraneous variables are automatically ____ across conditions.
Answers
By randomly assigning subjects to treatment conditions, many extraneous variables are automatically balanced across conditions.
Random assignment ensures that, on average, the distribution of these extraneous variables will be similar across different treatment groups.
This helps create comparable groups, reducing the likelihood of systematic differences between groups that could confound the treatment effect.
Random assignment minimizes the bias that can arise from confounding variables, allowing researchers to attribute observed differences in outcomes to the treatment rather than other factors.
It provides a solid foundation for making causal inferences and increases the internal validity of the study by reducing the potential influence of extraneous variables on the treatment effect.
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hey what's the amswer
\( \: if \: \: a + b + c = 0\)
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Answers
Answer:
Hope;This paste can help you.look it once.
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What are some parent functions with a domain of all real numbers?
Answers
Answer:
The identity function has a slope of m = 1 and a y-intercept of (0, 0) .
Step-by-step explanation:
The identity function is a special type of linear function having the form f(x) = x . The domain of this function is all real numbers and the range consists of all real numbers .
In circle T with m \angle STU= 94m∠STU=94 and ST=17ST=17 units, find the length of arc SU. Round to the nearest hundredth.
Answers
The length of the arc SU is given by 1.63978 units.
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: The angle ∠STU=94 and ST=17
Thus ST forms the radius of the circle.
Now we know the angle subtended by the arc is given by
SU=2πr×94°/360
=2×3.14×0.2611
=1.63978 units
Hence, The length of the arc SU is given by 1.63978 units.
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helppppppppppppppppppppppppppp thankssssssssss
Answers
\(\\ \bull\tt\longmapsto 100x=60(1200)\)
\(\\ \bull\tt\longmapsto 100x=72000\)
\(\\ \bull\tt\longmapsto x=\dfrac{72000}{100}\)
\(\\ \bull\tt\longmapsto x=720\)
Answer:
Let x represent the number of shares Jillian owns
\(60\% = \frac{60}{100} \\ \frac{60}{100} = \frac{x}{1200} \\ 100x = (60)(1200) \\ 100x = 72000 \\ x = \frac{72000}{100} \\ \boxed{x = 720}\)
Jillian owns b) 720 shares of the catering corporation