Find the inverse of one-sided Laplace transform of following signal. Then Find its poles and ROC. X(s) = (x+1)(22+4 48+4)
Answers
The inverse Laplace transform of \(X(s) = (s+1)/(s^2 + 4s + 4)\) is \(x(t) = e^-^t * (t + 1)\). 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 \((s + 2)^2\), 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 \((A/(s + 2)) + (B/(s + 2)^2)\). 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 \(e^-^2^t\), and the inverse Laplace transform of \(B/(s + 2)^2\) is \(t * e^-^2^t\).
Thus, the inverse Laplace transform of X(s) is \(x(t) = e^-^t * (t + 1)\).
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) = \((s+1)/(s^2 + 4s + 4)\) is \(x(t) = e^-^t * (t + 1)\). The poles are located at s = -2, and the ROC includes all values of s to the right of -2 on the real axis.
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Related Questions
pls help I will give brainliest
Answers
its B. 50°
Triangle Have 180°
180 - 90 = 9090 × 2 = 180Half of triangle Have 90°
90° - 40° = 50°Sarah is playing a video game that allows her to double her coins each hour. The game starts with 4 coins and Sarah plays the game for 2 hours. How many coins will she have at the end of the two hours.
Answers
Answer:
16 coins
Step-by-step explanation:
At first: 4 coins
First hour: 4 x 2 = 8
Second hour: 8 x 2 = 16
Total coins: 16 coins
3. Which list shows the lengths of three segments that could be the sides of a right triangle? A. 6 cm, 8 cm. 10 cm B. 5 cm. 7 cm. 9 cm C.2 cm. 4 cm. 6 cm D. 1 cm. 2 cm. 3 cm ОА B OD
Answers
Answer:
7c,m
Step-by-step explanation:
you bad at math im smart your not sike you are smart haha
c) From the top of a building 80 metres high, the
angle of depression of a car parked on the ground
is 52º. Find the distance of the car from the base of the building.
(Write your answer correct to t
Answers
The distance of the car from the base of the building, based on the given information, is approximately the height of the building (80 meters) divided by the tangent of the angle of depression (52º).
To find the distance of the car from the base of the building, we can use trigonometry and the given information:
Step 1: Draw a diagram to visualize the situation. Label the height of the building as 80 meters and the angle of depression as 52º.
Step 2: Identify the right triangle formed by the building, the distance to the car from the base of the building, and the line of sight to the car.
Step 3: The height of the building is the opposite side, and the distance to the car is the adjacent side. The angle of depression is the angle between the line of sight and the horizontal ground.
Step 4: Apply the tangent function: tan(52º) = opposite/adjacent.
Step 5: Substitute the known values: tan(52º) = 80 meters / adjacent.
Step 6: Rearrange the equation to solve for the adjacent side (distance to the car): adjacent = 80 meters / tan(52º).
Step 7: Calculate the value of tan(52º) using a calculator or trigonometric table.
Step 8: Substitute the value of tan(52º) and evaluate the expression.
Therefore, The distance of the car from the base of the building is the calculated value obtained in Step 8.
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It costs $60 per hour to rent a jet ski. The total cost of a jet ski rental
includes a flat fee of $20 plus the hourly fee. Which equation represents
the situation?
Answers
Answer:
y = 60x + 20
Step-by-step explanation:
The number of hours that we ski is a variable cost where each hour costs $60. On top of that, we have a fixed cost of $20 which stays the same no matter how long we ski.
So we can use an equation to find the totla cost C given the number of hours t as follows:
C(t) = 60t + 20
We can use this equation to find the cost of a skiing session by plugging in some value for t. For example, if we ski for 3 hours:
C(3) = 60(3) + 20 = $200
The equation can also be written using x and y and mean the same thing.
Piper went to the store to buy some apples. The price per pound of the apples is $5.25 per pound and she has a coupon for $4.75 off the final amount. With the coupon, how much would Piper have to pay to buy 3 pounds of apples? Also, write an expression for the cost to buy pp pounds of apples, assuming at least one pound is purchased.
Answers
Explain—— 5.25 per pound x 3pp =15.75
Coupon 4.75 off final amount
15.75 - 4.75=11.00
Answer:
Cost of 3 pounds:
5.25(3)−4.75=11
Cost of p pounds:5.25p-4.75
5.25p−4.75
Step-by-step explanation:
Since 1 pound of apples costs $5.25, 3 pounds of apples would cost $5.25 5.25×3 or $15.75. The coupon would save $4.75, so the final cost is $15.75-$4.75 or $11.
Cost of 3 pounds:
5.25(3)−4.75=11
Cost of p pounds:5.25p-4.75
5.25p−4.75
if someone do this soon I will give 100 points and brilliant answers
Answers
Step-by-step explanation:
sir here is the Ans so. mark as brainliiest please ..
b/Ans: perimeter = X+1/2y
= 50+100
150
Barbara got a flat tire and does not have a spare. She needs her car for work, so she goes to a business that offers payday loans in order to get the money to buy a new tire. She borrows $75 and plans to pay it back when she gets paid in 8 days. Barbara is charged a fee of $15 and the term on her loan is 8 days. Approximately what is the annual percentage rate on her loan?
Answers
Answer: 913%
Step-by-step explanation:
Based on the concept of payday loans, Barbara's annual percentage rate is 9.125%
What is the Annual Percentage Rate?The Annual Percentage Rate (APR) is a term that is used to describe the cost paid each year to borrow money, such as fees, expressed as a percentage.
In this case, to get the annual percentage rate (APR) on Barbara's loan calculate the effective interest rate for the 8-day period and then annualize it.
Given that Barbara borrowed $75 and was charged a fee of $15 for an 8-day term the total amount she needs to repay is $75 + $15 = $90.
To calculate the effective interest rate we can use the following formula:
Effective Interest Rate = (Total Interest / Principal) * (365 / Loan Term)
Total Interest = $15 (fee)
Principal = $75 (loan amount)
Loan Term = 8 days
Substituting the values into the formula:
Effective Interest Rate = (15 / 75) * (365 / 8)
Effective Interest Rate = 0.2 * 45.625
Effective Interest Rate = 9.125%
Therefore, APR = Effective Interest Rate * Compounding Frequency
APR = 9.125% * 1
APR = 9.125%
Hence, in this case, it is concluded the approximate annual percentage rate (APR) on Barbara's loan is around 9.125%.
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Jemima has to post 2 books to her sister. She weighs them on the kitchen
scales, which gives readings correct to the nearest 5g.
"Algebra made Easy" is weighed at 450g.
"Terrible Trigonometry" is weighed at 95g.
She packs them using wrapping that is weighed at 120g.
The post office charges 79p for the first 510g of any parcel, and then 11p for
each extra 40g.
Find the maximum that Jemima might have to pay to post the parcel.
Pls answer it’s urgent I’ll give brainliest
Answers
Answer:
All three products were already rounded to the nearest 5g.
"Algebra made Easy" 450g
“Terrible Trigonometry" 95g
Wrapping 120g
867.107844 Is the maximum Jemima might have to pay to post the parcel.
Step-by-step explanation:
510 divided by 79 = 6.455g per 510g
665g total of products so divide 665 by 510 now to get 1.30392157g per weight which brings us to the maximum total of 867.107844
\dfrac{-2}{3} \div 2\dfrac{1}{4} =
3
−2
÷2
4
1
Answers
Answer:
\(\dfrac{-2}{3} \div 2\dfrac{1}{4} = \dfrac{-8}{27}\)
Step-by-step explanation:
Given
\(\dfrac{-2}{3} \div 2\dfrac{1}{4} =\)
Required
Solve
Start by converting the mixed number to improper fraction
\(\dfrac{-2}{3} \div \dfrac{9}{4} =\)
Convert the division to muliplication
\(\dfrac{-2}{3} * \dfrac{4}{9} =\)
\(\dfrac{-2*4}{3*9}=\)
\(\dfrac{-8}{27}\)
Hence:
\(\dfrac{-2}{3} \div 2\dfrac{1}{4} = \dfrac{-8}{27}\)
Homework: Section 11.1 Question 7. Complete the square to find the x-intercepts of the function given by the equation listed. f(x)=x² +34x+104 What are the x-intercepts? **** (Simplify your answer. T
Answers
Answer:
x² + 34x + 104 = 0
x² + 34x = -104
x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²
x² + 34x + 17² = -104 + 17²
x² + 34x + 289 = 185
(x + 17)² = 185
x + 17 = +√185
x = -17 + √185
PLS HELP!!
Cruz had d $10 bills and 4 fewer $20 bills than he has $10 bills. Enter an algebraic expression to represent how much money Cruz has in dollars. Simplify the expression, if possible.
Answers
Answer:Here's the basic equation
m(d) = 10d + 20(d - 2) (the money total is the 10 dollar bills plus the 20 dollar bills (which are two less than the 10 dollars))
Step-by-step explanation:
To simplify it, start by distributing the 20:
m(d) = 10d + 20d - 40
add like terms
m(d) = 30d - 40
PLEASE HELP MATH 25 POINTS
Answers
Answer: y = x * 0.02
Step-by-step explanation:
When you multiply the number in x by 0.02 you end up with the product of y.
Answer:
y = x * 0.02
Step-by-step explanation:
Work out 3% of 860kg
need this asap!!!
Answers
Answer:
3% of (860 kilograms) =
25.8 kilograms
Answer:
Step-by-step explanation:
3 * 860/100
= 2580/100
= 25.8.
pls help …………………?………….
Answers
Answer:
The Last box. (y=1/2x-4)
Step-by-step explanation:
The formula is y=mx+b
b is the interception point on the y axis.
So the -4 is where the line crosses on the y axis.
mx is how many spaces it goes up or down.
If you look the box goes up or down twice then left or right once.
So that's your answer, hope this helps.
Thirty-five of the one hundred eighteen students who
took the test earned an A. How many of the students did
not earn an A on the test?
Answers
Subtract the number that got an A from total students:
118 - 35 = 83
83 students did not get an A
Answer: i think its c
Step-by-step explanation:
PLZZZZZ HELP!!!!! WILL CHOOSE BRAINLIEST
Answers
Answer:
what are you asking of me?
Answer:there is no question
how do i find a,b and k?
Answers
Answer:
a = 1
b = 2
k = -2
Step-by-step explanation:
Given:
\(\displaystyle \large{y=k(x-a)^2(x-b)}\)
First, find the a-value and b-value by observing the graph. Notice that once the graph hits x = 1, it just goes up or concave up - that indicates to be the double roots of function. Therefore:
Our a-value is 1
Second, find the b-value. Another x-intercept beside double roots x = 1 is x = 2 as shown in the graph. Therefore:
Our b-value is 2
Third, find the k-value. Right now we have the equation:
\(\displaystyle \large{y=k(x-1)^2(x-2)}\)
To find the k-value, simply find a point’s value (x,y) to substitute. According to the graph, you can try substitute (0,4) in:
\(\displaystyle \large{4=k(0-1)^2(0-2)}\\\displaystyle \large{4=k(-1)^2(-2)}\\\displaystyle \large{4=k(1)(-2)}\\\displaystyle \large{4=-2k}\\\displaystyle \large{k=-2}\)
Therefore, the value of k is -2
please help me with this its math!!
Answers
If this doesn’t look right, then I need you to tell me what kind of method you use to solve this then I will help more.
a) a bit string is a finite sequence of 0's and 1's. how many bit strings have length 9? 512 bit strings (b) how many bit strings of length 9 begin with three 0's? if a bit string of length 9 begins with three 0's, then positions remain to be filled in. since each of these positions can be filled with either a 0 or a 1, the number of bit string of length 9 that begin with three 0's is . (c) how many bit strings of length 9 begin and end with a 1? bit strings
Answers
(a) To answer this question, we need to understand that each position in the bit string can either be a 0 or a 1, and there are 9 positions in total. Therefore, there are 2 options for each position, giving us a total of 2^9 possible bit strings. This equals 512 bit strings.
(b) If a bit string of length 9 begins with three 0's, then the remaining 6 positions can either be a 0 or a 1. Since there are 2 options for each position, the number of bit strings of length 9 that begin with three 0's is 2^6 or 64 bit strings.
(c) For a bit string of length 9 to begin and end with a 1, the first and last positions must be a 1. This leaves us with 7 positions in between which can either be a 0 or a 1. Similar to part (b), there are 2 options for each position, giving us a total of 2^7 or 128 bit strings that begin and end with a 1.
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Match each equation to an equivalent equation with a perfect square on one side.
Answers
The equations to an equivalent equation with a perfect square on one side are below: x² + 8x = 2 ⇒ (x + 4)² = 18, x² + 10x = -13 ⇒ (x + 5)² = 12, x² - 14x = 5 ⇒ (x - 7)² = 54, x² + 2x = 0 ⇒ (x + 1)² = 1, x² + 4x -5 = 0 ⇒ (x + 2)² = 9 and x² -20x = -9 ⇒ (x - 10)² = 91.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
According to the given question, the required solution would be as:
x² + 8x = 2
x² + 2 × 4 × x = 2
Add both sides 16 in the above equation,
x² + 2 × 4 × x + 16 = 2 + 16
x² + 2 × 4 × x + 4² = 2 + 16
As per the formula : (a + b)² = a² + 2 × a × b + b²
(x + 4)² = 18
x² + 8x = 2 ⇒ (x + 4)² = 18
Evaluation each equation similarly, then we get
x² + 10x = -13 ⇒ (x + 5)² = 12
x² - 14x = 5 ⇒ (x - 7)² = 54
x² + 2x = 0 ⇒ (x + 1)² = 1
x² + 4x -5 = 0 ⇒ (x + 2)² = 9
x² -20x = -9 ⇒ (x - 10)² = 91
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Which equation gives the sum of infinity sigma 6( 1/3) HURRY PLEASE
Answers
Answer:
3rd option
Step-by-step explanation:
The sum to infinity of a geometric sequence is
S = \(\frac{a}{1-r}\)
where a is the first term and r the common ratio
The expression inside the summation is
6 \((\frac{1}{3}) ^{n-1}\)
which is in the form of the nth term of a geometric sequence
with a = 6 and r = \(\frac{1}{3}\) , then
S = \(\frac{6}{1-\frac{1}{3} }\) ← expression required
= \(\frac{6}{\frac{2}{3} }\)
= 9
Answer:
C I took the quiz
Step-by-step explanation:
14) through: (-3, 4) and (5,2)
A) x + 4y= 13 B) 4y= -1
C) x = -4
D) –3 y = 0
Answers
Answer:
a, the letter is a and you welcome
Answer:
A) x+4y=13
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-4)/(5-(-3))
m=-2/(5+3)
m=-2/8
simplify
m=-1/4
y-y1=m(x-x1)
y-4=-1/4(x-(-3))
y-4=-1/4(x+3)
y=-1/4x-3/4+4
y=-1/4x-3/4+16/4
y=-1/4x+13/4
y-(-1/4x)=13/4
y+1/4x=13/4
4(y+1/4x)=4(13/4)
4y+4/4x=13
4y+x=13
x+4y=13
Find the number of unique permutations of the word ALGEBRA.
Answers
Answer:
= 2520
Step-by-step explanation:
In 2520 distinct way the letter "ALGEBRA " can be Arranged
I think it's the answer
What is this answer to the picture i put below
Answers
I dont know sorry
So sorry really wish i could help
PLEASE help
Allen mixes 1 cup of water that is 150°F and 1 cup of cold chicken broth that is 50°F. The end temperature of the mixture would be about___________
. Chris combines 2 cups of soup that is 50°F with 1 cup of water that is 150°F. The end temperature of the mixture would be ______
Answers
Answer:
1) 100 degrees F
2) 50 degrees F
Step-by-step explanation:
its just simple subtraction
Dominica has a total of 22 coins in her pocket, all of
them are nickels and dimes. If the value of the coins
is $1.50, then how many nickels does Dominica
have?
Answers
Answer:
So there are 14 nickels (worth a total of 70 cents) and 8 dimes (worth a total of 80 cents)
Step-by-step explanation:
Answer:
she has 2 nickels
Step-by-step explanation:
dimes=10 cents
nickels=5 cents
10x14=140
1.40
5x2=10
1.40+10=1.50
If A is a 9x6 matrix, what is the largest possible dimension of the row space of A? If A is a 6x9 matrix, what is the largest possible dimension of the row space of A? Explain.
Answers
If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.
The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.
For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.
For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.
Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.
However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.
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What is the value of the expression 2.8*10^7/1.4*10^3
Answers
Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below.
Male 15,790 27,126 1385 8063 18,702 15,671 14,353 24,940
Female 25,392 13,278 18,414 17,806 12,951 16,335 16,497 18,493
Identify the test statistic
Identify the P-value
Answers
The p-value is less than alpha (α), reject the null hypothesis; fail to reject the null hypothesis. The given data represents the number of words spoken by eight different randomly selected couples
The hypothesis tests are used to evaluate the claims about the parameters of the population. In hypothesis testing, we assume a null hypothesis and test whether the null hypothesis is supported by the sample data or not. The following are the steps of hypothesis testing:
Step 1: Specify the null and alternative hypotheses. The null hypothesis is a statement of no effect or no difference. The alternative hypothesis is the opposite of the null hypothesis.
Step 2: Determine the level of significance. It is denoted by alpha (α) and represents the probability of making a type-I error.
Step 3: Identify the test statistic. The test statistic is a measure of how far the sample statistic deviates from the null hypothesis.
Step 4: Calculate the p-value. The p-value is the probability of obtaining a sample statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.
Step 5: Make a decision and interpret the results. If the p-value is less than alpha (α), reject the null hypothesis; otherwise, fail to reject the null hypothesis. The given data represents the number of words spoken by eight different randomly selected couples.
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