Answer:
5
Step-by-step explanation:
Pythagorean Theorem. The 13-meter ladder is leaning against a wall, so it's the hypotenuse.
It reaches 12 meters up, so 12 is one leg.
[tex]a^{2} +b^{2}=c^{2}[/tex]
[tex]a^{2}+12^{2}=13^{2}[/tex]
[tex]a^{2}+144=169[/tex]
[tex]a^{2}=25[/tex]
a = 5
Solve the following ordinary differential equations using Laplace trans- forms: (a) y(t) + y(t) +3y(t) = 0; y(0) = 1, y(0) = 2 (b) y(t) - 2y(t) + 4y(t) = 0; y(0) = 1, y(0) = 2 (c) y(t) + y(t) = sint; y(0) = 1, y(0) = 2 (d) y(t) +3y(t) = sint; y(0) = 1, y(0) = 2 (e) y(t) + 2y(t) = e';y(0) = 1, y(0) = 2
(a) The ordinary differential equation is given by y(t) + y(t) + 3y(t) = 0. Using Laplace transform, we have(L [y(t)] + L [y(t)] + 3L [y(t)]) = 0L [y(t)] (s + 1) + L [y(t)] (s + 1) + 3L [y(t)] = 0L [y(t)] (s + 1) = - 3L [y(t)]L [y(t)] = - 3L [y(t)] /(s + 1)Taking the inverse Laplace of both sides, we have y(t) = L -1 [- 3L [y(t)] /(s + 1)]y(t) = - 3L -1 [L [y(t)] /(s + 1)]
On comparison, we get y(t) = 3e^{-t} - 2e^{-3t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(b) The ordinary differential equation is given by y(t) - 2y(t) + 4y(t) = 0. Using Laplace transform, we have L [y(t)] - 2L [y(t)] + 4L [y(t)] = 0L [y(t)] = 0/(s - 2) + (- 4)/(s - 2)
Taking the inverse Laplace of both sides, we have y(t) = L -1 [0/(s - 2) - 4/(s - 2)]y(t) = 4e^{2t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(c) The ordinary differential equation is given by y(t) + y(t) = sint. Using Laplace transform, we have L [y(t)] + L [y(t)] = L [sint]L [y(t)] = L [sint]/(s + 1)
Taking the inverse Laplace of both sides, we have y(t) = L -1 [L [sint]/(s + 1)]y(t) = sin(t) - e^{-t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(d) The ordinary differential equation is given by y(t) + 3y(t) = sint. Using Laplace transform, we have L [y(t)] + 3L [y(t)] = L [sint]L [y(t)] = L [sint]/(s + 3)Taking the inverse Laplace of both sides, we have y(t) = L -1 [L [sint]/(s + 3)]y(t) = (1/10)(sin(t) - 3cos(t)) - (1/10)e^{-3t}.
The initial conditions are y(0) = 1 and y(0) = 2 respectively.(e) The ordinary differential equation is given by y(t) + 2y(t) = e^{t}. Using Laplace transform, we have L [y(t)] + 2L [y(t)] = L [e^{t}]L [y(t)] = 1/(s + 2)Taking the inverse Laplace of both sides, we havey(t) = L -1 [1/(s + 2)]y(t) = e^{-2t}The initial conditions are y(0) = 1 and y(0) = 2 respectively.
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HELP ME FIND AREA :D thanks :3
Answer:
the actual answer is 3,240 is the answer
Rectangle
EFGH
was translated 4 units to the left and 6 units up. Which rule
describes the translation that was applied to rectangle EFGH to create rectangle
E'F'G'H?
(x,y) → (X-4.7+6)
(x,y) → (X-6.7+4)
(x,y) → (X+4.7-6)
(x,y) → (-44,64)
Answer:
(x, y) -- [X-4, Y+6]
Verify the following properties of the Fourier transform = 1. (Fu)(E) = 27 (F-1u)(-5) 2. (F (eiat u)) (E) = (Fu)(8 + a)
The first property states that the Fourier transform of a function evaluated at a certain frequency is equal to 2π times the inverse Fourier transform of the function evaluated at the negative of that frequency.
The second property states that the Fourier transform of a modulated function is equal to the Fourier transform of the original function shifted by the modulation frequency.
To verify the given properties of the Fourier transform, we can use the definitions and properties of the Fourier transform. Here's how we can verify each property:
1. Property: (Fu)(ω) = 2π (F^-1u)(-ω)
To verify this property, we need to use the definitions of the Fourier transform and its inverse. Let's denote the Fourier transform operator as F and its inverse as F^-1.
According to the definition of the Fourier transform, for a function u(t), its Fourier transform is given by:
(Fu)(ω) = ∫[from -∞ to ∞] u(t) e^(-iωt) dt
Similarly, the inverse Fourier transform of a function U(ω) is given by:
(F^-1U)(t) = (1/2π) ∫[from -∞ to ∞] U(ω) e^(iωt) dω
Now, let's substitute -ω for ω in the inverse Fourier transform:
(F^-1u)(-ω) = (1/2π) ∫[from -∞ to ∞] u(t) e^(i(-ω)t) dt
= (1/2π) ∫[from -∞ to ∞] u(t) e^(iωt) dt
Comparing this with the Fourier transform, we see that (F^-1u)(-ω) is equal to (Fu)(ω) multiplied by 2π, which verifies the first property.
2. Property: (F(e^(iat)u))(ω) = (Fu)(ω + a)
To verify this property, we use the modulation property of the Fourier transform. According to this property, if u(t) has a Fourier transform U(ω), then the Fourier transform of e^(iat)u(t) is given by:
(F(e^(iat)u))(ω) = (Fu)(ω + a)
Applying this property to the given expression, we have:
(F(e^(iat)u))(ω) = (Fu)(ω + a)
This verifies the second property.
In summary, we have verified both properties of the Fourier transform as stated.
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can someone help me please?? my teacher gave me a worksheet of a game with no rules or nun nd expected me to know how to play, she is ignoring me. ion know what to do. what do i do??
You roll a single 6 sided die. What are the odds of rolling a 9?
A. 1/6
B. 0
C. 1/9
D. 9
Answer:
B. 0
Step-by-step explanation:
There aren't enough sides for you to roll a nine
Helppppp it’s due today
Manuel makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.
p and h are variables
Answer:
p = 8h
A very short answer, I know, but reading this out loud reads "Manuel's pay is equal to 8 dollars an hour."
Answer:
p=8h
Step-by-step explanation:
because he gets paid 8 dollars ever hour he works so if you multiple the hours he works to 8 dollars you get his total pay
I dont know how to do this
Answer:
a) 55°
b) 125°
c) 55°
d) 55°
Step-by-step explanation:
a) 180-(90+35) = 55
b) this angle forms a straight angle with ∡a
c) this angle is vertical, and congruent, with ∡a
d) 180-(70+55) = 55
Rationalise √2+√3/3√2-2√3=a-b√6
Answer: 3√6-6/6 + √2=a-b√6
Step-by-step explanation: multiply radicals in the denominator by conjugate to get (a+b)(a-b)=a^2-B^2 pattern.
please help 6th grade math please please help
i: 1
ii: 6
iii: 3
iv: 2
v: 4.5
vi: 2.5
In the figure shown, line AB is parallel to line CD. Part A: What is the measure of angle x? Show your work. (5 points) Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points) AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 65 degrees, angle QPR is equal to x, angle PRD is equal to 120 degrees.
Answer:
120 degrees
Step-by-step explanation:
im a god cuz happppy
Answer:
120 lol
Step-by-step explanation:
Somebody know this? thanks
Answer:
4 right angles
Step-by-step explanation:
a straight light intersects another straight line= creating 4 right angles
What does the C equal to in -1/6 +7/6 = c
Answer:
c = 1
Step-by-step explanation:
we have -1/6 + 7/6
since 6 is a common denominator we can do
[tex]\frac{-1}{6} +\frac{7}{6} = c\\\frac{-1+7}{6} = c\\\frac{6}{6} = c\\1 = c\\c = 1[/tex]
What is the perimeter of thjs
Answer:73 ft
Step-by-step explanation:
Answer:
(120 + 12.5pi) ft^2
Step-by-step explanation:
10ft x 12 ft = 120ft^2
10ft/2 = 5 ft (Radius)
Area of semi circle:
[tex]\frac{\pi r^{2} }{2} = \frac{\pi 5^{2} }{2} = 12.5\pi ft^{2}[/tex]
Area = (120 + 12.5pi) ft^2
I really need help!!!!!!
Answer:
y = 1.50x + 4 ;
Step-by-step explanation:
Given that bike rental cost $4 plus $1.50 per hour
From the information given, the change in y per unit change in x is the value of the slope ;
Therefore, Given that total cost = y and x) number of hours
Change in cost per change in number of hours) 1.50 = slope ; intercept = constant = $4
The equation, in slope intercept form :
y = mx + c
y = 1.50x + 4
Calculate the 90% confidence interval for the following sample Sample: 7.9, 8.3, 8.4, 9.6, 7.7, 8.1, 6.8, 7.5, 8.6, 8, 7.8,7.4, 8.4, 8.9, 8.5, 9.4, 6.9,7.7. Assume normality of the data.
The 90% confidence interval for the given sample is (7.58, 8.60).
To calculate the 90% confidence interval for the given sample assuming normality of the data, we need to use the formula as follows;Confidence interval = X ± Z α/2(σ/√n)Where, X is the sample meanZ α/2 is the Z-score for the desired level of confidenceσ is the population standard deviationn is the sample sizeFirst, we need to calculate the sample mean and standard deviation.Sample mean,
X= (7.9 + 8.3 + 8.4 + 9.6 + 7.7 + 8.1 + 6.8 + 7.5 + 8.6 + 8 + 7.8 + 7.4 + 8.4 + 8.9 + 8.5 + 9.4 + 6.9 + 7.7) / 18
= 8.09
Sample standard deviation,
σ = √[Σ(xi - X)² / (n - 1)]σ = √[(7.9 - 8.09)² + (8.3 - 8.09)² + (8.4 - 8.09)² + (9.6 - 8.09)² + (7.7 - 8.09)² + (8.1 - 8.09)² + (6.8 - 8.09)² + (7.5 - 8.09)² + (8.6 - 8.09)² + (8 - 8.09)² + (7.8 - 8.09)² + (7.4 - 8.09)² + (8.4 - 8.09)² + (8.9 - 8.09)² + (8.5 - 8.09)² + (9.4 - 8.09)² + (6.9 - 8.09)² + (7.7 - 8.09)² / (18 - 1)]σ = 0.761
Now, we need to find the Z α/2 value from the standard normal distribution table.
Z α/2 = 1.645 (for 90% confidence level)Putting the values in the formula,Confidence interval =
X ± Z α/2(σ/√n)
= 8.09 ± 1.645(0.761/√18)
= 8.09 ± 0.511
= (8.09 - 0.511, 8.09 + 0.511)
= (7.58, 8.60).
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Answer?
I 3 sum of Σ ? n=1 4 What is the sum of 04 03 01 02 O The series diverges.
The sum of the series Σ(n = 1 to 4) n is 10.
We have,
The concept used to find the sum of the series Σ(n=1 to 4) n is called summation or addition.
In mathematics, summation is a way to express the total of a series of numbers.
The notation Σ (capital sigma) is used to represent summation.
It is followed by the index variable (in this case, n) which indicates the values being summed, and the range or condition under which the summation is performed (in this case, n=1 to 4).
The series Σ(n=1 to 4) n represents the sum of the numbers from 1 to 4.
The notation Σ (capital sigma) denotes the sum and the expression
(n = 1 to 4) indicates the range of values over which the sum is taken.
To find the sum, we add up all the numbers in the given range.
In this case, we have:
1 + 2 + 3 + 4 = 10.
Thus,
The sum of the series Σ(n = 1 to 4) n is 10.
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Which is greater 7500,000 m or 750 km
Step-by-step explanation:
both are equal
pls Mark brainliest
i am a factor of 40 when you pair me with 15, my lcm of 15, i am not one
The number you are is 2.
Let's break down the information provided:
You are a factor of 40 when paired with 15.
Your least common multiple (LCM) with 15 is not equal to 1.
To find the number that satisfies these conditions, let's examine the factors of 40. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. Now, we need to find a number from this list that is a factor of 40 when paired with 15.
To find the LCM of 15 and each factor of 40, we can compare their multiples:
For 15 and 1: LCM = 15
For 15 and 2: LCM = 30
For 15 and 4: LCM = 60
For 15 and 5: LCM = 15 (already the smaller number)
For 15 and 8: LCM = 120
For 15 and 10: LCM = 30 (already the smaller number)
For 15 and 20: LCM = 60 (already the smaller number)
For 15 and 40: LCM = 120 (already the smaller number)
From the list, we can see that the LCM of 15 with 5, 10, 20, and 40 is equal to 15. However, the problem states that the LCM of 15 with the number is not equal to 1. Thus, the number that satisfies both conditions is 2, as the LCM of 15 and 2 is 30, and it is not equal to 1. Therefore, the number you are is 2.
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MSL7
Dificuit Dimensions
A tool box has the dimensions of 8 in by 7 in by 4 in. If Jacob plans to double all three
dimensions to build a larger tool box, he believes he would double the volume of the tool box,
Is he correct?
Jenica bowls three games and scores an average of 116 points per game. She scores 105 on her first game and 128 on her second game. What does she need to score on her third game to get a mean score of ?
Answer:
230
Step-by-step explanation:230
what is the inverses operation needed to solve for P?
800=p-275
A subtraction
B addition
C multiplication
D division ill mark brainlist
A car drove 5 miles in 30 minutes. How far will the car go in 1 hour?
Answer: 10 miles
Step-by-step explanation:
Practically, just look at it. 30 minutes = 5 miles, 60 minutes = 10 miles
Mathmatically, find the constant of proportionality.
30 minutes divided by 5 miles = 6 minutes per 1 mile. 60 minutes = 10 miles
the circumference of a circle is 64π. what is the radius of the circle?
The radius of the circle can be found by dividing the circumference by 2π. In this case, the radius is 32.
The formula for the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 64π.
To find the radius, we can rearrange the formula as r = C / (2π). Substituting the given value of the circumference, we have r = 64π / (2π) = 32.
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Find the distance between the points (–7,–9) and (–2,4).
Answer:
√194 or 13.9
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√[-2 - (-7)² + [4 - (-9)]
√(5)² + (13)²
√25 + 169
√194
= 13.9
algebra 1 student journal 5.2 puzzle time did you hear about the pug that built himself a home
No, I haven't heard about the pug that built himself a home. Could you please provide more information or context about the puzzle in Algebra 1 Student Journal 5.2? I'll do my best to assist you with it.
Did you hear about the pug that built himself a home?" is more of a riddle or a joke rather than a puzzle from an Algebra 1 Student Journal. It doesn't appear to be directly related to an algebraic problem or concept.
If you have any specific algebraic problems or questions from the Algebra 1 Student Journal, please let me know, and I'll be happy to assist you with them.
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Just give me some ideas for this please.
Using what you know about fair and unfair games, as well as expected value, design a game that will be fair to both you and the player. Be creative in your design, trying not to mimic anything that you have already seen in this course or in searching the internet. Include a thorough description as well as a visual representation of the game that includes evidence of fairness.
Answer:
For game ideas, try to make a game that everyone will want to play. Make it fun, challenging, but still beatable, but not too easy. One thing you could do is a trivia game! With lots of different subjects so people can choose what they get questions about. Also, do a lot of research to get the questions! Hope this helped :)
Step-by-step explanation:
Answer:
KING OF QUESTIONS!!!
Step-by-step explanation:
Each player starts out with 10 tokens ( tokens can be anything I recommend spare change or coins. ) the tokens will be used as point tallies at the end of the game. But to determine who goes first the question master asks a question from the starting deck( The easiest questions) and starting with player one the players answer and whoever answers with the correct answer will go first, the other players will form an orderly line from closest to the correct answer to farthest. ( If there are more than 1 successful answers you pull another card from the next deck. This is an increase in difficulty. And it will keep increasing until there is one person with the correct or closest answer or until they reach the end of the final deck. Remember that this event is highly unlikely) After this is done the game begins. The question master asks a question the players will answer. The players that get it correct will receive 2 token. The players that do not but are close get 1 and the player to get the farthest from the correct answer loses 1 token. ( Tokens are worth 1 point.)
Roles:
Player 1 ( Answers the questions.)
Player 2 ( Answers the questions.)
Player 3 ( Answers the questions.)
Player 4 ( Answers the questions.)
Question Master & Token Master ( Asks the questions and gives the token to the correct answer. )
How to Win:
Quick Match- Play until a player reaches 30 tokens.
Long Match- Play until all but one player is eliminated.
Ways to Lose- If a player loses all of there tokens or is cheating they are eliminated, this happens only when the player is caught cheating or stealing tokens from other players or when the player loses all of these tokens due to incorrect answers.
why does the quadratic formula work all the time
the quadratic formula work all the time because it is suitable for every equation.
Use The Figure Below to Solve For x.
Answer:
x=-1
Step-by-step explanation:
Hello there!
The information we are given:
We are told that the distance from point a to c is x + 10
We are told that the distance from a to b is 5
we are also told that the distance from b to c is 2x+6
Because from point A to B and B to C is inside the total of A to C we can add the two together and create a equation to solve for x
so the sum of the two parts 5 + 2x + 6
*combine like terms*
11 + 2x
is equal to the total distance (x+10)
now we solve for x
11 + 2x = x + 10
step 1 subtract x from each side by
2x - x = x
x -x cancels out
now we have 11 + x = 10
step 2 subtract 11 from each side
11-11 cancels out
10 - 11 = -1
we're left with x = -1
Now lets plug in x and see if A to C is equal to A to B + B to C
(-1) + 10 = 5 + 2(-1) + 6
10 - 1= 9
2*-1=-2
6-2=4
4+5=9
9=9
which is true so we can conclude that x = -1