In the accompanying diagram of triangle ABC , D is a point on AC , AB is extended to E, and DE is drawn so that triangle ADE~ triangle ABC . If m

Step-by-step explanation:

both are equal

pls Mark brainliest

(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.

Know more about differential equation:

https://brainly.com/question/32538700

#SPJ11

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

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

Answer:

the actual answer is 3,240 is the answer

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.

To learn more about Fourier transform visit : https://brainly.com/question/28984681

#SPJ11

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

Answer:

4 right angles

Step-by-step explanation:

a straight light intersects  another straight line= creating 4 right angles

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).

To know more about confidence interval :

https://brainly.com/question/32546207

#SPJ11

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.

Answer:

The area of the parallelogram is 20cm²

Answer:

A = 20 cm²

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the height ) , then

A = 5 × 4 = 20 cm²

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]

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

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.

Learn more about the sum of the series here:

https://brainly.com/question/31774665

#SPJ4

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.

To know more about Algebra:- https://brainly.com/question/27895575

#SPJ11

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

the quadratic formula work all the time because it is suitable for every equation.

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.

i: 1

ii: 6

iii: 3

iv: 2

v: 4.5

vi: 2.5

Answer:

230

Step-by-step explanation:230

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.

Answer: p+(-q)

Step-by-step explanation:

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.

To learn more about  circumference

brainly.com/question/28757341

#SPJ11

Answer:

120 degrees

Step-by-step explanation:

im a god cuz happppy

Answer:

120 lol

Step-by-step explanation:

Answer:

B. 0

Step-by-step explanation:

There aren't enough sides for you to roll a nine

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