Hello i would really appreciate it if you help!

The general solution to the homogeneous system of differential equations is:

x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |

                                                        |-1 |

where c₁ and c₂ are constants.

To find the general solution to the homogeneous system of differential equations -11x' = Ax, where A = [-26 4; 1 1], we first need to find the eigenvalues and eigenvectors of matrix A.

To find the eigenvalues, we solve the characteristic equation:

det(A - λI) = 0

Substituting the values, we get:

| -26-λ 4 |

| 1 1-λ |

Expanding the determinant, we have:

(-26-λ)(1-λ) - 4 = 0

Simplifying and solving the equation, we find the eigenvalues:

λ₁ = -7

λ₂ = -20

Next, let's find the corresponding eigenvectors.

For λ₁ = -7:

(A + 7I)v₁ = 0

| -19 4 |

| 1 8 |

Solving the system of equations, we find the eigenvector corresponding to λ₁:

v₁ = | 4 |

      |-1 |

For λ₂ = -20:

(A + 20I)v₂ = 0

| -6 4 |

| 1 21 |

Solving the system of equations, we find the eigenvector corresponding to λ₂:

v₂ = | 2 |

      |-1 |

Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:

Substituting the values of the eigenvalues and eigenvectors, we get:

x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |

                                                        |-1 |

Simplifying this expression, we get:

x(t) = | 4c₁ * [tex]e^{(-7t)[/tex] + 2c₂ * [tex]e^{(-20t)[/tex] |

|-c₁ * [tex]e^{(-7t)[/tex] - c₂ * [tex]e^{(-20t)[/tex]) |

Therefore, the general solution to the homogeneous system of differential equations is:

x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |

|-1 |

where c₁ and c₂ are constants.

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Step-by-step explanation:

The line JK is tangent to the circle h so <KJH is a right angle.

[tex]a^2+b^2=c^2[/tex]

[tex]15^2+20^2=x^2[/tex]

[tex]625=x^2\\x=25[/tex]

Hope that helps :)

Answer:

12 units²

Step-by-step explanation:

The height is 2, and the width is 12.

Now multiply and that gives us 24. But that's not the full answer.

Since a triangle's area is half of a square, we divide by 2, leaving us with 12. (plus the label which is units²)

9514 1404 393

Answer:

  17.8 cm²

Step-by-step explanation:

The ratio of surface areas is the square of the ratio of the linear dimensions. The small/large linear dimension ratio is 2/5, so the surface area of the smaller cone is ...

  A = (2/5)²(111 cm²) = 17.76 cm²

The area of the smaller cone is about 17.8 cm².

Answer:  [tex]17.8 cm^{2}[/tex]

Answer:

84.82

Step-by-step explanation:

π·32·3≈84.823

Answer:

The volume of a cylinder with a height of 3 and a radius of 3 is 84.823 or you could say 84.8.

Step-by-step explanation:

The solution of the integral (1/6)ln|9x²+1| +(1/3)arctan (3x) +(1/6)arctan((3x)²)- (1/18)(3x)²/(9x²+1) + (1/90)(3x)⁴/(9x²+1) + C.

We have the following integral to solve.∫ [(1+cos(arctan (3x))+(arctan (3x))⁵)/(1+9x²2)]dx

Let's begin by using the substitution u = arctan(3x).

We need to convert this integral into a U-form. By substituting the above expression, we have the following new expression.

∫ [(1+cos u)+u⁵]/[1+9(3tanu)²] *(1/3) du=∫ [(1+cos u)+u⁵]/(9tan²u+1) *(1/3) du

Let's now consider the numerator.

We have 1+cosu+u⁵ in the numerator. Let's break down the integral into 3 parts. The first part is ∫(1)/(9tan²u+1) *(1/3) du.

We can convert the denominator to a perfect square of the form 3²tan²u+1 which simplifies to (3tanu+1)(3tanu-1)+2.

Let's now factorize

= ∫(1)/(9tan²u+1) *(1/3) du

=∫(1)/[(3tanu+1)(3tanu-1)+2] *(1/3) du

Now let's perform partial fraction decomposition. We have 1/[(3tanu+1)(3tanu-1)+2] which we can write as

= A/(3tanu+1)+B/(3tanu-1)+C/(3tan²u+1) where A, B, and C are constants to be determined.

We now have 1= A(3tanu-1)(3tan²u+1)+ B(3tanu+1)(3tan²u+1)+ C(3tanu+1)(3tanu-1).

Let's now set up the system of equations.

The first equation is

1= A(3tanu-1)(3tan²u+1)+ B(3tanu+1)(3tan²u+1)+ C(3tanu+1)(3tanu-1)

Putting u=0, we get

A = 1/4

Putting u =pi/3, we get

B=1/4 Putting

u = arctan(1/√(3)), we get C=1/2. Now that we have A, B, and C, let's substitute them back to our integral.

We have

= ∫(1)/[(3tanu+1)(3tanu-1)+2] *(1/3) du

= (1/4)∫(1)/(3tanu+1) du + (1/4)∫(1)/(3tanu-1) du +(1/2)∫(1)/(3tan²u+1) du

Let's now solve the integral and simplify.

= ∫(1)/(3tanu+1) du

= (1/6)ln|3tanu+1|- (1/6)ln|3tanu-1|+ (1/3)arctan (3tanu).

Similarly,

= ∫(1)/(3tanu-1) du

= (-1/6)ln|3tanu+1|+ (1/6)ln|3tanu-1|+ (1/3)arctan (3tanu).

The third integral we can solve by substitution

v = √(3)tanu.

We then get

=  ∫(1)/(3tan²u+1) du= (1/√(3))∫(1)/(v²+3) dv

= (1/sqrt(3))arctan(v/√(3))

= (1/√(3))arctan((√(3)tanu)/√(3)).

We can now put back all the values to get the solution.

= ∫ [(1+cos(arctan (3x))+(arctan (3x))⁵)/(1+9x²)]dx

= (1/3)∫ [(1+cos u)+u⁵]/(9tan²u+1) du

=(1/3)[(1/4)(ln|3tanu+1|- ln|3tanu-1|+ 2arctan (3tanu))+(1/4)(-ln|3tanu+1|+ ln|3tanu-1|+ 2arctan (3tanu))+(1/2)(1/√(3))(arctan((sqrt(3)tanu)/√(3)))]+ C

We can simplify the above expression to get

=- ∫ [(1+cos(arctan (3x))+(arctan (3x))^5)/(1+9x²)]dx

= (1/6)ln|9x²+1| +(1/3)arctan (3x) +(1/6)arctan((3x)²)- (1/18)(3x)²/(9x²+1) + (1/90)(3x)⁴/(9x²+1) + C

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The volume of 40 of the concrete slabs given the dimensions of one  concrete slab is 384 yd³.

The concrete slab has the shape of a rectangular prism. So, the volume of a rectangular prism would be used to determine the volume of the  concrete slabs.

Volume of one  concrete slab = length x width x height

4 x 2 x 1.2 = 9.6 yd³

Volume of 40  concrete slabs = 40 x 9.6 = 384 yd³

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Answer:

Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume. SOO just remember to divide the diameter by two to get the radius. If you were asked to find the radius instead of the diameter, you would simply divide 7 feet by 2 because the radius is one-half the measure of the diameter. The radius of the circle is 3.5 feet. You can also use the circumference and radius equation.

Step-by-step explanation:

brainliest?

Answer:

6.58

Step-by-step explanation:

ahahahaha lol

Answer:

6.58

i hope this helps:)

Step-by-step explanation:

brainliest please?

Answer:

Blank 1: 6

Blank 2: 30

1/2 = 6/12 = 30/60

Blank 3: 30

1/4 = 3/12 = 15/60

Answer:

a and c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: not sure

Step-by-step explanation:

Answer:

684 π

Step-by-step explanation:

volume of a sphere = (4/3) x (n) x (r^3)

n = 22/7

r = radius

volume of larger sphere

4/3 x n x 9³ = 972 n

4/3 x n x 6³ =288n

972n - 288n = 684n

Answer:

x= 28

do i have to explain

Step-by-step explanation:

Answer:

the distance between the two points is √130.

Step-by-step explanation:

a^2 + b^2 = c^2

a^2 = 9^2 = 81

b^2 = 7^2 = 49

c^2 = 81 + 49 = 130

c = √130

Answer:

$24.45

Step-by-step explanation:

6.65 + 4 + 7.15 + 6.65 = 24.45

Answer:

20 is the greatest common denominator. You can find this by listing the factors of each number. The highest number that can fit into both individual numbers is the common denominator. Since 40 is just 20 doubled, and 20 is just 20 once, it fits into both numbers and is also the highest number that can fit.

Answer:

if im corect the anwser is 3.14 (Side note) this is the wrong question i was anwsering to

Answer:

1. 61

2. -8

3. 731

4. -16

5. -5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The arithmetic sequence usually write as [tex]a_{n}=a_{1} +(n-1)d[/tex], where a1 is the first term and d is a common difference.

[tex]a_{n} = a_{1}+(n-1)d\\a_{n} = 0+(n-1)0.5\\[/tex]

Answer: AB = 15 because sides AB and AD are congruent

Step-by-step explanation:

The analysis involves calculating probabilities, bounding the probabilities based on worst-case scenarios, and considering the implications of the Chernoff bound to demonstrate the existence of tournaments without a certain number of winners.

In a tournament between N teams, where each team plays each other, the concept of a k-winner is introduced. A team i is considered a k-winner if there is a group of k teams that were each beaten by team i. The probability that a given team i is a k-winner can be calculated when the results of each game are decided by a fair coin flip. This probability depends on the number of teams and the specific value of k.

Using this probability for a given team, we can bound the probability that there exists a k-winner in a tournament of size N. This bound takes into account the probabilities of individual teams being k-winners and considers the worst-case scenario.

For a specific value of N, such as N = 100, we can determine the smallest k for which the probability of having k-winners is less than 1. This can be done by evaluating the probabilities for different values of k until the desired condition is met.

When N = 100 and k is determined as in the previous step, it can be argued that there exist possible tournaments with no k-winners. This can be demonstrated by constructing specific scenarios or by analyzing the probabilities of different outcomes.

Using the Chernoff bound, it can be shown that for a value a greater than 1/2, the probability of having any oN-winners (where oN is an arbitrary constant) goes to 0 as N approaches infinity. This conclusion implies that there exist tournaments without N-winners for sufficiently large values of N.

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Answer:

40

where the line starts (75) and ends (115)

115-75=40

thats the quick way to solve... hope this helps!

Step-by-step explanation:

Brainliest?

Answer:

11.2 minutes

Step-by-step explanation:

If the element decreases by 6.1, every minute, it means that the mass lost every minute = 0.061 x 700g = 42.7g

The mass remaining after a minute = 657.30g

The equation that can be used to solve this question is :

700 - 42.7m = 220

m = minutes

Collect like terms

700 - 220 = 42.7m

480 = 42.7m

divide both sides of the equation by 42.7

m = 11.241218 minutes

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

Here, the hundredth is less than 5, so zero would be added to 2. the answer is 11.2 minutes

Answer:

18.4

Step-by-step explanation:

I answered the question

Answer:

t = 12.6

Step-by-step explanation:

8.4 x 1.5 = 12.6

to check it, do 12.6 ÷ 1.5 = 8.4

Answer: The runner will sprint 4,200 inches during this week

Step-by-step explanation:

50 * 7 = 350

350 * 12 = 4200

Answer:

It's 4200in

in feets its 350ft

Step-by-step explanation:

Answer:

https://brainly.com/question/13518166

Step-by-step explanation:

Answer:

-0.9

Step-by-step explanation:

Answer:

x =-.9

Step-by-step explanation:

x-4.88=-5.78

Add 4.88 to each side

x-4.88+4.88=-5.78+4.88

x =-.9