Drag the operations signs to make the number sentence true. Use each operation sign once. +–×÷ 4 (3 2) 6 1 = 14

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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Answer:

a and c

Step-by-step explanation:

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: 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:

1. 61

2. -8

3. 731

4. -16

5. -5

Step-by-step explanation:

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:

$24.45

Step-by-step explanation:

6.65 + 4 + 7.15 + 6.65 = 24.45

Answer:

Step-by-step explanation:

Answer:

Blank 1: 6

Blank 2: 30

1/2 = 6/12 = 30/60

Blank 3: 30

1/4 = 3/12 = 15/60

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:

6.58

Step-by-step explanation:

ahahahaha lol

Answer:

6.58

i hope this helps:)

Step-by-step explanation:

brainliest please?

The property which is represented in the equation : "2 + (√6 + √4) = (2 + √6) + √4" is (a) Associative.

The "Associative-Property" is a fundamental property of addition that states that the grouping of numbers being added does not affect the sum. In other words, when adding three or more numbers, the way they are grouped does not change the result.

In the given equation : 2 + (√6 + √4) = (2 + √6) + √4, we see that the numbers (√6 + √4) and (2 + √6) are grouped differently, but the sum remains the same. This is because the associative property , which allows us to rearrange the brackets and change the grouping without affecting the final result.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

State the name of the property illustrated : 2 + (√6 + √4) = (2 + √6) + √4

(a) Associative

(b) Distributive

(c) Commutative

(d) Both associative and commutative.

Answer:

x= 28

do i have to explain

Step-by-step explanation:

Answer:

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Step-by-step explanation:

The statement that eta-squared, partial eta-squared, and R-squared are all measures of effect size that refer to the proportion of variance explained within a study. This statement is true.

In order to better understand what eta-squared, partial eta-squared, and R-squared are, we must first understand what the proportion of variance explained is. The proportion of variance explained refers to the amount of variation in one variable that is accounted for by another variable or variables. All three of these measures are measures of effect size, which means they are used to determine the strength of the relationship between two variables. They also all refer to the proportion of variance explained within a study. However, they differ in terms of how much variance they account for. Eta-squared is a measure of effect size that is used in ANOVA to determine the proportion of variance in the dependent variable that is accounted for by the independent variable. Partial eta-squared, on the other hand, is used to determine the proportion of variance that is accounted for by the independent variable when controlling for other variables.

Finally, R-squared is a measure of effect size that is used in regression analysis to determine the proportion of variance in the dependent variable that is accounted for by the independent variable.

In conclusion, all three of these measures of effect size are used to determine the proportion of variance explained within a study.

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Answer: not sure

Step-by-step explanation:

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:

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)

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:

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 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:

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:

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

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:

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:

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 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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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