Solve for X:
10/3=x/-5/2

Answer:

Step-by-step explanation:

the answer would be 73 since the angle is split in half which means that they are both equal to each other

The system of linear differential equations is homogeneous and the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

Given the system of linear differential equations can be put in the form (A - λI)X = 0, where λ and X are the eigenvalue and eigenvector of the matrix A, respectively. Determine λ and X and determine whether the system is homogeneous or non-homogeneous. Choose the largest interval such that a unique solution of the initial value problem is guaranteed to exist.For the given system of linear differential equations:

dx/dt = 4x + 6y

dy/dt = -2x - 4y

the matrix A is given by:

 [4   6 ][-2 -4 ]

The eigenvalue λ can be found from the characteristic equation det(A - λI) = 0 as follows:

[4 - λ   6    ][-2    -4 - λ] = 0λ² - λ - 8 = 0

Solving the above equation, we get, λ = -1 and λ = 8.

Therefore, λ1 = -1 and λ2 = 8 are the eigenvalues of matrix A.

To find the eigenvectors, we solve the equation (A - λI)X = 0 for each λ separately.

For λ1 = -1, we get[A - (-1)I]X = 0

⇒[5   6 ][x    ] = 0[-2   -3][y    ]      [x    ][-2y  ]

Therefore, the eigenvector corresponding to

λ1 = -1 is

X1 = [x y]T = [2 -1]T.

For λ2 = 8, we get

[A - 8I]X = 0⇒[-4   6 ][x    ]

= 0[-2  -12][y    ]  [x    ][3y   ]

Therefore, the eigenvector corresponding to

λ2 = 8 is

X2 = [x y]T = [3 1/2]T.

The given system of linear differential equations can be written in the matrix form as

dX/dt = AX,

where A is the matrix [4 6][-2 -4] and X is the column vector [x y]T.

The general solution of this system is given by

X(t) = c1 e^(λ1t)X1 + c2 e^(λ2t)X2,

where c1 and c2 are constants of integration and X1 and X2 are the eigenvectors corresponding to the eigenvalues λ1 and λ2, respectively. Therefore, the general solution of the given system is given by

x(t) = 2c1 e^(-t) + 3/2 c2 e^(8t)y(t)

= -c1 e^(-t) + 1/2 c2 e^(8t)

where c1 and c2 are constants of integration to be determined from the initial conditions. Since the system of differential equations is homogeneous, the trivial solution x(t) = y(t) = 0 is a solution of the system. Hence, the system is homogeneous.

The given initial value problem has initial conditions x(0) = 1 and y(0) = 0.

Therefore, we have

c1 + 3/2 c2 = 1 and

-c1 + 1/2 c2 = 0

Solving these two equations, we get c1 = 1/5 and c2 = 2/5.

Therefore, the particular solution of the given initial value problem is given by

x(t) = (2/5) e^(-t) + (6/5) e^(8t)y(t)

= -(1/5) e^(-t) + (1/5) e^(8t)

Hence, the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

The system of linear differential equations is homogeneous and the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

To know more about differential equations visit:

https://brainly.com/question/32645495

#SPJ11

Answer:

Number = 12

Step-by-step explanation:

2n-7=n+5 (+7 to both sides)

2n=n+12 (-n to both sides)

n=12

Answer:

Answer would be 12

Step-by-step explanation:

i'm not always accurate but your welcome!

When diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

Step 1: Create an equation that connects a sphere's volume to radius as the first step.

V = 4/3*π*r³

Step 2: Calculate each side's derivative in respect to time (Let the time be "t").

(d/dt)V = (d/dt)(4/3*π*r³)

dV/dt = 4πr²*dr/dt

Step 3: The problem description informs us that the diameter is 600 m, hence r must be 30 mm.

Additionally, it is stated that now the radius of a sphere is expanding at a rate of 2 mm/s; as a result, dr/dt must equal 2 mm/s.

We are interested in dV/dt, or the rate of change of the sphere's volume.

dV/dt = 4π(30mm)²*(2mm/s)

dV/dt = 22,620 mm³/s

So, when diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

To know more about the volume change, here

https://brainly.com/question/25736513

#SPJ4

Answer:

A

Step-by-step explanation:

Pick any two sides....their sum must be greater than the third side....

  a+b > c

  a+c > b

  c + b > a

The words savage and savory are neither similar nor contradictory.

Contradiction is a term used to indicate mutually opposite things. It is commonly used in statements where both the statements cannot be true.

Savage is a word the meaning of which is wild or non cultivated in a context as an adjective. In another context, savage can be used as a noun to define an uncivilized or a brutal human.

On the other hand, savory is a completely different term which is used to define the taste of the dishes, typically in a positive way.

Hence the terms savage and savory are neither similar nor contradictory words.

To learn more about Contradictions, click:

https://brainly.com/question/445700

#SPJ1

The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

Learn more about angles at:

https://brainly.com/question/25716982

#SPJ1

Answer:

Eagle Ridge 2 Times

Black Bear 1 time and Doe Run 2 Times

Eagle Ridge 1 time and Doe Run 1 time

B,D,E

Step-by-step explanation:

Took a test 100%

Answer: D. Law Of Cosines

Step-by-step explanation: A law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

Note: Answer is confirmed by Buzz/Acceleration Education.

All My Other Answers:

https://brainly.com/app/profile/13253466/answers

The sum of the interior angle of the triangle is 180 degrees. Then by the sine rule, angle E can be determined. Then the correct option is A.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

For triangle DEF, the length of side e and the measures of angles D and F are known.

We know that the sum of the interior angle of the triangle is 180 degrees. Then the angle E can be determined.

Hence the sine rule is easy to apply.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ2

The statement is true. If the row [0 0 0 1 0] is in echelon form of an augmented matrix, then the associated linear system is always consistent. This means there is at least one solution to the system of linear equations.

Echelon form is a type of row-echelon form that has specific properties. In echelon form, the leading coefficient (non-zero element) of each row is strictly to the right of the leading coefficient of the row above it. In the given row [0 0 0 1 0], the leading coefficient is 1, and it is the only non-zero element in the row.

In an augmented matrix, the rightmost column represents the constants or the right-hand side of the linear equations. Since the leading coefficient in the given row is 1 and there are no non-zero elements to the left of it, this implies that the associated linear equation is of the form 0x + 0y + 0z + w = 0. This equation simplifies to w = 0.

Since w is a free variable and its value can be chosen as 0, the linear system is consistent. Every consistent system has at least one solution, and in this case, the solution is when w = 0, while x, y, and z can take any values.

Therefore, if [0 0 0 1 0] is one row in an echelon form of an augmented matrix, the associated linear system is always consistent.

Learn more about echelon form here: brainly.com/question/28767094

#SPJ11

Answer:

10 meters

Step-by-step explanation:

Area of a square is represented by the following formula:

A= s²

Plug in your area and solve.

√100 m² =√ s² (square both side)

10 m² = s

Thus, your one side length is 10

Using mathematical operations, Betsie should buy the 250 envelopes from Letters2go Shop at a total cost of £319.

To determine the total cost, we first determine the unit cost of an envelope at each shop.

The unit cost is multiplied by the number of envelopes required less the cost of free envelopes at Value World.

The mathematical operations used include division and multiplication.

Deals:

Letters2go

Pack of 25 envelopes for £3.19

Value World

Pack of 10 envelopes for £1.99

Buy 2 packs get 1 pack free

                                              Letters2go         Value World

Cost per pack                           £3.19                     £1.99

Cost per envelope                   £0.1276                £0.199

The number of envelopes         250                     250

The number of packs                 10 (250/25)        25 (250/10)

Cost of free envelopes                                         £24.875 (25/2 x £1.99)

Total cost of envelopes        £319 (£3.19 x 10)    £472.63 (£1.99 x 250 - $24.875)                    

Thus, using mathematical operations, the total cost of 250 envelopes at Letter2go is less than the total cost at Value World.

Learn more about mathematical operations at https://brainly.com/question/20628271

#SPJ1

Given:

Equation of Curve is:

To find: Equation of tangent to the curve at point

Equation of tangent to the curve is given by:

where, m is slope of line.

Now, m is derivative of y with respect to x at given point.

Hence,

At given point, the slope m is:

Therefore,the equation of tangent to the curve is given as:

Thus the required equation of tangent to the curve is

Answer:  w = 30

Step-by-step explanation: A triangle is 180 degrees, always. One angle is 60 and the other above is 90. We add them together and get 150. Subtract it from 180 and we get 30 degrees.

P.S.: I'm sorry that I put only w, that's the only one I could work out . Also sorry if I'm wrong, maths is not my very strong subject.

Since the given line equation describes one of the parallel lines, we can determine the equation of the other parallel line by keeping the same slope but choosing a different y-intercept.

Given line equation:

y = (1/4)x - 1/2

To keep the same slope, we use the same coefficient of x, which is 1/4. Now, we can select a different y-intercept, let's say b.

The equation of the other parallel line can be represented as:

y = (1/4)x + b

In this equation, the only difference from the given line equation is the y-intercept, which we denoted as b. The value of b can be any real number, as long as it differs from -1/2 (the y-intercept of the given line).

Therefore, the equation of the other parallel line can be written as y = (1/4)x + b, where b can be any real number except -1/2.

Learn more about equation here:

https://brainly.com/question/29538993

#SPJ11

Answer:

2.Ellipse

Step-by-step explanation:

The given equation represents an ellipse.

Standard form of ellipse is given as:

\( \frac{x^2}{a^2} +\frac{y^2}{b^2} = 1\\\\

\implies \frac{x^2}{16} - \frac{y^2}{4} = 1\\\)

Answer:

it would be In 17 hours

Step-by-step explanation:

let me know if I am wrong or right thxs

Answer:

4 4/17 hours

Step-by-step explanation:

In one hour Jacob can paint 1/9 of the fence

In one hour Molly can paint 1/8 of the fence

This equation can determine how long it would take if they worked together:

1/9x + 1/8x = 1

multiply each term by lcm of 72 to eliminate denominators to get:

8x + 9x = 72

17x = 72

x = 72/17

x = 4 4/17 hours

Answer:

30.67

Step-by-step explanation:

Given the following

Opposite side = x

Adjacent = 17

Angle = 61degrees

Using the SOH  CAH TOA identity

tan theta = opp/adj

tan 61 = x/17

x = 17tan61

x = 17(1.8040)

x = 30.67

Hence the value of x is 30.67

The absolute maximum of the function f(x, y) = xy + 1 subject to the constraint x² + y² ≤ 1 is √2, and the absolute minimum is -√2.

To find the absolute maximum and minimum of a function subject to a constraint using the method of Lagrange multipliers, we need to consider the Lagrange function L(x, y, λ) = f(x, y) - λ(g(x, y) - c), where f(x, y) is the given function, g(x, y) is the constraint, λ is the Lagrange multiplier, and c is the constant associated with the constraint.

In this case, the given function is f(x, y) = xy + 1, and the constraint is x² + y² ≤ 1. We can rewrite the constraint as g(x, y) = x² + y² - 1 = 0.

Now, we need to find the critical points by taking the partial derivatives of the Lagrange function with respect to x, y, and λ and setting them equal to zero:

∂L/∂x = y - 2λx = 0

∂L/∂y = x - 2λy = 0

∂L/∂λ = -(x² + y² - 1) = 0

Solving these equations simultaneously, we obtain three possibilities:

1. If λ = 0, then y - 2λx = 0 and x - 2λy = 0 become y = 0 and x = 0, respectively. However, this does not satisfy the constraint x² + y² ≤ 1.

2. If x = 0, then y - 2λx = 0 and -(x² + y² - 1) = 0 simplify to y = 0 and y² = 1. This gives us two solutions: (0, 1) and (0, -1). Evaluating the function f(x, y) = xy + 1 at these points, we find f(0, 1) = 1 and f(0, -1) = -1.

3. If y = 0, then x - 2λy = 0 and -(x² + y² - 1) = 0 simplify to x = 0 and x² = 1. This gives us two solutions: (1, 0) and (-1, 0). Evaluating the function f(x, y) = xy + 1 at these points, we find f(1, 0) = 1 and f(-1, 0) = -1.

Now, we need to consider the boundary of the constraint, x² + y² = 1. To do this, we can parameterize the circle by letting x = cosθ and y = sinθ, where 0 ≤ θ ≤ 2π. Substituting these into the function f(x, y) = xy + 1, we have f(θ) = cosθsinθ + 1 = 0.5sin(2θ) + 1.

Taking the derivative of f(θ) with respect to θ, we have f'(θ) = cos(2θ). Setting f'(θ) = 0, we find θ = π/4 and θ = 5π/4 as critical points. Evaluating f(θ) at these points, we get f(π/4) = √2 and f(5π/4) = -√2.

Comparing all the values we obtained, we find that the absolute maximum is √2, and the absolute minimum is -√2.

Learn more about constraint

brainly.com/question/17156848

#SPJ11

Answer:

0.976 or 97.6%

Step-by-step explanation:

To calculate the frequency of the recessive allele, we need to use the information provided about the frequency of the dominant trait.

Let's assume that the particular dominant trait is determined by a single gene with two alleles: the dominant allele (A) and the recessive allele (a).

Given that 45 out of 1,000 babies are born with the dominant trait, we can infer that the remaining babies (1,000 - 45 = 955) do not have the dominant trait and can be considered as the recessive trait carriers.

The frequency of the recessive allele (q) can be calculated using the Hardy-Weinberg equation:

q = sqrt((Recessive individuals) / (Total individuals))

In this case, the total number of individuals is 1,000, and the number of recessive individuals is 955.

q = sqrt(955 / 1,000)

Using a calculator, we can find the value:

q ≈ 0.976

Therefore, the frequency of the recessive allele is approximately 0.976 or 97.6%.

Answer:

130

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

80x.90= 72

Answer:

72 is your answer

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

2 x 7 = 14

Number should be in between 26 and 31

So,

14 x 2 = 28

28 has one of its prime factors as 2 and 7.

Hence,

28 is the number which is in between 26 and 31 it has the prime factors of 2 and 7.

Answer:

Step-by-step explanation: Given prime factors: 2, 7

 By multiplying, 2 X 7= 14

 Given, number is between 26 and 31

       therefore, 14 X 2= 28 (since 2 is a prime factor)

        ans: 28

Alvin's total payment to the store if the donations wasn't taxed is $54.18.

Cost of shirts = $12.50

Cost of pants = $27

Cost of socks = $6.25

Donation to charity = $5

Tax = 7.5%

Total = $12.50 + $27 + $6.25

= $45.75

Total payment = $45.75 + (0.075 ×45.75) + 5

= $54.18125

Hence, the total payment Alvin made to the store is $54.18

Read more on tax:

https://brainly.com/question/25783927

#SPJ1

Answer: 68 mph

Step-by-step explanation:

Given the expression:

We use the distributive property for -1:

Now, we factorize x:

The coordinates of P'Q'R'S' and P"Q"R"S" are P'(-2, 3), Q'(1, 3), R'(1, 1) ,S'(-2, 1) and P''(-6, 1), Q''(-3, 1), R''(-3, -1), S''(-6, -1).

A dilation is a transformation that yields a picture that differs in size while maintaining the original image's shape

The coordinates of the rectangle are P(-6,9), Q(3,9), R(3,3), and S(-6,3).

To find the coordinates of the rectangle after the dilation by a scale factor of 1/3, multiply each coordinate of the original rectangle by 1/3:

P'(-6/3, 9/3), Q'(3/3, 9/3), R'(3/3, 3/3), and S'(-6/3, 3/3)

Simplify the coordinates:

P'(-2, 3), Q'(1, 3), R'(1, 1), and S'(-2, 1)

Now, the coordinates of the rectangle P'Q'R'S' after the translation of 4 units to the left and 2 units down are:

P''(-2 - 4, 3 - 2), Q''(1-4, 3 - 2), R''(1 - 4, 1 - 2), and S''(-2 - 4, 1 - 2)

Simplify the coordinates:

P''(-6, 1), Q''(-3, 1), R''(-3, -1), and S''(-6, -1)

Hence, the coordinates of P'Q'R'S' and P"Q"R"S" are P'(-2, 3), Q'(1, 3), R'(1, 1) ,S'(-2, 1) and P''(-6, 1), Q''(-3, 1), R''(-3, -1), and S''(-6, -1).

Learn more about the dilation:

https://brainly.com/question/13176891

#SPJ1