I kinda need help. Math isn't my best subject.

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow these steps:

Calculate the characteristic equation by subtracting the identity matrix I multiplied by the scalar λ from matrix A, and set the determinant of this resulting matrix equal to zero. The characteristic equation is given by det(A - λI) = 0.Solve the characteristic equation to find the eigenvalues (λ).

Let's assume we have a 2x2 matrix A:

  | a  b |

A = | c d |

To find the eigenvalues, we need to calculate the characteristic equation:

det(A - λI) = 0,

where I is the 2x2 identity matrix and λ is the eigenvalue.

A - λI = | a-λ b |

| c d-λ |

The determinant of this matrix is:

(a-λ)(d-λ) - bc = 0,

which simplifies to:

λ² - (a+d)λ + (ad - bc) = 0.

This quadratic equation gives us the eigenvalues.

Solve the quadratic equation to find the values of λ. The solutions will be the eigenvalues.

Once you have the eigenvalues, substitute each value back into the equation (A - λI)v = 0 and solve for v to find the corresponding eigenvectors.

For each eigenvalue, set up the homogeneous system of equations:

(A - λI)v = 0,

where v is the eigenvector.

Solve this system of equations to find the eigenvectors corresponding to each eigenvalue.

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow the steps mentioned above. The characteristic equation gives the eigenvalues, and by solving the corresponding homogeneous system of equations, you can determine the eigenvectors.

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Answer:

95°

Step-by-step explanation:

Here we have angles of 30° and 55°, so the remaining angle is:

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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E, D, and A.

well because it can be divide my 5.

\(\\ \rm\longmapsto (a-b)\sqrt{a-b}\)

\(\\ \rm\longmapsto (a-b)(a-b)^{\frac{1}{2}}\)

\(\\ \rm\longmapsto (a-b)^{1+\dfrac{1}{2}}\)

\(\\ \rm\longmapsto (a-b)^{\dfrac{3}{2}}\)

Answer:

\(\dashrightarrow \: { \tt{(a - b) \sqrt{a - b} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{1} {(a - b)}^{ \frac{1}{2} } }}\)

• from law of indices:

\({ \boxed{ \rm{ ({x}^{n} )( {x}^{m} ) = {x}^{(n + m)} }}}\)

therefore:

\(\dashrightarrow \: { \tt{ {(a - b)}^{(1 + \frac{1}{2} )} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{ \frac{3}{2} } }}\)

The angle of elevation of the point T on the top of the pole from the point A on the level ground, obtained using Pythagorean Theorem and the relationship between similar triangles is about 39.3°.

Similar triangles are triangles that have the same shape (the sizes may be different) and in which the ratio of the corresponding sides are equivalent.

The triangles ΔXBA, ΔXAC, and ΔABC are right triangles, such that the angles, ∠ABX in triangle ΔXBA is congruent to triangle ∠CAX in triangle ΔXAC, and ∠ABC in ΔABC.

The 90° angle in the right triangles are congruent (All 90° angle are congruent), therefore;

ΔXBA ~ ΔXAC ~ ΔABC by AA (Angle-Angle), similarity postulate

The length of the hypotenuse in the right triangle, ΔABC, \(\overline{BC}\), can be obtained using Pythagorean Theorem as follows;

\(\overline{BC}\)² = 14² + 25² = 821

\(\overline{BC}\) = √(821)

\(\overline{BC}\)/\(\overline{AC}\) = \(\overline{AB}\)/\(\overline{AX}\)

√(821)/25 = 14/\(\overline{AX}\)

\(\overline{AX}\) = 25 × (14/(√(821)) = 350/(√(821))

Let θ represent the angle of T from A, we get;

tan(θ) = 10/(350/(√(821)))

θ = arctan(10/(350/(√(821)))) ≈ 39.3°

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Answer:

B

Step-by-step explanation:

because all the angles add up to 180

To find the value of x and the length of the piece of carpet, we can set up an equation based on the given information.

The area of the rectangular piece of carpet is 60 square feet, and the width is 2 feet. The length is represented by (x^2 - 19) feet.

The formula for the area of a rectangle is length times width. Therefore, we have:

Length * Width = Area

(x^2 - 19) * 2 = 60

Now, we can solve this equation using the square root property.

Divide both sides of the equation by 2:

(x^2 - 19) = 60 / 2

x^2 - 19 = 30

Add 19 to both sides of the equation:

x^2 = 30 + 19

x^2 = 49

Take the square root of both sides:

√(x^2) = √49

x = ±7

Therefore, the value of x is ±7.

To find the length of the piece of carpet, we substitute the value of x back into the equation:

Length = x^2 - 19

Length = (±7)^2 - 19

Length = 49 - 19

Length = 30

The length of the piece of carpet is 30 feet.

So, the value of x is ±7, and the length of the piece of carpet is 30 feet.

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The rate of heat flow across the sphere S is 6k((4/3)πa³), where k is the constant of proportionality and a is the radius of the sphere.

To find the rate of heat flow across a sphere with radius "a" and center at the origin, we need to calculate the surface integral of the temperature gradient over the sphere.

The temperature "u" in the metal ball is proportional to the square of the distance from the center.

Let's express it as u(x, y, z) = k(x² + y² + z²), where k is the constant of proportionality.

To find the temperature gradient, we take the partial derivatives of "u" with respect to each variable:

∇u = (∂u/∂x, ∂u/∂y, ∂u/∂z) = (2kx, 2ky, 2kz)

Now, let's calculate the rate of heat flow across the sphere using the surface integral formula:

Heat flow = ∬S (∇u) · dS

Here, S represents the surface of the sphere, and dS is the differential area vector.

Since the surface of the sphere is given by the equation x² + y² + z² = a², we can express it as S = {(x, y, z) : x² + y² + z² = a²}.

To find the heat flow, we need to calculate the dot product (∇u) ·

dS and integrate it over the surface of the sphere S.

The dot product (∇u) · dS is equal to 2k(x, y, z) ·

(dS/dA), where dA is the magnitude of the differential area vector dS.

By taking the dot product, we have:

(∇u) · dS = 2k(x, y, z) · (dS/dA) = 2k(x, y, z) · (dS/dA) = 2k(x, y, z) · (dS/dA)

Now, we can use the divergence theorem to rewrite the surface integral as a volume integral:

Heat flow = ∬S (∇u) · dS = ∭V (∇ · (∇u)) dV

Since (∇ · (∇u)) is the Laplacian operator (∇²u), we can rewrite the integral as:

Heat flow = ∭V (∇²u) dV

The Laplacian of u is given by (∇^2u) = ∂²u/∂x² + ∂²u/∂y² + ∂²u/∂z².

Now, we substitute the expression for u(x, y, z) into the Laplacian:

(∇^2u) = ∂²u/∂x² + ∂²u/∂y² + ∂²u/∂z² = 2k + 2k + 2k = 6k

Finally, we integrate the Laplacian over the volume of the sphere V, which is given by V = (4/3)πa³:

Heat flow = ∭V (∇²u) dV = ∭V (6k) dV = 6k ∭V dV = 6k(V) = 6k((4/3)πa³) .

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To schedule the tasks on two machines in a way that minimizes the time for both machines to finish their tasks, we can use the "Longest Processing Time" algorithm.

1. Sort the list of times in descending order: (18, 16, 12, 8, 6).

2. Assign the tasks one by one to the machine with the currently shorter total processing time.

  Machine 1: (18) -> Total time: 18

  Machine 2: (16) -> Total time: 16

  Machine 1: (12) -> Total time: 30

  Machine 2: (8) -> Total time: 24

  Machine 1: (6) -> Total time: 36

3. The best time for both machines to finish their tasks is the maximum of the two total times: 36.

the correct answer is:

D) 35 (Incorrect)

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The shape in the figure is

A rectangle is a type of quadrilateral, which is a polygon with four sides. It is characterized by having two adjacent sides of equal length.

In addition to the equal side lengths a rectangle also has opposite sides that are parallel to each other hence a parallelogram.

other properties of rectangle

The rectangle is tilted so it is not parallel to the horizontal

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A difference of 336.49 SAT points is predicted to lead to a colgpa difference of 50.

A coefficient is a numerical value that represents the degree of association or effect of one variable on another.

(i) It makes sense for the coefficient on hsperc to be negative because as hsperc increases, there is a smaller percentage of students who perform better than the individual. Therefore, higher hsperc is associated with lower colgpa.

(ii) When hsperc = 20 and sat = 1,050, the predicted college GPA can be calculated by plugging in the values into the equation:

colgpa = 1.392 - .0135(20) + .00148(1,050) = 1.120

(iii) Holding hsperc constant, the predicted difference in college GPA for two students with SAT scores that differ by 140 points is:

∆colgpa = .00148(140) = .2072

Therefore, the predicted difference in college GPA is about .21 grade points, which can be considered a moderate difference.

(iv) To find the difference in SAT scores that leads to a predicted colgpa difference of .50, we can set up the equation as follows:

.50 = .00148(x)

where x is the difference in SAT scores. Solving for x, we get:

x = 336.49

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Answer:

-11/12 + 5/12

-11+5/12

-6/12

-1/2

Answer:

-6/12

Step-by-step explanation:

1. Change the signs. Two negatives make a positive.

     -11/12 + 5/12

2. Add them together.

     -6/12

3. Simplify

-1/2

12 times 1 and 1/2 = 18 dollars

12 for day 18 for night

12 times 15=180

18 times 7=126

180 +126=306

c is correct

Answer:

b) y

Step-by-step explanation:

joannes speed = 250/2.5 =100km/h

francois speed = 100-10 = 90km/h

after 5h, francois would have travelled 450

If the wait() and signal() semaphore operations are not executed atomically, then mutual exclusion may be violated as a wait operation atomically decrements the value associated with a semaphore.

Semaphores refers to integer variables utilized to solve the critical section problem by using two atomic operations, wait and signal that are used for process synchronization. The wait operation decreases the value of its argument S, if it is positive and if S is negative zero or negative, then no operation occurs. The signal operation increases the value of its argument S. Operation wait() and signal() must be completely atomic or else it violates the mutual exclusion. Mutual exclusion refers to the property of process synchronization which asserts that “no two processes can exist in the critical section at any given point of time”.

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The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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Answer:

1.      1 tablespoon Dijon mustard

2.     Combine six Tablespoons of cocoa powder and two Tablespoon of vegetable oil, butter or shortening

3.     2 cups of all-purpose flour, 3 teaspoons baking powder, and ½ teaspoon salt

3.      One teaspoon of dried basil leaves

4.      Combine 1 3/4 cups all-purpose flour with 1/4 cup cornstarch

Step-by-step explanation:

CAn I have brainliest? TYSMMMMMMMMMM

7 is an odd number since it can't be divided evenly by 2.

A negative number taken to an odd power will always be negative.

For example, -1⁵ is -1 because 5 is an odd number.

Answer:

Step-by-step explanation:

Answer:

-21 3/23

Step-by-step explanation:

-27 / 23 is -1 4/13, -1 4/23 *18 is -21.13 or -21 3/23

Given

Mass, Volume, and Density

Procedure

Mass, volume and density are three of an object's most basic properties. Mass is how heavy something is, volume tells you how big it is, and density is mass divided by volume. Although mass and volume are properties you deal with every day, the idea of density is a little less obvious and takes careful thought.

The value of x in sequence of number is 10.

Here, first term of sequence is x and each term there after is twice the previous term. Also Fifth term is 160.

What is geometric series?

Geometric series is an infinite series of the form:

\(a+ar+a r^{2} +ar^{3} +..........\)

where r is known as common ratio.

Now, first term is x and each term there after is twice the previous term.

So the series will be;

x , 2x , 4x , 8x, ..........

Clearly this series is geometric series with common ratio 2.

And the nth term of geometric series is \(ar^{n-1}\)

⇒ fifth term is 160

\(ar^{5-1} = 160\\ar^{4} = 160\\a 2^{4} =160\\a=\frac{160}{16} \\a=10\)

Here, first term is x.

The value of x in sequence of number is 10.

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Answer:

6 sides

Step-by-step explanation:

Interior angle and exterior angle are linear pair.

Let exterior angle = x

x + 120 = 180

x = 180 - 120

x = 60

Number of sides (n) = 360 ÷ measurement of exterior angle

           n = 360 ÷ 60

n = 6

Answer:

6 sides

Step-by-step explanation:

The exterior angle and interior angle sum to 180° , then

exterior angle + 120° = 180° ( subtract 120° from both sides )

exterior angle = 60°

The sum of the exterior angles of a polygon = 360°

To find number of sides n , divide sum by measure of one exterior angle

n = 360° ÷ 60° = 6

Answer:

\(a.\) \(\frac{49}{50}\)

\(b.\) \(8\)

Step-by-step explanation:

\(a.\)  \(\frac{1}{2} +\frac{2}{5} +\frac{2}{25}\)

To solve this, we must first find the LEAST COMMON MULTIPLE (LCM).

To find the LCM, we must list the multiples of the denominators, then find the smallest multiple that all three numbers have in common.

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

25: 25, 50

The LCM is 50.

Now that we have found the LCM, we will change the fractions so that all three have a denominator of 50.

To do this, we multiply the numerator and the denominator by the same number.

\(\frac{1}{2} *\frac{25}{25} =\frac{25}{50}\)

\(\frac{2}{5} *\frac{10}{10} =\frac{20}{50} \\\)

\(\frac{2}{25} *\frac{2}{2} =\frac{4}{50}\)

Now that all fractions have the same denominator, we can add them. Remember, when adding fractions, the denominators stay the same. Only add the numerators.

\(\frac{25}{50} +\frac{20}{50} +\frac{4}{50} \\\\=\frac{49}{50}\)

_______________________________________________________

\(b.\)  \(\frac{2}{3} *\frac{30}{7} *\frac{14}{5}\)

To multiply fractions, multiply the numerators, then the denominators. Lastly, simplify the product.

\(2*30*14=840\\3*7*5=105\)

\(\frac{840}{105} =\frac{8}{1}\)

apply the absolute rule,

solve each inequality independently,

find the intersection of both solutions

Answer:

The solution to the inequality in interval notation is:

Given the coordinates above, the area of the trapezoid is approximately 41. See the explanation below.

A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.

For the calculation showing the above solution:

Step 1 - Given:

A = (-3,2)

B = (1, 5)  = ⊥

C = (-7, -3)

D = (0.-2)

Step 2 - To get the distance between the points we need to use the formula for Distance between two points which is given as:

d=√((x2 – x1)² + (y2 – y1)²).

Distance of Line AB =

√((1 – (-3))² + (5 – 2)²).

= √[(4)² + (3)²]

= √( 16 + 9)
= √25

AB= 5

Repeat this for  BC, CD, DA and we'd get the following

BC =  11.313708498985
CD = 7.0710678118655

DA = 5

Step 3  - From the above structure, [see attached] we then apply the formula for the area of a Trapezoid (Trapezium) which is given as:

A = [(a+b)/2] h

Where a = 5

b = 11.313708498985

h = 5

=  [(5+11.313708498985)/2] 5

= 40.7842712475

\(\approx\) 41

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You just literally mark the graph, you see the 1st points (2,12) go on the X axis to 2, then go up to 12 and mark that as a point. and continue with this tactic with the rest.

Answer:

I think this is correct. <3

Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

The specific solution for the system of differential equations with initial conditions r(0) = 2 and y(0) = 5 is: \(r(t) = e^{(7t)} * [2, 1] + (5/3) * e^{(2t)} * [-1, 2]; \y(t) = e^{(7t)} * [2, 1] + (5/3) * e^{(2t)} * [-1, 2].\)

(a) Writing the system of differential equations in matrix form:

The given system of differential equations is:

dr/dt = 6x + 2y

dy/dt = 2x + 3y

Let's define the vector function:

X(t) = [x(t), y(t)]

Now, we can rewrite the system of differential equations in matrix form as:

dX/dt = A * X(t)

Where A is the coefficient matrix and X(t) is the vector function.

The coefficient matrix A is given by:

A = [[6, 2],

[2, 3]]

Thus, the system of differential equations in matrix form is:

dX/dt = A * X(t)

(b) Finding the general solution using methods discussed:

To find the general solution, we need to find the eigenvalues and eigenvectors of the coefficient matrix A.

The eigenvalues (λ) can be found by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix.

The characteristic equation for matrix A is:

det(A - λI) = det([[6-λ, 2], [2, 3-λ]])

= (6-λ)(3-λ) - 4

= λ² - 9λ + 14

= 0

Solving this quadratic equation, we find two eigenvalues: λ₁ = 7 and λ₂ = 2.

Next, we find the corresponding eigenvectors for each eigenvalue by solving the system (A - λI) * v = 0, where v is the eigenvector.

For λ₁ = 7:

(A - 7I) * v₁ = 0

[[6-7, 2], [2, 3-7]] * v₁ = 0

[[-1, 2], [2, -4]] * v₁ = 0

Solving this system, we find the eigenvector v₁ = [2, 1].

For λ₂ = 2:

(A - 2I) * v₂ = 0

[[6-2, 2], [2, 3-2]] * v₂ = 0

[[4, 2], [2, 1]] * v₂ = 0

Solving this system, we find the eigenvector v₂ = [-1, 2].

Now, we can write the general solution as:

X(t) = c₁ * e^(λ₁t) * v₁ + c₂ * e^(λ₂t) * v₂

Where c₁ and c₂ are constants determined by the initial conditions.

(c) Determining r(t) and y(t) that fulfill the initial conditions:

Given initial conditions: r(0) = 2 and y(0) = 5.

Using the general solution, we can substitute the initial conditions to find the specific values of the constants c₁ and c₂.

r(0) = c₁ * e^(λ₁0) * v₁ + c₂ * e^(λ₂0) * v₂

= c₁ * v₁

2 = c₁ * [2, 1]

From this equation, we can determine that c₁ = 1.

Similarly, for y(0):

y(0) = c₁ * e^(λ₁0) * v₁ + c₂ * e^(λ₂0) * v₂

= c₂ * v₂

5 = c₂ * [-1, 2]

From this equation, we can determine that c₂ = 5/3.

Now, we can substitute the values of c₁ and c₂ into the general solution:

\(r(t) = 1 * e^{(7t)} * [2, 1] + (5/3) * e^{(2t)} * [-1, 2]\)

\(y(t) = 1 * e^{(7t)} * [2, 1] + (5/3) * e^{(2t)} * [-1, 2]\)

Therefore, the specific solution for r(t) and y(t) that fulfill the initial conditions r(0) = 2 and y(0) = 5 is:

\(r(t) = 1 * e^{(7t)} * [2, 1] + (5/3) * e^{(2t)} * [-1, 2]\)

\(y(t) = 1 * e^{(7t)} * [2, 1] + (5/3) * e^{(2t)} * [-1, 2]\)

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