Linier ALgebra : Let W E R^nxn, s E R, and λ an eigenvalue of W. Prove that λ – s is an eigenvalue of W – sλ. (As usual, I = Inxn denotes the n x n identity matrix.)

Answer:

10.39; 6

Step-by-step explanation:

Horizontal component= |v| Cos theta = 12 Cos 60° = 6

Vertical component= |v| Sin theta = 12 Sin 60° = 10.39

Answer:

x = 25

Step-by-step explanation:

We know

5x - 35 is a right angle, meaning it must be 90 degree.

Let's solve

5x - 35 = 90

5x = 125

x = 25

The total number of participants in all the activities is represented by the expression 5.5s + 11.

The given information about the number of participants in each activity can be represented in the following table:

ActivityNumber of ParticipantsGolfing3(s-2)Snorkeling s Parasailings+14Surfing(1)/(2)(s+5)

To find the total number of participants in all the activities, we can add the number of participants in each activity:

Total number of participants = 3(s-2) + s + (s+14) + (1)/(2)(s+5)

Simplifying the expression gives:

Total number of participants = 5.5s + 11

Therefore, the total number of participants in all the activities is represented by the expression 5.5s + 11.

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Answer:

1.5 inches of stell will make 1 spring

Step-by-step explanation:

If 450 inches of steel are used to make 300 springs, we can simply divide the inces by the spring count to obtain a unit of inches/(1 spring).

(450 inches of steel)/(300 springs) = (1.5 inches of steel)/)1 spring)

The value of a is 92.17 when b=3 and c=7.

Jointly proportional refers to a relationship between two or more variables in which all of the variables increase or decrease together in the same ratio. For example, if one variable doubles, the other variables double as well.

The variable a is jointly proportional to b and c, which means that a = k*b*c, where k is the constant of proportionality.

We can use the given values of a, b, and c to find the value of k:
79 = k*6*3
79 = 18k
k = 79/18

Now that we know the value of k, we can use it to find the value of a when b=3 and c=7:
a = k*b*c
a = (79/18)*3*7
a = 92.17

Therefore, the value of a when b=3 and c=7 is 92.17.

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The natural logarithm function is ln(p) = ln(100) - 0.35t

From the question, we have the following parameters that can be used in our computation:

The table of values

The function can be represented as

p = ae^kt

Using the points on the table, we have

ae^(k * 0) = 100

So, we have

a = 100

This gives

p = 100e^kt

Using another point, we have

70.5y = 100e^(k * 1)

70.5y = 100e^k

So, we have

e^k = 0.705

Take the natural logarithm of both sides

k = ln(0.705)

k = -0.35

The function becomes

p = 100e^(-0.35t)

Take the natural logarithm of both sides

ln(p) = ln(100) - 0.35t

Hence, the function is ln(p) = ln(100) - 0.35t

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Answer:1 4/10

Step-by-step explanation:

We can reduce this to lowest terms by dividing the numerator and denominator or 4/10 by 2 to get the equivalent fraction 1 and 2/5

The simplified rational expression of (5)/(2)-(1)/(2d) is (5d-2)/(2d).

To add rational expressions with different denominators, we first need to find a common denominator. In this case, the common denominator is 2d.

Once we have the common denominator, we can multiply each fraction by a factor that will give us the common denominator. For the first fraction, we need to multiply by d in the numerator and denominator. For the second fraction, we need to multiply by 2 in the numerator and denominator.

After multiplying, we can combine the numerators and keep the common denominator.

So, the steps to simplify (5)/(2)-(1)/(2d) are as follows:

1. Find the common denominator: 2d
2. Multiply the first fraction by d/d: (5d)/(2d)
3. Multiply the second fraction by 2/2: (2)/(2d)
4. Combine the numerators and keep the common denominator: (5d-2)/(2d)
5. Simplify the numerator: (5d-2)/(2d)

Therefore, the simplified rational expression is (5d-2)/(2d).

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Equation Slope-Intercept Form Slope y-Intercept

y = 2x + 5 y = 2x + 5 2 5

4x - 3y = 12 y = (4/3)x - 4 4/3 -4

x = 7 Does not exist Does not exist Does not exist

3y = 9 y = 3 0 3

For the first equation, y = 2x + 5, it is already in slope-intercept form. The slope is the coefficient of x, which is 2, and the y-intercept is the constant term, which is 5.

For the second equation, 4x - 3y = 12, we can rearrange it to get it in slope-intercept form by isolating y on one side of the equation. We can do this by subtracting 4x from both sides and then dividing by -3: 4x - 3y = 12 -3y = -4x + 12 y = (4/3)x - 4

The slope is the coefficient of x, which is 4/3, and the y-intercept is the constant term, which is -4. For the third equation, x = 7, there is no y term, so it cannot be written in slope-intercept form and the slope and y-intercept do not exist.

For the fourth equation, 3y = 9, we can rearrange it to get it in slope-intercept form by dividing both sides by 3: 3y = 9 y = 3 The slope is 0, since there is no x term, and the y-intercept is the constant term, which is 3.

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Based on the information, we can infer that the surface area of the pyramid is: 105 inches²

To find the surface area of the pyramids we must perform the following procedure:

We must find the surface of each of the faces and the base.

According to this procedure, each face of the pyramid measures 20 inches². Then we must multiply this value by the number of faces of the pyramid (4).

We must add the surfaces of the faces and the base.

According to the above, the surface area of the pyramid would be 105 inches².

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Answer:

The missing variable "x" = 20

And the Angle measure = 98°

Step-by-step explanation:

Explaination is given in the picture...

Thank you!

Answer:

the angles are 82 degrees and 98 degrees (5(20) -2), and the missing variable (x) is 20.

Step-by-step explanation:

Let us first look at SL. SL is a straight line and has an angle measure of 180 degrees. Angle RTL is 82 degrees and splits SL into 2. The angle right next to RTL is RTS, which is (5x-2) degrees. Since all of SL adds to 180 degrees, this means that RTL and RTS will add up to 180 degrees, since they are in the middle of it.

82 + 5x-2 = 180

80 +5x = 180

5x = 100

x = 20

Therefore, the angles are 82 degrees and 98 degrees (5(20) -2), and the missing variable (x) is 20.

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1.  A transition matrix is regular if there is a positive integer k such that P^k has all positive elements.

2. The value of x2 =  [128,295, 44,557]T.

3. The value of x = [0.701, 0.299, 0]T .

1. P is a regular transition matrix because it has all positive elements, meaning that it is possible for any state to transition to any other state.

2. To find the state vector x2, we need to multiply the initial state vector x0 by the transition matrix P twice:
x2 = P^2 * x0
= P * P * x0
= P * [72 * 10 + 75 * 7, 32 * 10 + 31 * 7]T
= P * [945, 457]T
= [72 * 945 + 75 * 457, 32 * 945 + 31 * 457]T
= [128,295, 44,557]T

3. To find the steady state vector, we need to solve the equation Px = x for x. This means that we need to find the eigenvector of P corresponding to the eigenvalue

1. We can do this by finding the null space of (P - I), where I is the identity matrix:

(P - I)x = 0
=> [71 -75 0, -32 30 0, 0 0 -1]x = 0
=> x = c[75, 32, 0]T, where c is a constant.

To find the steady state vector, we need to normalize this eigenvector so that it sums to 1:
x = [75/107, 32/107, 0]T
= [0.701, 0.299, 0]T

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The estimated quotient of the given dividend 2 1 / 2 divided by the divisor 1 7/9 is equal to 1.41 ( round off up to the two decimals ).

Divisor = 1 7/9

Convert the divisor (mixed fraction ) into improper fraction,

1 7 /9

= [( 9× 1 ) + 7]/ 9

= 16/9

Dividend = 2 1 / 2

Convert the dividend (mixed fraction ) into improper fraction,

2 1 / 2

=[ ( 2 ×2 ) + 1] /2

= 5 /2

Divide the 5 / 2 by 16 /9 to get the estimated quotient ,

( 5 / 2 ) ÷ ( 16 / 9)

= ( 5 / 2 ) × ( 9 / 16 )

= ( 5 × 9 ) / ( 2 × 16 )

= 45 / 32

= 1.40625

= 1.41 ( round off up to the two decimals )

Therefore, the estimated quotient of the division is equal to 1.41( round off up to the two decimals ).

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Answer:

62.5%

Step-by-step explanation:

the product of the two numbers=xy

the product of the altered numbers=(0.75x)(0.5y) OR 0.375xy

finally you subtract this from one to get your decrease: 1-0.375=0.625

then simply convert that to a percent, leaving you with 62.5%. hope this helps!

So the total pressure experienced by the fish on the surface is 100450 Pa.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

When an object is submerged in a fluid, it experiences pressure due to the weight of the fluid above it. This pressure is called hydrostatic pressure, and it increases with depth. The formula to calculate hydrostatic pressure is:

P = ρgh

where P is the hydrostatic pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the object below the surface.

In this case, the fish is at a depth of 10m, so h = 10m. The density of water is given as 1025kg/m3, and the acceleration due to gravity is approximately 9.8m/s2. Therefore, the hydrostatic pressure experienced by the fish is:

P = (1025 kg/m3) x (9.8 m/s2) x (10 m)

= 100450 Pa

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Complete question:

"What is the total pressure experienced by a fish on the surface if it is at a depth of 10m? The density of water is 1025kg/m3"

Richard will make a profit of $6,600.00 by selling 30 pieces of Mir487 i.e. Option C

Given :

Price of broken transistor = $10.13

Price of Broken Mir487 = $29.87

Price of selling fixed Mir487 = $259.93

So, cost of making the product i.e. CP

             = Price of Broken Mir487  + Price of broken transistor

             = $29.87 + $10.13

             = $40

Finally, he sells the product i.e. SP = $259.93

Profit on one product = SP - CP

                                    = $259.93 - $40

                                    = $219.93

Profit on 30 products = 30 * Profit on one product

                                    = 30 * $219.93

                                    = $6,597.9

                                    = approximately $ 6,600.00

Thus, Richard will make a profit of  $ 6,600.00 by selling 30 pieces of Mir487.

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nobody wants to help you .

To express (14, 10, 14) as a linear combination of u = (3, 1, 7), v = (1, -1, 6), and w = (7, 5, 5), we need to find values for a, b, and c such that:

(14, 10, 14) = a(3, 1, 7) + b(1, -1, 6) + c(7, 5, 5)

This can be written as a system of equations:

14 = 3a + b + 7c

10 = a - b + 5c

14 = 7a + 6b + 5c

We can solve this system of equations using any method we prefer, such as substitution or elimination. One possible solution is:

a = 1

b = 2

c = 1

Therefore, the linear combination of u, v, and w that gives us (14, 10, 14) is:

(14, 10, 14) = 1(3, 1, 7) + 2(1, -1, 6) + 1(7, 5, 5)

= (3, 1, 7) + (2, -2, 12) + (7, 5, 5)

= (14, 10, 14)

So, the linear combination is 1u + 2v + 1w.

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Using the definition of the tangent function, we will get that:

5√(6)/12 = sin(θ)

Here you need to remember how the tangent function is defined, we know that:

tan(θ) = sin(θ)/cos(θ)

Here we know that:

tan(θ) = √15/3

cos(θ) = √10/4

Replacing that we can write:

√15/3 = sin(θ)*(4/√10)

Solving for the sine, we will get:

(√15/3)*(√10/4) = sin(θ)

(√15*√10)/(3*4) = sin(θ)

(√150)/(12) = sin(θ)

(√(25*6))/(12) = sin(θ)

5√(6)/12 = sin(θ)

That is the answer.

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Answer:

33 degrees

Step-by-step explanation:

Angles BFG + GFC = 90

5r +68 + 8r +113 =90

1

Collect like terms

13r + 181 = 90

Subract 181 from both sides

13r = 90-181

13r = - 91

r = - 7

Now insert the value of r into BFG (5r +68)

5r + 68 = 5(-7) +68

= -35 + 68

=33

Check your answer by inserting the value of r into 8r +113

8r + 113 =8(-7) +113

-56+113= 57

The two angles 33 and 57 must add up to 90, a rt angle

The value of angle XYZ is 0.020 degrees using the cosine function.

Simply put, inverse trigonometric functions are the opposites of the fundamental trigonometric functions sine, cosine, tangent, cotangent, secant, and cosecant. The terms arcus functions, antitrigonometric functions, and cyclometric functions are also used to describe them. To find the angle for any trigonometric ratio, apply these inverse trigonometric functions. The fields of engineering, physics, geometry, and navigation all heavily utilise the inverse trigonometry functions.

From the given right triangle we observe that:

cos y = 6 / 15 = adjacent side /hypotenuse

y = arccos(6/15)

y = 0.020 degrees

Hence, the value of angle XYZ is 0.020 degrees using the cosine function.

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The orthonormal basis for this matrix.

To find the orthonormal basis for the given matrix, you will need to begin by taking the right and left singular vectors of the matrix.

The right singular vector for this matrix is 3(1     -1     1     1).

The left singular vector for this matrix is 2(-2     2     2     -2).

Now, divide each vector by its length to make them unit vectors, and you will get the orthonormal basis for the given matrix.

The orthonormal basis for this matrix is 1/3(1     -1     1     1)  1/2(-2     2     2     -2).

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Opposite interior bof a quadrilateral are supplementary if and only if the quadrilateral is cyclic.

A quadrilateral is called cyclic if its vertices lie on a circle. This means that there is a circumcircle that passes through all four vertices of the quadrilateral. If opposite interior angles of a quadrilateral are supplementary, then the sum of these angles is 180 degrees. This means that the opposite angles of a cyclic quadrilateral are supplementary.

To prove this, let us consider a quadrilateral ABCD that is cyclic. Let O be the center of the circumcircle that passes through all four vertices of the quadrilateral.

Since the quadrilateral is cyclic, angle AOB and angle COD are both subtended by the same arc, and therefore they are equal. Similarly, angle BOC and angle DOA are both subtended by the same arc, and therefore they are equal.

Now, let us consider the sum of the opposite interior angles of the quadrilateral.

Angle A + angle C = angle AOB + angle BOC + angle COD + angle DOA = 2(angle AOB) + 2(angle BOC) = 2(180) = 360

Since the sum of the opposite interior angles of the quadrilateral is 360 degrees, this means that the opposite interior angles of the quadrilateral are supplementary.

Therefore, opposite interior angles of a quadrilateral are supplementary if and only if the quadrilateral is cyclic.

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If you have a 3600 m³ cube, then you can fit 3600 kiloliters in the cube.

A kiloliter (kL) is defined as a unit of volume which is used to measure liquids. It is equal to 1,000 liters, and it is used to measure large volumes of water, oil, and other liquids.

We know that 1 cubic meter is equal to 1 kiloliter,

We have to convert 3600 meter cube to Kiloliter,

So , we multiply by 3600,

On multiplying,

We get,

⇒ 3600 meter cube = 3600 × 1 Kiloliter,

⇒ 3600 meter cube = 3600 Kiloliter,

Therefore, 3600 Kiloliter can fill in the cube having the volume as 3600 meter cube.

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The measure of angle 2 is 70° and the measure of angle 3 is also 70°°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

From the given information ∠1 and ∠3 are pairs of alternate interior angles.

Therefore, m∠1 = m∠B = 70°.

We also know that the vertically opposite angles are equal,

Here ∠1 and ∠2 are vertically opposite angles,

Therefore, m∠1 = m∠2 = 70°.

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The required slope of the line shown in the graph is 4/3, and the lines representing the rise and run are shown in the graph.

The slope of a line is a measure of how steeply the line is inclined with respect to the horizontal axis.

Here,

To calculate the slope of a line from the rise and run values, we use the formula:

slope = rise/run

In this case, rise = 6 and run = 4.5. Substituting these values into the formula, we get:

slope = 6 / 4.5

Simplifying the fraction by dividing both the numerator and denominator by 1.5,

slope = 4/3

Therefore, the slope of the line is 4/3.

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The answer of the given question based on statistical measures the answer is, Min: 2,Max: 15,Med: 8,Q1: 4,Q3: 13.

Statistics is  branch of mathematics that deals with collection, analysis, interpretation, presentation, and organization of the  data. It provides way to summarize and describe numerical information in  meaningful way, and it enables us to make the informed decisions based on that information. Statistics is used in many things , including business, finance, health, engineering, social sciences, and more.

To create the box and whisker plot:

Draw a number line that includes all the data points.

Mark the minimum and maximum values with a horizontal line.

Locate the median and draw a vertical line through it.

Draw a box from the first quartile (Q1) to the third quartile (Q3).

Draw whiskers from the box to the minimum and maximum values.

Here is the completed box and whisker plot:

           O

           1

2  3  4  5  6  7  8

          |--------|

          9

10 11 12 13 14 15 16 17 18

     |--------------|

              X

The box represents the middle 50% of the data, with the bottom of the box at Q1 and the top of the box at Q3. The median is marked by a vertical line inside the box. The whiskers extend from the box to the minimum and maximum values, with any data points outside the whiskers shown as individual points (outliers).

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