solve by completing the square 3x^2+4x-6=0

The values of the elements of the matrix will ψ(t)⟩=e−iE1t/ℏ|2⟩

Let's say the block matrix is used to represent the 2n by 2n matrix A.

Displaystyle A="begin" "bmatrix" "a&b" "c&d" "end"

where n-by-n matrices a, b, c, and d. The requirement that b and c be symmetric and that a + dT = 0 are similar to the requirement that A be Hamiltonian. The fact that A is of the form A = JS with S symmetric is another equivalent requirement.

Two Hamiltonian matrices can be added together (as can any linear combination), and their commutator is also Hamiltonian. The space of all Hamiltonian matrices is hence a Lie algebra, indicated by the symbol sp (2n). Sp(2n) has a dimension of 2n2 + n.

H^=E0(|1⟩⟨1|+|3⟩⟨3|)+E1|2⟩⟨2|+A(|1⟩⟨3|+|3⟩⟨1|)H^=E0(|1⟩⟨1|+|3⟩⟨3|)+E1|2⟩⟨2|+A(|1⟩⟨3|+|3⟩⟨1|)

It is then straightforward to see that :

• |2⟩|2⟩ is an eigen state with eigen value E1E1 as you have already noticed. Hence if the initial state is |2⟩|2⟩ then

|ψ(t)⟩=e−iE1t/ℏ|2⟩

• (|1⟩+|3⟩)(|1⟩+|3⟩) and (|1⟩−|3⟩)(|1⟩−|3⟩) are eigen states with respective eigen values of E0+AE0+A and E0−AE0−A. Hence if the initial state is |3⟩=12[(|1⟩+|3⟩)−(|1⟩−|3⟩)]|3⟩=12[(|1⟩+|3⟩)−(|1⟩−|3⟩)], then

|ψ(t)⟩=12[e−i(E0+A)t/ℏ(|1⟩+|3⟩)−e−i(E0−A)t/ℏ(|1⟩−|3⟩)]

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incomplete question: complete question is

Let

⎡⎣⎢E00A0E10A0E0⎤⎦⎥[E00A0E10A0E0]

be the matrix representation of the Hamiltonian for a three-state system with basis states |1>,|2>and |3>|1>,|2>and |3>.

a. If the state of the system at time tt = 00 is |ψ(0)>=|2>|ψ(0)>=|2> what is |ψ(t)>|ψ(t)>?

b. If the state of the system at time tt = 00 is |ψ(0)>=|3>|ψ(0)>=|3> what is |ψ(t)>|ψ(t)>?

25.48 was spent on a pass and lunch for each student.

Total money spend on passes = 683.47

Total no. of people = 38 + 3

                                = 41

Money spend on pass for each person = 683.47/41

                                                                 = 16.67

Total money spend on lunch = 334.78

Total no. of students = 38

Money spend on lunch for each student = 334.78/38

                                                                   = 8.81

Total = 16.67 + 8.81

        = 25.48

Hence, 25.48 was spent on a pass and lunch for each student.

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Answer:

7w ≤ -25

Step-by-step explanation:

If 7 x W is at most -25 then it cant be greater than -25 but can be equal to it.

Hope this helped!

There can be up to 12 lots which could be made out of 2 acre land.

What is acre?

Acre is a measurement unit which is used to measure length of land .

In the British Imperial and United States Customary systems, 1 acre equal to 43,560 square feet.

Main body:

so 1 acre = 43560 feet ²

So in 2 acre of land = 2*43560

                                 = 87120 sq. ft.

Width of 1 plot = 72.5 feet

Depth of 1 plot = 100 feet

Area of 1 plot = 100*72.5

                      = 7250 sq. ft.

Total no. of plots = Total are of land / area of 1 plot

                            = 87120/ 7250

                            ≈12

Hence total plots that can be made out of 2 acre land is 12.

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The circumference and the area of the circle in terms of "π" are 24π and 144π.

We are given a circle. The coordinates of the center of the circle are (12, -1). The circle passes through a point. The coordinates of the passing point are (0, -1). We need to find the circumference and area of the circle.

Let the radius, circumference, and area of the circle be denoted by the variables "r", "C", and "A", respectively. The radius is the distance between the center of the circle and a point on its boundary. We will use the distance formula.

r = √[(12 - 0)² + (-1 - (-1))²]

r = √[144 + 0]

r = 12

The radius of the given circle is 12 units.

The circumference of the circle is calculated below.

C = 2πr

C = 2π×12

C = 24π

The area of the circle is calculated below.

A = πr²

A = π(12)²

A = 144π

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Answer:

Q29. ∠CAD = (180° - 92°) ÷ 2 (angle sum of triangle; base angles of an isosceles triangle)

                    = 44°

Q30. Since triangle ACD is an isosceles triangle,

∴ ∠ACD = ∠CAD = 44°

Q31. ∠ACB = 180° - 44° (adjacent angles on a straight line)

                   = 136°

Q32. ∠ABC = (180 °- 136°) ÷ 2 (angle sum of triangle; base angles of an isosceles triangle)

                   = 22°

The expression for the other number is (n-1) when n is the greater of two consecutive numbers.

Given that,

We have to write an expression for the other number if n is the greater of two successive numbers.

We know that,

One is equal to the difference between any two consecutive numbers.

Let us take

x be the smaller of two consecutive number

n be the larger of two consecutive numbers

We have that

n-x=1

Solve for x

x=n-1

Therefore, The expression for the other number is (n-1) when n is the greater of two consecutive numbers.

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Answer:

81,-247, 729

Step-by-step explanation:

each time its multiplying it by -3

so -27x-3=81

Answer: 729

Step-by-step explanation: The thing that happens every time is -3 is multiplied: 1, -3, 9, -27,  81, -243, 729

hope this helps!

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Applying the trigonometry ratio, SOH, the height, h = 6.2172 cm.

Area of the region that is shaded in the circle = 47.1784 cm²

Recall the formulas for the trigonometric ratios, which are given as SOHCAHTOA, where:

Find the height, h, of the triangle using the sine ratio of trigonometry:

∅ = 51°

Opposite length = h

Hypotenuse = 8 cm

sin 51 = h/8

h = 8(sin 51)

h = 6.2172 cm

Area of the triangle = 1/2(base)(height) = 1/2(8)(6.2172)

Area of the triangle = 24.8688 cm²

Area of the sector =  /360 × r² = 129/360 × (8²)

Area of the sector = 72.0472 cm²

Area of the shaded region = area of the sector - area of the triangle

= 72.0472 - 24.8688

= 47.1784 cm²

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a) The scale of the drawing is in the ratio of 1 in:1.8ft.

b) The scale factor of the drawing is 0.0463.

The scale factor refers to the ratio between the scales of an original object and the scale drawing.

To scale down the original measurement, the scale factor formula is the dimension of the new shape ÷ the dimension of the original shape.

To scale up the original measurement, the scale factor formula is the dimension of the original shape ÷ the dimension of the new shape.

1 foot = 12 inches

Height of drawing = 5 inches

Height of fountain = 9 feet = 108 inches (9 x 12)

The scale of drawing to the fountain = 5 inches:9 feet = 1 inch:1.8 feet

Scale Factor = Dimension of the new shape ÷ Dimension of the original shape

= 5 ÷ 108

= 0.046296

= 0.0463

Thus, the actual fountain was scaled down by a scale factor of 0.0463.

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The ordered pair (x,y) obtained from the linear equations is: (-2,-12)

What is Linear Equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason. A linear equation is expressed using the linear equation formula. There are several ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form. To discover how a linear equation is stated in its standard form, let's take an example.

The equation is given:

8x-3y=20

5x-y=2

Using the substitution method for solving the linear equations:

From the equation:

5x-y=2;

we can transform this equation as:

⇒-y = 2-5x;

⇒y = 5x-2;

Now substituting the value of y in the other equation: we get;

⇒8x-3(5x-2)=20

⇒8x -15x+6 = 20;

⇒-7x=14;

x = -2;

Now putting the value of x in the equation to get the value of y;

So,

y = 5(-2) -2;

y = -12;

Hence the value of x and y are -2 and -12 respectively;

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Answer:

Particle A is a proton and particle B is a neutron

Step-by-step explanation:

Total number of rolls are 60, they used 1 and half roll per week. So, 40 weeks will it take them to run out of rolls of paper towels.

Paper towels are the disposable paper made up from the paper. It is an absorbent, which designed to absorb liquid. It is made up of pulp like tissue paper which are meant to be single time use only.

Paper towel is made up of cellulose fibers who are bigger in size consist of many small molecules linked together. Paper towels are used in drying, wiping, cleaning, toilets etc.

For given information,

Total rolls= 60

They used up 1 roll in 1.5 week or 1 week and half

So,

60 + 60*1/2

60+30= 90 weeks

Thus, total number of rolls are 60, they used 1 and half roll per week. So, 40 weeks will it take them to run out of rolls of paper towels.

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Answer:

D

Given the inequation symbols > and < , the lines will be dotted.

The three sides are equally distant from the center and the distance is  L/√3

Let the triangle be  ΔABC  with vertices A,B and C with length of each side L. Each angle will be 60°

L=AB=BC=CA

Draw 3 angle bisectors(or 3 altitudes or 3 medians). These all meet at a single point which is the center of the equilateral triangle. Let the centre be D.

Now consider the  ΔADB . The  ∠ADB=120°  ( ∵∠BCA=60° . The angle bisector makes  ∠DAB=∠DBA=30°)

Using Sine rule for triangles:

a/sin(A)=b/sin(B)=c/sin(C)

Where a is the length of side opp. to the side of  ∠A . Similarly, b and c are also defined as the length of side opp. to the ∠B and  ∠C  respectively.

Then, in this case, in  ΔADB

Lsin(120°)=ADsin(30°)=BDsin(30°)

⇒AD=Lsin(30°)/sin(120°)=Lx(1/2)/(√3/2)

⇒AD=L/√3

Similarly, DB=L/√3

Thus the three sides are equally distant from the center and the distance is  L/√3

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Answer:

1

Step-by-step explanation:

a). The representation of the given expression as an equation is; 0.5n = 10.

b). The solution set is; {0.025, 0.25, 1, 10}.

It follows from the task content that the given statement be represented as an equation.

Since the given word phrase is; The product of 0.5 and a number is 10.

Let the number be n;

a). Hence, the required equation is; 0.5n = 10.

b). However, to determine the solution set using the replacement set; {0.05,0.5,2,20} according to the expression; 0.5n.

When; n = 0.05; the result is; 0.025.

When; n = 0.5; the result is; 0.25.

When; n = 2; the result is; 1.

When; n = 20; the result is; 10.

Therefore, the required solution set is; {0.025, 0.25, 1, 10}.

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The probability will be .56, .24,0.06 and .21 respectively in the question.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Presumably, the events are independent.

the probability that they both hit the target :

p(both hits) = .8*.7 = .56.

Jiri hits but Benita misses:

P(Benita hits &Jiri misses) = P(Benita hits)×P(Jiri misses) = .8 * .3= .24

they both miss the target:

p(both misses) = .2*.3 = 0.06

Benita hits but Jiri misses:

P(Benita misses &Jiri hits) = .2*.7 = .21

Hence the probability will be .56, .24,0.06 and .21 respectively in the question.

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Answer:

301.76

Step-by-step explanation:

I'll add a diagram for better understanding.  

Look at the diagram

The angle with a question mark in purple is the the bearing from the phone to the transmitter.

To figure out that angle we will have to figure out the angle inside the triangle on that side and we will subtract that from 360 to find the answer.

Since this is a right angled triangle, we can use SOH CAH TOA to figure out the angle inside.

For the angle we have to figure out, 21 is the opposite and 13 is adjacent.

so we will use TOA

tan[tex]x\\[/tex] = O/A

tan[tex]x[/tex] = 21/13

tan inverse(21/13) = [tex]x[/tex]

[tex]x[/tex] = 58.2405

This is the phone's angle inside the triangle
subtract this from 360 to find the bearing

360 - 58.2405 = 301.76

Using the equation of line, the equation parallel to y=5 and passing through (3,-5) is y+5=0.

In the given question,

We have to find an equation parallel to y=5 and passing through (3,-5).

The equation parallel to y=5.

Point is (3,-5).

We firstly find the slope of y=5

Expressing the equation in the general form

y=0×x+5

On comparing to the y=mx+c, we get slope(m) = 0.

The given point is (3,-5) in which [tex]x_{1}[/tex]=3 and [tex]y_{1}[/tex]= -5

Now finding the equation.

So the Equation of line is

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

Now putting the value

y-(-5)=0(x-3)

Simplifying

y+5=0

Hence, the equation parallel to y=5 and passing through (3,-5) is y+5=0.

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Answer:

When the boat is 6 m from the dock, it is approaching the dock at the rate of √37/6 m/sec.

Step-by-step explanation:

Let x = distance of the boat from the dock at time t

    y = length of rope at time t

Draw a right triangle with horizontal leg x, vertical leg 1, and hypotenuse y.

We know that dy/dt = -1 and want to find dx/dt when x = 6.

By the Pythagorean Theorem, x2 + 12 = y2.

   2x(dx/dt) = 2y(dy/dt)

        dx/dt = y(dy/dt) / x     When x = 6, y2 = 36 + 1 = 37

                                                            So, y = √37

         dx/dt = -√37 / 6

When the boat is 6 m from the dock, it is approaching the dock at the rate of √37/6 m/sec.

The solution to the equation are 5 or -1 after applying the quadratic formula.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

x² - 4x² - 5 = 0

The above equation is a quadratic equation:

Using the quadratic formula:

[tex]\rm $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

Plug the values in the formula:

[tex]\rm $x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(-5)}}{2(1)}$[/tex]

After solving:

x = 5 or -1

Thus, the solution to the equation is 5 or -1 after applying the quadratic formula.

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Answer: b=12x

Step-by-step explanation:

The bakery shipped out b boxes of bagels.

Each box contained 12 bagels

b is the number o boxes

x is the number of bagels in each box

Answer:

The perfect square number for 11 is 121.

Step-by-step explanation:

The term "square" in math represents multiplying a number twice, in this case:

11 x 11 = 121.

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If they want to be 99% sure that their estimate will be within 3% of the true population percentage then the required sample size is n = 4161.

When there is no known population, the sample size can be calculated by determining the minimal sample size needed to accurately estimate proportions while taking the standard normal deviation into account.

We have been given the confidence level = c= 99%

Estimate percentage= 3%

We want to find the sample size when the true percentage is not given

Therefore Assume that true proportion = p = 0.5

Therefore the sample size is calculated as:

N= p(1-p) (zc/e) square

N = 4161

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The measure of angle 3 is 22.5°.

Given,

∠1 = (x-18)°

∠2 = (3x+36)°

∠1 + ∠2 = 180°  (Straight Line)

x - 18 + 3x + 36 = 180

            4x + 18 = 180

                   4x = 180 - 18

                   4x = 162

                     x = 162/4

                     x = 40.5

∠3 = ∠1 (Alternate opposite angles)

    = x - 18

    = 40.5 - 18

    = 22.5

Hence, ∠3 is 22.5°.

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