absolute value of 7 and one
eigth

Answer:

Step-by-step explanation:

Given that:    

The equation of the damped vibrating spring is y" + by' +2y = 0

(a) To convert this 2nd order equation to a system of two first-order equations;

let y₁ = y

y'₁ = y' = y₂

So;

y'₂ = y"₁ = -2y₁ -by₂

Thus; the system of the two first-order equation is:

y₁' = y₂

y₂' = -2y₁ - by₂

(b)

The eigenvalue of the system in terms of b is:

[tex]\left|\begin{array}{cc}- \lambda &1&-2\ & -b- \lambda \end{array}\right|=0[/tex]

[tex]-\lambda(-b - \lambda) + 2 = 0 \ \\ \\\lambda^2 +\lambda b + 2 = 0[/tex]

[tex]\lambda = \dfrac{-b \pm \sqrt{b^2 - 8}}{2}[/tex]

[tex]\lambda_1 = \dfrac{-b + \sqrt{b^2 -8}}{2} ; \ \lambda _2 = \dfrac{-b - \sqrt{b^2 -8}}{2}[/tex]

(c)

Suppose [tex]b > 2\sqrt{2}[/tex], then  λ₂ < 0 and λ₁ < 0. Thus, the node is stable at equilibrium.

(d)

From λ² + λb + 2 = 0

If b = 3; we get

[tex]\lambda^2 + 3\lambda + 2 = 0 \\ \\ (\lambda + 1) ( \lambda + 2 ) = 0\\ \\ \lambda = -1 \ or \ \lambda = -2 \\ \\[/tex]

Now, the eigenvector relating to λ = -1 be:

[tex]v = \left[\begin{array}{ccc}+1&1\\-2&-2\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]

[tex]\sim v = \left[\begin{array}{ccc}1&1\\0&0\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]

Let v₂ = 1, v₁ = -1

[tex]v = \left[\begin{array}{c}-1\\1\\\end{array}\right][/tex]

Let Eigenvector relating to  λ = -2 be:

[tex]m = \left[\begin{array}{ccc}2&1\\-2&-1\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]

[tex]\sim v = \left[\begin{array}{ccc}2&1\\0&0\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]

Let m₂ = 1, m₁ = -1/2

[tex]m = \left[\begin{array}{c}-1/2 \\1\\\end{array}\right][/tex]

∴

[tex]\left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= C_1 e^{-t} \left[\begin{array}{c}-1\\1\\\end{array}\right] + C_2e^{-2t} \left[\begin{array}{c}-1/2\\1\\\end{array}\right][/tex]

So as t → ∞

[tex]\mathbf{ \left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= \left[\begin{array}{c}0\\0\\\end{array}\right] \ \ so \ stable \ at \ node \ \infty }[/tex]

Answer:

241/81 cm^2

Step-by-step explanation:

[tex]2\: lenghts = wide\\\\lenght=x\\\\2x=wide\\\\Perimeter = 2(wide+lenght)\\\\P=2(2x+x)\\\\P=2(3x)\\\\P=7\frac{1}{3}\\\\\frac{22}{3}=6x\\\\x=\frac{22}{3*6}\\\\x=\frac{11}{9}\\\\width = 2x=2(\frac{11}{9})=\frac{22}{9}[/tex]

[tex]Area = lenght\times width\\\\Area = \frac{11}{9}\times\frac{22}{9}\\\\A=\frac{11*22}{9*9}\\\\A=\frac{242}{81}cm^2[/tex]

Answer:

[tex]2\frac{80}{81}[/tex] cm²

Step-by-step explanation:

A = lw

P = 2(l + w)

~~~~~~~~~~~

l = 2w

2(2w + w) = [tex]7\frac{1}{3}[/tex]

2(3w) = [tex]\frac{22}{3}[/tex]

3w = [tex]\frac{11}{3}[/tex]

w = [tex]\frac{11}{9}[/tex]

l = [tex]\frac{22}{9}[/tex]

A = [tex]\frac{22}{9}[/tex] × [tex]\frac{11}{9}[/tex] = [tex]\frac{242}{81}[/tex] = [tex]2\frac{80}{81}[/tex] cm²

Answer:

-1.333333

Step-by-step explanation:

:)

have a very nice day

Answer:

he can make 4 packages hope this helps

Answer:

Step-by-step explanation:

If you graph both the focus and the directrix you will see that the directrix is below the focus...12 units below to be exact. The focus is on the vertical line x = 4, so the vertex also has an x coordinate (which is actually h since h and k represent the vertex) of 4. The vertex is exactly halfway between the focus and the directrix, so that means that the vertex is at (4, 0). h = 4, k = 0. The standard form for this parabola (we know it opens upwards since the parabola ALWAYS wraps itself around the focus and is directed away from the directrix) is:

[tex](x-h)^2=4p(y-k)[/tex]

p is the number of units between the focus and the vertex, or the vertex and the directrix (which is the same number of units since the vertex is smack dab in the middle of them!). That means that p = 6. Filling in 6 for p, 4 for h, and 0 for k we have:

[tex](x-4)^2=4(6)(y-0)[/tex] and simplify to

[tex](x-4)^2=24y[/tex] which is the first choice you're given.

The equation that shows the parabola when parabola has the focus at (4, 6) and the directrix y = –6 should be considered as the (x – 4)2 = 24y.

In terms of mathematics, a parabola represent the plane curve  in which there is the mirror-symmetrical and should be made of U-shaped.

Since there has the focus at (4, 6) and the directrix y = –6

So the first equation should be considered.

Learn more about parabola here: https://brainly.com/question/8063993

Answer:

(7,4)

Step-by-step explanation:

The x always goes first and the y goes second

Answer:

7,4

Step-by-step explanation:

x,y

Answer:

= −6x+10

Step-by-step explanation:

Answer:

-6x+10

Step-by-step explanation:

Multiply the 2 by each figure in the parenthesis. So, it becomes the sum of (2)-3x and 2(5), which is -6x+10.

You would multiply each number by 20

Step-by-step explanation:

It says that right there

Answer:

I believe the answer is 42 minutes :)

51.1 and 64.9

Step-by-step explanation:

Answer: 55.1 and 64.9

On edge.

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Answer:

V = 167.55

Step-by-step explanation:

V = pir^2 h/3

V = pi(4)^2 (10/3)

The approximate volume of water in Anuj's cup is 42 cubic cm.

Volume is a measure of capacity that an object holds.

Formula for finding the volume of cone

volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]

where,

r is the radius of cone

h is the height of cone

π = 3.14

According to the given question

paper cups are of the shape of cone.

and,

diameter = 8cm

⇒ radius = [tex]\frac{8}{2}[/tex] = 4cm

the approximate volume  of water in cup = [tex]\frac{1}{3} \pi r^{2} h[/tex]

=[tex]\frac{1}{3}[/tex]×[tex]2^{2}[/tex]×π×10

=[tex]\frac{1}{3}[/tex]×4×3.14×10

= 41.86 = 42 cubic cm.

Hence, the approximate volume of water in Anuj's cup is 42 cubic cm.

Learn more about the volume of cone here:

https://brainly.com/question/1984638

#SPJ2

Answer:

-74+3i

Step-by-step explanation:

Answer:

Step-by-step explanation:

(5 + 3i) + (2 - 81)

5 + 3i + 2 - 81

74 + 3i

Answer:

Please check the explanation.

Step-by-step explanation:

We know that when 'y' varies directly with 'x', the equation becomes

y ∝ x

y = kx

where 'k' is called the constant of proportionality.

From the table, it is clear that 'y' varies directly with 'x'

Let us check the value of k for all the points

k = y/x

For the point (130, 9.10)

For the point (145, 10.15)

For the point (150, 10.50)

For the point (185, 12.95)

Thus, the value of proportionality constant is same.

i.e. k = 0.07

Determining the cost of 21 feet of the wire

21 feet = 252 inch

Using the equation

y = kx

Thus, the cost of 252-inch wire will be:

y = kx

substituting k = 0.07, and x = 252

y = 0.07 × 252

y = 17.64 Dollars

Thus, the cost of 21 feet wire will be: 17.64 Dollars

Determining the cost of 15 yards of the wire

15 yards = 540 inches

Using the equation

y = kx

Thus, the cost of 15 yards of wire will be:

y = kx

substituting k = 0.07, and x = 540

y  =  0.07 × 540

y = 37.8 Dollars

Thus, the cost of 15 yards of wire will be: 37.8 Dollars

Answer:

25 meters per second

Step-by-step explanation:

Divide to find m/s.

750 / 30 = 25

Check in necessary.

25 * 30 = 750

Answer:

25 per sec

Step-by-step explanation:

Answer:

i guess the answer is 680.

Answer:

2/5

Step-by-step explanation:

(2,2) and (7,4) 4-2/7-2=2/5

Answer:

[tex]f(10) = 173[/tex]

Step-by-step explanation:

Given

Exponential Function

[tex](x_1,y_1) = (3,10.125)[/tex]

[tex](x_2,y_2) = (6,34.2)[/tex]

Required

Determine f(10)

We have that

[tex]y = ab^x[/tex]

First, we need to solve for the values of a and b

For [tex](x_1,y_1) = (3,10.125)[/tex]

[tex]10.125 = ab^3[/tex] --- (1)

For [tex](x_2,y_2) = (6,34.2)[/tex]

[tex]34.2 = ab^6[/tex] ---- (2)

Divide (2) by (1)

[tex]\frac{34.2}{10.125} = \frac{ab^6}{ab^3}[/tex]

[tex]\frac{34.2}{10.125} = \frac{b^6}{b^3}[/tex]

[tex]3.38= b^{6-3}[/tex]

[tex]3.38= b^{3}[/tex]

Take cube root of both sides

[tex]b = \sqrt[3]{3.38}[/tex]

[tex]b = 1.5[/tex]

Substitute 1.5 for b in [tex]10.125 = ab^3[/tex]

[tex]10.125 = a * 1.5^3[/tex]

[tex]10.125 = a * 3.375[/tex]

Solve for a

[tex]a = \frac{10.125}{3.375}[/tex]

[tex]a = 3[/tex]

To solve for f(10).

This implies that x = 10

So, we have:

[tex]y = ab^x[/tex] which becomes

[tex]y = 3 * 1.5^{10[/tex]

[tex]y = 3 * 57.6650390625[/tex]

[tex]y = 172.995117188[/tex]

[tex]y = 173[/tex] -- approximated

Hence:

[tex]f(10) = 173[/tex]

Answer:

The values of given expressions are:

1. gh = -21

2. g^2 - h = 46

3. g + h^2 = 2

4. g + h  = -4

5. h - g  = 10

6. g - h = -10

Step-by-step explanation:

Given values of g and h are:

g = -7

h = 3

1. gh

The two numbers are being multiplied

Putting the values

[tex]gh = (-7)(3) = -21[/tex]

2. g^2-h

Putting the values

[tex]=(-7)^2-3\\=49-3\\=46[/tex]

3. g+h^2

Putting the values

[tex]= -7 + (3)^2\\=-7+9\\=2[/tex]

4. g+h

Putting the values

[tex]= -7+3\\=-4[/tex]

5. h-g

Putting the values

[tex]= 3 - (-7)\\=3+7\\=10[/tex]

6. g-h

Putting values

[tex]=-7-3\\=-10[/tex]

Hence,

The values of given expressions are:

1. gh = -21

2. g^2 - h = 46

3. g + h^2 = 2

4. g + h  = -4

5. h - g  = 10

6. g - h = -10

Answer:

1) - 21

2) 46

3) 2

4) -4

5) 10

6) -10

Step-by-step explanation:

[tex]1)gh = - 7(3) \\ \: \: \: \: \: \: = - 21[/tex]

[tex]2){g}^{2} - h = ( - 7 {)}^{2} - 3 \\ \: \: \: \: \: \: \: \: \: \: \: = 49 - 3 \\ \: \: \: = 46[/tex]

[tex]3)g + {h}^{2} = - 7 + {3}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 7 + 9 \\ \: \: \: \: = 2[/tex]

[tex]4)g + h = - 7 + 3 \\ \: \: \: \: \: \: \: = - 4[/tex]

[tex]5)h - g = 3 - ( - 7) \\ \: \: = 10[/tex]

[tex]6)g - h = - 7 - 3 \\ \: \: \: \: \: \: \: \: \: \: = - 10[/tex]

Answer:

8 pies and 2 coffees

Step-by-step explanation:

10 men bought pie or a cup of coffee.

x=pie

y=coffee

x+y=10

0.6x+0.5y=5.8

0.6x+0.6y=6

0.1y=0.2

y=2

x=8

Hope this helps plz hit the crown :D

Step-by-step explanation:

B. 426 people per square. mile

Answer:

0 cavities

minimum is 0 cavities. there are people having 0 cavities. see the graph.

hope it helps!

Answer:

0

Step-by-step explanation:

The minimum is the smallest value in the dataset. The smallest number of cavities is 0.

please give thanks by clicking the heart button! :)

Answer:

y=(4/3)x-8

Step-by-step explanation:

Slope-intercept form: y=mx+b

4x-3y=24

3y=4x-24 (isolating the 3y)

y=(4/3)x-8 (dividing both sides by 3)

Hope this helps!

Answer:

-5

Step-by-step explanation:

The equation given is written in slope-intercept form (y = mx + b). In this form, 'm' represents the slope of a line and 'b' represents the y-intercept of the line. Since the equation asks for the slope, we can simply look at the value of 'm' in the equation. Then, we will find the slope.

slope - intercept form

y = mx + b

given equation

-y = -5x + 9

values

m = slope = -5

b = y-intercept = 9

Answer:

Step-by-step explanation:

Answer:

mark the answer below as brainliest x

Step-by-step explanation:

Answer:

Step-by-step explanation:

500×30=15000

Answer:

Simplification is a method for solving a system of equations

Step-by-step explanation:

-Graphing is a real way to solve a System of Equations

-Substitution is a real way to Solve Systems of Equations

-Elimination is a real way to solve Systems of Equations

so, Simplifcation can't be one

Take 2x-4y=6 and 4x+2y=17 for example.

They are both in standard form, so you could change them to y=mx+b and graph it. The intersection is the correct answer.

You can also solve one of the equations for y or x, and substitute that into the other equation, and solve for both x and y

or, you could add the two equations together and solve for x and y.

You can't simplify them.

Answer:

what is this......................

Step-by-step explanation:

0.33 so says my mother bc she divide

Answer:

The probability of drawing a different marble is 0.25. The probability of drawing a red marble = 0.5

I do not know if this is correct please forgive me if I am wrong.

If I am right hope this helps!