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Nataly [62]
3 years ago
10

Which of the following statements provides the correct freezing and boiling points of water on the Celsius and Fahrenheit temper

ature scales?
Mathematics
1 answer:
dalvyx [7]3 years ago
6 0

Answer: i need a pic

Step-by-step explanation:

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Let y 00 + by0 + 2y = 0 be the equation of a damped vibrating spring with mass m = 1, damping coefficient b > 0, and spring c
stira [4]

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:

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

-\lambda(-b - \lambda) + 2 = 0 \ \\ \\\lambda^2 +\lambda b + 2 = 0

\lambda = \dfrac{-b \pm \sqrt{b^2 - 8}}{2}

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

(c)

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

(d)

From λ² + λb + 2 = 0

If b = 3; we get

\lambda^2 + 3\lambda + 2 = 0 \\ \\ (\lambda + 1) ( \lambda + 2 ) = 0\\ \\ \lambda = -1 \ or   \  \lambda = -2 \\ \\

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

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]

\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]

Let v₂ = 1, v₁ = -1

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

Let Eigenvector relating to  λ = -2 be:

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]

\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]

Let m₂ = 1, m₁ = -1/2

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

∴

\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]

So as t → ∞

\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 }

5 0
2 years ago
A wrestler weighed 112 1/2 a pound before his meet after he weighed 49/50 of his original weight what does he weigh now
aleksandr82 [10.1K]

Answer:

110 1/4 lb

Step-by-step explanation:

To answer this, multiply 112 1/2 pounds by 49/50:

225 lb     49      11025 lb

---------- * ----- = -------------- = 110 25/100 lb = 110 1/4 lb

  2           50          100        

8 0
3 years ago
Enter the coordinates of the point<br> on the unit circle at the given angle. 0°
Zanzabum

Answer:

is there a photo to go with this??

Step-by-step explanation:

?

8 0
3 years ago
Suppose the path of a baseball follows the path graphed by the quadratic function ƒ(d) = –0.6d2 + 5.4d + 0.8 where d is the hori
Vinil7 [7]

Answer:


Domain is all real numbers


Range is


y\le 12.95



Step-by-step explanation:


The given function is


f(d)=-0.6d^2+5.4d+0.8


This is a maximum quadratic function therefore the domain is all real numbers.


Let us complete the square to find the vertex.



f(d)=-0.6(d^2-9d)+0.8



f(d)=-0.6(d^2+9d)+-0.6(\frac{9}{2})^2- -0.6(\frac{9}{2})^2+ 0.8




f(d)=-0.6(d-\frac{9}{2})^2+\frac{243}{20}+ 0.8





f(d)=-0.6(d-\frac{9}{2})^2+\frac{259}{20}






Therefore the range is




y\le \frac{259}{20}



y\le 12.95


See graph




5 0
3 years ago
Read 2 more answers
How many subsets does the set A have? A={-3,-2,-1,0,1,2,3}
lions [1.4K]

Answer:

128

Step-by-step explanation:

You find the number of subsets of a set by using the formula 2^{\text{ number of elements}.

We have 7 elements so that means we have 2^{7}=128 subsets.

6 0
3 years ago
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