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suter [353]
3 years ago
6

g Problem 2. (4 points) Suppose we convert the difference equation x(t+ 1) = 7x(t) + 8x(t−1), t = 1, 2, 3, · · · with x(0) = 1 a

nd x(1) = 3 into the matrix form ? x(t + 1) x(t) ? = ? 7 8 1 0? ? x(t) x(t − 1)? , t = 1, 2, 3, · · · Which of the following statements must be TRUE? (I) The matrix A = ? 7 8 1 0? is diagonalizable, for example, with P = ? −1 8 1 1? , there exists a matrix D = ? −1 0 0 8? such that P −1AP = D. (II) Suppose we let u(t+1) = ? x(t + 1) x(t) ? , then there exists an 2 by 2 invertible matrix P and a diagonal matrix D such that u(t) = P Dt−1P −1 ? 3 1 ? (III) Suppose we let u(t + 1) = ? x(t + 1) x(t) ? , then u(t) = 5 9 (−1)t−1 ? −1 1 ? + 4 9 (8)t−1 ? 8 1 ? , t = 0, 1, 2, · · · (A) I only (B) II only (C) I and II only (D) II and III only (E) I, II, and III
Mathematics
1 answer:
miss Akunina [59]3 years ago
6 0

Answer:

From the equations given

7x(t)+8x(t-1)=x(t+1)

where t=1,2,3

and initial conditions are

x(0)=1

x(1)=3

From the given data

Option C is correct

II and III only

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Sophia manages a landfill. She decides to measure the rate at which trash increases in volume to fill the landfill as the number
goblinko [34]

Answer:

\frac{m^3}{h}, \frac{cm^3}{h},  \frac{km^3}{h}

Step-by-step explanation:

If you look at the objects thrown as garbage, it's a two- or three-dimensional item that takes up space and also has mass and this is a solid waste.

And the landfill that dumps such garbage is also three-dimensional.

Hence, the volume module, if the object inside is a solid, either would be

m^3,cm^4,Km^3

As household numbers rise, landfill space increases.

So,

household\ number = Proportionality\times  landfill\ space

If H represents the number of household keeps,  then it will be a sufficient unit for the purpose of Sophia that is

\frac{m^3}{h}, \frac{cm^3}{h},  \frac{km^3}{h}

7 0
3 years ago
Factor the quadratic equation 0=15x squared + 39 x-18
leva [86]

Answer:

The factors of given quadratic equation

<em>   </em>x = \frac{9}{15} and x = -2<em />

Step-by-step explanation:

<u><em>Explanation:-</em></u>

<em>Given quadratic equation 15x² +39 x -18 =0</em>

<em> The factors of 270 = 30 × 9</em>

<em>The quadratic equation 15x² +39 x -18 =0</em>

<em>                                    ⇒ 15 x² +30 x-9x -18=0</em>

<em>                                 ⇒ 15x(x+2) -9( x+2) =0</em>

<em>                                ⇒( 15x -9)(x+2) = 0</em>

<em>                       15x - 9=0    and  x+2 =0</em>

<em>                       15 x =9   and  x = -2</em>

<em>                       </em>x = \frac{9}{15} and x = -2<em />

<u><em></em></u>

3 0
3 years ago
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Kaylis [27]
A square i believe.

Hope this helps !
8 0
2 years ago
Read 2 more answers
Projected time:30 seconds, actual time 27 seconds
slega [8]
3 seconds and what are you saying need more information
3 0
3 years ago
See if you can find x ??
777dan777 [17]

Answer:

just do 130 +5x+19=180

4 0
3 years ago
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