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Oksanka [162]
3 years ago
12

How do I do this? please detail steps.

Mathematics
1 answer:
vladimir2022 [97]3 years ago
7 0
Define
{x} =   \left[\begin{array}{ccc}x_{1}\\x_{2}\end{array}\right]

Then
x₁ = cos(t) x₁(0) + sin(t) x₂(0)
x₂ = -sin(t) x₁(0) + cos(t) x₂(0)

Differentiate to obtain
x₁' = -sin(t) x₁(0) + cos(t) x₂(0)
x₂' = -cos(t) x₁(0) - sin(t) x₂(0)

That is,
\dot{x} =   \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right] x(0)

Note that
\left[\begin{array}{ccc}0&1\\-1&09\end{array}\right]   \left[\begin{array}{ccc}cos(t)&sin(t)\\-sin(t)&cos(t)\end{array}\right] =  \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right]

Therefore
x(t) =   \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right] x(t)

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Answer:

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Step-by-step explanation:

Let the width be represented by l - 5, where l is the length.

Use the area formula, A = lw, and plug in l - 5 as w, and 36 as the area. Then, simplify and factor

A = lw

36 = l(l - 5)

36 = l² - 5l

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Factor:

(l - 9)(l + 4)

Set equal to zero and solve for both solutions:

(l - 9)(l + 4) = 0

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The length cannot be negative, so the answer has to be 9.

The length is 9 centimeters

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