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lesya [120]
3 years ago
12

Show that any three linear operators A, B, and Ĉ satisfy the following (Ja- cobi) identity (10 pt) [[A, B] Ĉ] + [[B,C), A] + [[C

, A, B) = 0
Physics
1 answer:
DerKrebs [107]3 years ago
7 0

Answer:

Three linear operators A,B, and C will satisfy the condition [[A, B],C] + [[B,C), A] + [[C, A], B] = 0.

Explanation:

According to the question we have to prove.

[[A, B],C] + [[B,C), A] + [[C, A], B] = 0

Now taking Left hand side of the equation and solve.

[[A, B],C] + [[B,C), A] + [[C, A], B]

Now use commutator property on it as,

=[A,B] C-C[A,B]+[B,C]A-A[B,C]+[C,A]B-B[C,A]\\=(AB-BA)C-C(AB-BA)+(BC-CA)A-A(BC-CB)+(CA-AC)B-B(CA-AC)\\=ABC-BAC-CAB+CBA+BCA-CAB-ABC+ACB+CAB-ACB-BCA+BAC\\=0

Therefore, it is proved that [[A, B],C] + [[B,C), A] + [[C, A], B] = 0.

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If the resistors are arranged in a shape of a square, then they are in a series type of circuit. This circuit arrangement is a non-branching, one-way flow of electrons. The total resistance in a series circuit is the summation of the individual resistances, If you place the ohmmeter (measures resistance) on two non-adjacent sides, then, you are measuring the resistance of two of the resistors.

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The height of a projectile t seconds after it is launched straight up in the air is given by f (t )equals negative 16 t squared
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Answer:

\displaystyle a(5)=-32

Explanation:

<u>Instant Acceleration</u>

The kinetic magnitudes are usually related as scalar or vector equations. By doing so, we are assuming the acceleration is constant over time. But when the acceleration is variable, the relations are in the form of calculus equations, specifically using derivatives and/or integrals.

Let f(t) be the distance traveled by an object as a function of the time t. The instant speed v(t) is defined as:

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Or equivalently

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The given height of a projectile is

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Let's compute the speed

\displaystyle v(t)=-32t+238

And the acceleration

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It's a constant value regardless of the time t, thus

\boxed{\displaystyle a(5)=-32}

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