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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

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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3 years ago

A vacuum cleaner produces sound with a measured sound level of 75.0 dB. (a) What is the intensity of this sound in W/m2? W/m2 (b

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Answer:

Part a)

$I = 3.16 \times 10^{-5} W/m^2$

Part b)

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Explanation:

Part a)

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here we know that

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now we have

$75 = 10 Log(\frac{I}{10^{-12}})$

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Part b)

Intensity of sound wave is given as

$I = \frac{1}{2}\rho A^2\omega^2 c$

here we know that

$A = \frac{P_o}{Bk}$

so we have

$I = \frac{1}{2}\rho(\frac{P_o}{Bk})^2\omega^2 c$

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3 years ago

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AVprozaik [17]

Answer:

T_finalmix = 59.5 [°C].

Explanation:

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Now replacing:

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