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ArbitrLikvidat [17]
3 years ago
13

Prove the theorem (AB )^T= B^T. A^T

Mathematics
1 answer:
Lisa [10]3 years ago
3 0

Answer:

(AB)^T = B^T.A^T  (Proved)

Step-by-step explanation:

Given  (AB )^T= B^T. A^T;

To prove this expression, we need to apply multiplication law, power law and division law of indices respectively, as shown below.

(AB)^T = B^T.A^T\\\\Start, from \ Right \ hand \ side\\\\B^T.A^T = \frac{B^T.A^T}{A^T}.\frac{B^T.A^T}{B^T} (multiply \ through) \\\\                = \frac{A^{2T}.B^{2T}}{A^T.B^T} \\\\=\frac{(AB)^{2T}}{(AB)^T} \ \ (factor \ out \ the power)\\\\= (AB)^{2T-T}  \ (apply \ division \ law \ of \ indices; \ \frac{x^a}{x^b} = x^{a-b})\\\\= (AB)^T \ (Proved)

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Use the distributive property to remove the parentheses.<br> (w-4)7
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A representative of a car manufacturer in the United States made the following claim in a news report. "Ten years ago, only 53 p
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According to the p-value, the correct option regarding the decision of the test hypothesis is:

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<h3>What are the hypothesis tested?</h3>

At the null hypothesis, we test if the proportion is still of 0.53, that is:

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2 years ago
the north pole is in the middle of the ocean. A person at sea level at the north pole would be 3,949 miles from the center of th
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Answer:

7,897.30 miles

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It is given that the North Pole is at a distance of 3,949 miles from the center of the earth.

We also know that the sea floor is below 2.4 miles from the sea level.

It is given that a submarine is located at the sea floor near North Pole. Hence, the distance of the submarine from the center of the earth would be

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On the other hand, the South Pole is given to be at an elevation of 1.7 miles from the sea level.

Since we know that the sea level is at a distance of 3949 miles from the center of the earth, we can immediately calculate the distance of the South Pole from the center of the earth to be

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Putting all of this together, we see that the center of the earth is at a distance of 3946.6 miles from the submarine near the North Pole, and the center of the earth in turn is 3950.7 miles from the South Pole.

Hence, the distance between the submarine and a person on the South Pole = 3946.6 + 3950.7 = 7897.3 miles.

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