You perform a perfect landing and have safely brought Captain Argos to Cartus. H

Question

You perform a perfect landing and have safely brought Captain Argos to Cartus. He can now deliver the semiconductors and the secret metallic box. In the meanwhile you stay in the ship. Although he is still upset about his chair..... Unbeknownst to you the Padisha Emperor is preparing to attack Cartus and one of his scouting ships recognizes you. The Emperor orders a "quiet" attack on your ship while waiting to put his battleships in position. The padishan ship shoots a small invisible Gatox ray that hits the main engine of your ship. All your energy controls shut down. After a brief inspection you discover that the rays have damaged one of the nevusian energy rings that propels your ship. This ring has the shape of a torus and is made of nutonion. The nevusian manual of the engine describes the energy ring as the surface z^2 + (Squareroot x^2 + y^2 - 4)^2 = 1, where the units are denuneters. The Gatox ray has crossed the torus transversally and pulverized the nutonion producing a hole that you model as a cylinder y^2 + z^2 = 0.35 Calculate the exact amount of nutonion needed. Nutonion is very expensive, so be careful with your calculations

Explanation / Answer

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Given Energy ring as the surface :-

z^2 + (sqrt ( x^2+y^2) -4) ^2 = 1

Also given hole as a cyliner = y^2+ z^2 = 0.35

We know the exact amount of nutonion needed = z^2 + (sqrt ( x^2+y^2) -4) ^2 / y^2+ z^2 = 1/0.35 = 2.857

Since nutonion is very expensive, so upto three significant figures it shall be calcualted hence exact answer is 2.857

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