In order to get a weight reduction, a 15 cm diameter solid steel shaft rotating at 150 rpm. The shaft is 3 meters long and the d
ensity of steel is 8.05 g/cm3. This shaft is replaced by a Titanium (p = 4.506 g/cm3) tube with a 15 cm OD and an 10 cm ID. Determine the reduction in kinetic energy in this system.
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Answer:
prove that | S | = | E | ; every element of S there is an Image on E , while not every element on E has an image on S
Explanation:
Given that S = { p q |p, q are prime numbers greater than 0}
E = {0, −2, 2, −4, 4, −6, 6, · · · }
To prove by constructing a bijection from S to E
detailed solution attached below
After the bijection :
<em>prove that | S | = | E |</em> : every element of S there is an Image on E , while not every element on E has an image on S
∴ we can say sets E and S are infinite sets
