Discrete Math Chapter 5 DBA Application The Blitzer Bonus on page 299 gives Einstein's special-relativity equation for the aging rate of an astronaut R o' relative to the aging rate of a friend on Earth R f of light. Read the information on page 299 then solve the following problem. You are moving at 90% of the speed of light. Substitute .9c in the equation shown. What is your aging rate (two decimal places) relative to a friend on Earth? If 100 weeks have passed for your friend, how long, to the nearest week, were you gone? , where v is the astronaut's speed and c is the speed 40 points TR T A Radical Idea: Time Is Relative R, relative to the aging rate of a friend, R, on Earth. In this formula, v is the astronaut's speed and is the speed of light. As the astronaut's speed approaches the speed of light, we can substitute for v. RNVO Simplify the radicand: 1 1 = O. R0 Vo =0 0 Multiply: RO = O, Irrational Numbers and Other Kinds of Roots _m:_:o:u_ numbers appear in the form of roots other than square roots. The symbol N represents the cube root of a number. For example, V8 =2because2-2-2 =8 and V64 = 4 because 4-4-4 = 64, Although these cube roots are rational numbers, most cube roots are not. For example, V217 = 6.0092 because (6.0092) = 216.995, not exactly 217. There is no end to the kinds of roots for numbers. For example, represents the fourth root of a number. Thus, V81 = 3 because 3-3-3-3 = 8I. Although the fourth root of 81 is rational, most fourth roots, fifth roots, and so on tend to be irrational. Digital Image The Museum of Modem At/ Licensed by Scala/Art Resource, NY; 2017 Salvador Dal, Fundaci Gala-Saivador Dall, Adists Rights Soclety What does travel in space have to do with square roots? Imagine that in the future we will be able to travel at velocities approaching the speed of light (approximately 186,000 miles per second). According to Einstein's theory of special relativity, time would pass more quickly on Earth than it would in the moving spaceship. The special- relativity equation gives the aging rate of an astronaut, Einstein's equation gives the aging rate of an astronaut, R, relative to the aging rate of a friend, R/, on Earth. The velocity, is approaching the speed of light, & so let v = A