Aperturbation in the temperature of a stream leaving a chemical reactor follows a decaying sinusoidal variation, according to the following mathematical equation,
t(t)=5e^(-at ).sin⁡(wt)
where a and w are constant.
then show that the temperature t (t) is maximum at time “t”. also verify that t= 1/w.〖tan〗^(-1) (w/a)
determine the maximum temperature value at t= 1/w.〖tan〗^(-1) (w/a).

19. explain why a magnet from your refrigerator could not be used to lift something as heavy as a car. (chapter 7 – pages 202-203) 20. can a magnet ever have a single pole? explain your answer. (chapter 7 – page 208) 21. what happens to the wavelength of a wave if the frequency is increased? (chapter 9 – pages 280-281) 22. an ocean wave has a wavelength of 10 m and a frequency of 4.0 hz. what is the velocity of the wave? show the appropriate equation from your book and show your work with units. (chapter 9 – page 282) 23. as you sit outside, the sound of a siren becomes lower in pitch. is the emergency vehicle moving away from or towards you? explain how you know. (chapter 10 – page 315-316) 24. why are two astronauts in space unable to hear one another? (chapter 10 – page 307) 25. explain in at least 3 sentences how electromagnetic waves form. (chapter 11 – page 338-339) 26. using the chart on page 345 in your textbook, what are the three types of electromagnetic wave with wavelengths shorter than those of visible light. give an example of each. (chapter 11 – pages 345-351) 27. explain why a leaf usually appears to be green, but a rose typically appears red. (chapter 12 – page 373) 28. what is the difference in light that is refracted compared to light that is reflected? think in terms of speed of light as well as what happens to light waves when they interact with a medium. (chapter 12 – pages 369-370) 29. how are concave and convex lenses different? (chapter 13 – page 408-410) 30. what type of mirror is used in rearview mirrors in cars? why is it important that these mirrors have the warning, “objects in mirror are closer than they appear.”? (chapter 13 – page 405)

Write the function getkthdigit(n, k) that takes a possibly-negative int n and a non-negative int k, and returns the kth digit of n, starting from 0, counting from the right

What is the orbital period of a spacecraft in a low orbit near the surface of mars? the radius of mars is 3.4×106m.