Handwri.te and show all work and steps

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Part 1 - Application An airplane is flying on a bearing of 170 at 495 mph. Find the component form of the velocity of the airplane. Be sure to show and explain your work. Part 2 - Find the error(s) and solve the problem correctly. Be sure to show and explain your work. An airplane is ying on a compass heading (bearing) of 170 at 460 mph. A wind is blowing with the bearing 200 at 80 mph. a. Find the component form of the velocity of the airplane. b. Find the actual ground speed and direction of the airplane Answer: a. v = 460 = b. Find the wind vector w = 80 = Velocity vector = v + w = Actual speedl |v + w| |\\/( 528.19) 2 + (52.52) 2z530.79 mph Actual direction: 9 = 180 + tan '1(_:9)= 95-68 Be sure to show and explain all work. 10 points each Application The table below shows the February balance of a simple interest savings account each year from 2015 to 2021 2015 2016 2017 2018 2019 2020 2021 Ba'ance $12,000 14018 16036 18054 20072 22090 24108 Do the balances form an arithmetic or geometric sequence? What is the d or the I'? Write a formula for the balance in the account n years after February 2015. Find the sum of the February balances from 2015 to 2032, inclusive. Find the error(s) and solve the problem correctly. Determine whether the sequence converges or diverges. How do you know if it converges or diverges? If it converges, give the limit. 5111 n+1 Answer: Diverges because of the degree of the numerator and denominator. Part 1 - Application Write an equation for the orbit of Saturn in the form of +- 1 a Table 8.1 Semimajor Axes and Eccentricities of the Planets and Pluto Object Semimajor Axis (Gm) Eccentricity Mercury 57.9 0.2056 Venus 108.2 0.0068 Earth 149.6 0.0167 Mars 227.9 0.0934 Jupiter 778.3 0.0485 Saturn 1427 0.0560 Uranus 2869 0.0461 Neptune 1497 0.0050 Pluto 5900 0.2484 Source: Shupe et al., National Geographic Atlas of the World (rev. 6th ed.). Washington, DC: National Geographic Society, 1992, plate 116, and other sources. Part 2 - Find the error(s) and solve the problem correctly. Convert the polar equation to rectangular form and identify the graph. Support your answer by sketching the graph. Show and explain your work. r = - 4 cos 0 Answer: Cosine graph reflected over x-axis with amplitude 4 AAAAAAPart 1 - Exploration Let f (x) = 30 1+2 3-x a. Use tables and graphs to find lim f(x) and lim f(x) x - 00 x - - 00 b. Identify any horizontal asymptotes C. What is the y-intercept? d. How is the numerator of the fraction for f related to part b? e. Sketch the graph. Part 2 - Find the error(s) and solve the problem correctly. Find the derivative, if it exists, of the function at the specified point. f (x) = x - 4x + 3 at x = 1 Answer: f(1) = 1 - 4(1) + 3= 0 Part 3 - Discussion Question Explain in your own words how the derivative of a function can be viewed geometrically