Question

Show work and provide proper units for your answers 1. Given: Mars has a polar diameter of 6752 kilometers, and the Mars Reconnaissance Orbiter(MRO) comes as close to the planet as 255 kilometers at the south pole and 320 kilometers at the north pole. a. What is the diameter of the orbit of the MRO? 320Km (2 pts.) 255 km b. How far does the MRO travel in one orbit? (3 pts.) HINT: MRO's orbit is near enough to circular that the circumference formula for a circle (C-t) can be used 2. a. Find the value of (-1). (Recall that i is the imaginary unit. To obtain i on the graphics calculator, press the 2nad key and then the. key. Approximate your answer to 9 decimal places. (2 pts.) b. What famous number is the value in part a. an approximation of? (2 pts.) c. Which famous mathematician is credited with the discovery of the number approximated in part a.? (1 pt.)

Answer 1

1)

a) Diameter of the orbit of MRO = Polar diameter of mars + distance between MRO and mars at south pole + distance between MRO and mars at north pole.

Therefore, Diameter of the orbit of MRO = 6752 + 255 + 320 = 7327 kilometer

b) Distance traveled by MRO in an orbit = Circumference of the circle with diameter of 7327 km

C-nd k 7327- 23027.7143

MRO traveled approximately 23,027 kilometers and 71 meters in an orbit.

2)

a) $(-1)^\frac{-i}{\pi }=2.71828182846\approx 2.718281829$    (using calculator)

b) 2.718281829 is an approximated value of 'e'

c) The famous number 'e' was discovered by a famous mathematician 'Leonhard Euler'