COMPLETE ALL. THEY MUST HAVE STEP BY STEP WITH EXPLANATIONS.

ORIGINAL ANSWERS

I WILL GIVE GOOD OR BAD FEEDBACK BASED ON THE FINAL SCORE. SO PLEASE TUTORS DO YOUR BEST, I NEED EXPERTS ON CALCULUS HERE, TAKE YOUR TIME BUT DO IT EXCELLENT. THANK YOU

Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 100. The comet follows a parabolic path with directrix x = 70 and vertex at (60, 0). Part A: Write the equation of the planet's orbit in standard form. Show your work. (2 points) Part B: Write the equation of the comet's path in standard form. Show your work. (4 points) Part C: Identify all points where the planet's orbit intersects the path of the comet. Show your work and round answers to the hundredths place. (4 points)A system of equations is made up of an ellipse and a hyperbole. Part A: Create the equation of an ellipse centered at the origin, with a vertical major axis of 12 units and a minor axis of 6 units. Show your work. (3 points) Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (5, 0), and asymptotes of y - 12x. Show your work. (4 points) Part C: Determine the domain of each conic section and use it to explain why there is no solution to the system. (3 points) An architect has designed two tunnels. Tunnel A is modeled by x2 + yz + 20x -69 = 0, and tunnel B is modeled by x2 - 40x + 16y + 160 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels. Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points) Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. (4 points) Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work. (7 points)2 2 In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by (x 211:): + {127:1 and Comet H is modeled by (X11143) _% =1. where all measurements are in astronomical units. Part A: What are the vertices for the path of Comet E? Show your won<. points part b: which comet travels closer to the sun give evidence support your answer. pomts c: what key feature does represent for both comets lionfish are considered an invasive species with annual growth rate of a scientist estimates there in certain bay after first year. a: write explicit equation f that represents number n years. show all necessary math work. how many will be years round nearest whole and if scientists remove fish per year from is recursive sequence given. assuming pattern continues list next four terms sequence. sign positive or negative justify reasoning mathematically without determining value applicant receives job offer two different companies. starting salary increase b yea determine whether can represented by arithmetic geometric series total received mathematically. provide greater income hiker on appalachian trail planned distance covered each day. days traveled miles. miles did travel day answer mile sn this hundredths place work>