PROJECT ON PARAMETRIC EQUATIONS 1. Preliminary definitions and data Your OSIS number is nine-digit combination 2ABCDEFGH. Digits ABCDEFGH will be used to generate initial data for the project. Below combinations 2AB, CDE, and FGH are considered as usual forms of three-digit numbers representation. For example, if OSIS# is 201345678, then 2AB=201, CDE=345, FGH=678. Please determine YOUR numbers very carefully because if you make a smallest error in initial data, there is no way to get correct answers and in this case, even if the method of solution is correct, no credit will be given. 2. Project task On the standard coordinate grid at initial moment, ship Tiger is at the position (0, CDE), ship Lion is at the position (FGH, 0). Tiger sails along the straight line to the position (2AB+FGH, 0). ((2AB PLUS FGH,0)). At the same time, Lion sails along the straight line to the position (0, CDE+2AB). ((0,CDE PLUS 2AB)). (PLUS is written here as word because arithmetic symbol of addition may be not displayed correctly in Skedula email.) Both ships will reach their destinations in two hours (120 minutes). In the example above, 2AB+FGH=678+201=879, CDE+2AB=345+201=546, therefore Tiger will move from position (0, 345) to position (879, 0), Lion will move from position (678, 0) to position (0, 546). Task: A. Find the point of intersection of the paths of the ships. B. At what time from the moment of departure (in minutes) each of the ships will pass the point of intersection of the paths. C. At what time (in minutes after departure) the distance between Lion and Tiger will be the shortest? D. What is the shortest distance between Lion and Tiger? If the shortest distance is equal 0, it means that the two ships collide. E. What will be the positions of both ships at the moment when the distance between them is the shortest? All numeric results should be calculated with 3 digits after decimal point. 3. Grading Correct answer to the question A 20 points (10 points for each of coordinates x,y.) Correct answer to the question B 20 points. Correct answer to the question C 20 points. Correct answer to the question D 20 points. Correct answer to the question E 20 points (5 points for each coordinate of each ship.) Project submitted on time 5 points. TOTAL up to 105 points. No credit will be given for incorrect answers regardless of the reason of error, THE PROJECT SHOULD BE COMPLETED BEFORE THE SPRING BREAK. IT CAN BE SUBMITTED FOR FULL CREDIT ON MONDAY APRIL 5TH. Every school day of delay after April 5 will result in 10 points off, regardless of the reason. A Google form to enter your results will be created. In that form, write ONLY DECIMAL NUMBERS. Be VERY ATTENTIVE writing your answers. NEVER write ordinary fractions. ONLY decimals. NEVER write literal expressions like x= or something else like that. NEVER write any units or any other words in your answers. Do not hesitate to ask questions if something in this task is not clear.

Osis: 219640620