Suppose that the position of one particle at time t isgiven by the equations x1 andy1. meanwhile, the position of a secondparticle is given by the equations x2 andy2.
x1 = 3sin(t)
y1 = 2cos(t)
0 ≤ t ≤ 2π

x2 = -3 +cos(t)
y2 = 1 + sin(t)
0 ≤ t ≤ 2π

(a) graph the paths of both particles. (do this on paper. yourinstructor may ask you to turn in this work.) how many points ofintersection are there?
(b) find the collision point, where the particles are atthe same place at the same time.
(c) if the x-coordinate of the second particle is given byx2 = 3 +cos(t) instead, is there still a collision?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Find each value of the five-number summary for this set of data. [note: type your answers as numbers. do not round.] 150, 120, 136, 180, 158, 175, 124, 162 minimum maximum median upper quartile lower quartile

What is 617.3 miles and each gallon of gas the car can travel 41 miles select a reasonable estimate of the number of gallons of gas karl used.