In applying the euclidean algorithm to find the gcd(a, b) for some integers a and b, some remainder ri is a prime number. prove that gcd(a, b) = ri or 1. when does each case occur? hint: consider ri+1.

Find the coordinates of point x that lies along the directed line segment from y(-8, 8) to t(-15, -13) and partitions the segment in the ratio of 5: 2.

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a.what is the independent and dependent variables? b.find the amplitude and the period of the function. c.create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.

Select all the expressions that will include a remainder.