As you know, when a course ends, students start to forget the material they have learned. one model (called the ebbinghaus model) assumes that the rate at which a student forgets material is proportional to the difference between the material currently remembered and some positive constant, a. a. let y=f(t)be the fraction of the original material remembered t weeks after the course has ended. set up a differential equation for y, using k as any constant of proportionality you may need (let k> 0). your equation will contain two constants; the constant a (also positive) is less than y for all t.

Bring the fraction a/a-4 to a denominator of 16-a^2

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

Written as a simplified polynomial in standard form, what is the result when (2x+8)^2(2x+8) 2 is subtracted from 8x^2-38x 2 −3?