Acontaminated rag has been decaying for 48 hours and its activity measured to be 10.72% of its original activity. what it the half-life isotope?
a- 0.04652 hrsb- 48 hrsc- 24.09 hrsd- 14.9 hrs

14.9 hrs

Explanation: Let N₀ and N be numbers of atoms in the beginning and after 48 hours of duration respectively. λ be the disintegration constant.

dN₀ / dt = λN₀

dN / dt = λN

Given

dN / dt = .1072 x dN₀ / dt

λN = .1072 x λN₀

N = .1072 x N₀

N₀e^{-\lambda 48 =.1072 x N₀

e^{-\lambda 48 =.1072

Taking ln on both sides

- λ x 48 = ln .1072

λ x 48 = 2.233

λ = 2.233 / 48

= .693 /λ

=( .693 /2.233 )X 48

= 14.9 hrs.

compass can be used day and night, cloudy or sunny

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.