Radioactive decay
find the half-life of a radioactive material for which 99.57% of the initial amount remains after 1 year.

t=160.82 years

Step-by-step explanation:

exponential decay function is

If initial amount A_1 is 100 then material remaining is 99.57

divide both sides by 100, question says 1 year so t=1

take ln on both sides

k=-.00431  

t=1, A= 50 remaining (half life)

divide both sides by 100

take ln on both sides

t=160.82 years

i think it is 18

step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.