The element plutonium-239 is highly radioactive. Nuclear reactors
can produce and also use this element. The heat that plutonium-239 emits has helped to
power equipment on the moon. If the half-life of plutonium-239 is 24,360 years, what is
the value of k for this element?

Step-by-step explanation:

The decay rate of a radioactive isotope (also called activity of the isotope) is given by:

where

r is the decay rate

k is the decay constant

N is the number of nuclei in the radioactive sample

The decay constant of a radioactive isotope is also related to the half-life of the isotope by the formula

where

is the half-life of the isotope, which is the time taken for the sample to halve, compared to its initial amount

In this problem, the half-life of plutioniun-239 is

Therefore, the k-factor (decay constant) is:

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl