Radioactive isotope X has a half-life of 500,000 years. This isotope may be found in some types of volcanic rocks. A particular sample of volcanic rock taken from a layer that covered up some of the earliest known human-like footprints contains 0.125 mg of isotope X. The volcanic rock sample originally contained 8.00 mg of isotope X. How long ago were these footprints made. I need the equation. Thanks. please I am stuck on this question. PLEASE

The age of the earliest known human-like footprints is approximately 3000000 years.

Explanation:

Decay of isotopes is represented by the following ordinary differential equation:

(Eq. 1)

Where:

- First derivative of mass with respect to time, measured in miligrams per year.

- Current mass of the isotope, measured in miligrams.

- Time constant, measured in years.

Now we proceed to obtain the solution of the differential equation:

(Eq. 2)

Where:

- Initial mass of the isotope, measured in miligrams.

- Time, measured in years.

- Time constant, measured in years.

We proceed to clear time within the formula presented above:

In addition, time constant can be found as a function of half-life:

(Eq. 3)

If we know that , and , the age of the earliest known human-like footprints is:

The age of the earliest known human-like footprints is approximately 3000000 years.

question: ray weighs 100 kilograms, his wrestling partner, bobby, weighs 50 kilograms. if ray moves at 4 m s , how fast will bobby have to run at him to apply an equal amount of kinetic energy?

answer: 8 m/s he needs to run twice as fast to keep up so he has some work to do

explanation:   if the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared.

question answered by

(jacemorris04)

5 structural isomers

the isomers are:

n-exane :   ch3ch2ch2ch2ch2ch3

2-methylpentane :   ch3ch(ch3)ch2ch2ch3

3-methylpentane :   ch3ch2ch(ch3)ch2ch3

2,3-dimethylbutane :   (ch3)2chch(ch3)2

2,2-dimethylbutane :   (ch3)3cch2ch3