A rock sample containing an isotope with a half-life of 28 million years has an initial mass of 184 grams. how much time has ela
1 answer:
<h2>Half Life</h2>
The half life period is the time in which only half of the given population remains. It can be represented through this equation:
- <em>t</em> = time passed
- <em>a</em> = y-intercept
- <em>h</em> = half life
We're given:
- <em>h</em> = 28 million years
- <em>a</em> = 184 grams (this is the initial mass, after 0 time has passed)
For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.
This can be calculated simply by multiplying the given half-life by 3:
28 million years x 3
= 84 million years
<h2>Answer</h2>84 million years
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Answer:
We have 4 solutions:
- No 10-foot truck, 10 14-foot trucks, and 15 24-foot trucks
- 2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks
- 4 10-foot trucks, 4 14-foot trucks, and 17 24-foot trucks
- 6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks
Step-by-step explanation:
Let the number of 10-foot truck with a capacity of 350 cubic feet purchased=a
Let the number of 14-foot truck with a capacity of 700 cubic feet purchased=b
Let the number of 24-foot truck with a capacity of 1,400 cubic feet purchased=c
The company wants to purchase 25 trucks, therefore.
- a+b+c=25
Furthermore, the combined capacity of the trucks is 28,000 cubic feet.
- 350a+700b+1400c=28000
Since the number of equations is less than the number of variables, you can not use a matrix equation to solve this problem. The solution is most easily found using an augmented matrix.
The augmented matrix is presented below:
Using the calculator, the reduced row echelon form is:
where
a- 2c=-30 means a =2c-30
b+3c=55 means b= 55-3c
We alter the value of c as long as neither a nor b becomes negative. Suitable values for c are 15, 16, 17, and 18:
We can easily verify that, for each solution, the number of trucks adds up to 25 and the fleet capacity is 28,000 cubic feet.
We therefore have 4 solutions:
- No 10-foot truck, 10 14-foot trucks, and 15 24-foot trucks
- 2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks
- 4 10-foot trucks, 4 14-foot trucks, and 17 24-foot trucks
- 6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks
Answer:
2x - 6y = 18
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Given
x = 2y + 6
Multiply through by 3 to clear the fraction
2x = 6y + 18 ( subtract 6y from both sides )
2x - 6y = 18 ← in standard form