To solve this we are going to use the half life equation
![N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) }](https://tex.z-dn.net/?f=N%28t%29%3DN_%7B0%7D%20e%5E%7B%28%20%5Cfrac%7B-0.693t%7D%7Bt%20_%7B1%2F2%7D%20%7D%29%20%7D%20)
Where:
![N_{0}](https://tex.z-dn.net/?f=N_%7B0%7D%20)
is the initial sample
![t](https://tex.z-dn.net/?f=t)
is the time in years
![t_{1/2}](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%20)
is the half life of the substance
![N(t)](https://tex.z-dn.net/?f=N%28t%29)
is the remainder quantity after
![t](https://tex.z-dn.net/?f=t)
years
From the problem we know that:
![N_{0} =100](https://tex.z-dn.net/?f=N_%7B0%7D%20%3D100)
![t=200](https://tex.z-dn.net/?f=t%3D200)
![t_{1/2} =1600](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%20%3D1600)
Lets replace those values in our equation to find
![N(t)](https://tex.z-dn.net/?f=N%28t%29)
:
![N(200) =100e^{( \frac{(-0.693)(200)}{1600}) }](https://tex.z-dn.net/?f=N%28200%29%20%3D100e%5E%7B%28%20%5Cfrac%7B%28-0.693%29%28200%29%7D%7B1600%7D%29%20%7D%20)
![N(200)=100e^{( \frac{-138.6}{1600} )}](https://tex.z-dn.net/?f=N%28200%29%3D100e%5E%7B%28%20%5Cfrac%7B-138.6%7D%7B1600%7D%20%29%7D%20)
![N(200)=100e^{-0.086625}](https://tex.z-dn.net/?f=N%28200%29%3D100e%5E%7B-0.086625%7D%20)
![N(200)=91.7](https://tex.z-dn.net/?f=N%28200%29%3D91.7)
We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be
91.7 grams.
Answer:
4 ft.
Step-by-step explanation:
We can consider the orignial square's sides to be x, so area of the original figure: ![x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D)
The new rectangle's sides will be x and x+8, so the area of the new figure will be x^2+8x.
We know that the new area is 3 times the old one. So our equation will be:
x^2+8x=3x^2
our answer will be x=4.
Therfore, the length of the side of the old flower bed is 4 ft.
Answer:
10/3
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Step-by-step explanation:
<u>Step 1: Define</u>
1/3(4 + 18) - 2²
<u>Step 2: Evaluate</u>
- (Parenthesis) Add: 1/3(22) - 2²
- Exponents: 1/3(22) - 4
- Multiply: 22/3 - 4
- Subtract: 10/3
My guess would probably be ( 1 , 2 ) I searched it up and that’s where the points where , Hope I helped
An integer is just a whole number, so like 3 or 6 or 17. any number without a decimal.
The question is asking what number is less than 2 and 8.
the answer could be 5 or 3 or 4