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:
Height of slide = 5 feet (Approx.)
Step-by-step explanation:
Given:
Length of slide = 12 feet
Angle of depression = 25°
Find:
Height of slide
Computation:
Length of slide = Hypotenuse
Height of slide = Perpendicular
Using trigonometry function;
Sin θ = Perpendicular / Hypotenuse
Sin 25 = Height of slide / 12
0.422 = Height of slide / 12
Height of slide = 12 x 0.422
Height of slide = 5.064
Height of slide = 5 feet (Approx.)
The value of x in the equation is 4.2.
<h3>How to calculate the value?</h3>
It should be noted that the equation given is:
12(-11x + 5) + 7 = 2 (x-9) - 451
This will be computed thus:
12(-11x + 5) + 7 = 2 (x-9) - 451
-132x + 60 + 7 = 2x - 28 - 451
Collect like terms
-132x - 2x = - 28 - 451 - 60 - 7
-130x = -546
Divide
x = 546/130
x = 4.2
The value of x in the equation is 4.2.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Answer: 875 is the answer for your question
350 x 2.5 = 875 or 875 divided by 2.5 = 350
Pls mark me as brainliest
In order to answer this question, we must break this mathematical expression up into a series of mathematical operations (exponent, multiplication,division, addition, and/or subtraction):
"4 times a number" - The word "times" implies that we have to multiply 4 by an unknown number. We can simply label this unknown number as x.
"cubed" - In order to "cube" a number, we must raise it to the third power, or have an exponent of 3. Our unknown number of x now becomes x3 because we raised it to the third power.
"decreased by 7" - The word "decreased" implies that we must subtract 7 from the product of 4 multiplied by x3
With all of the information we now have, we can form an algebraic expression for this problem.
"4 times a number cubed decreased by 3" now becomes:
4x3 - 7