Answer:
t = 8588 years
Step-by-step explanation:
From the given information:
Using the formula:
![k = \dfrac{In (2)}{t_{1/2}}](https://tex.z-dn.net/?f=k%20%3D%20%5Cdfrac%7BIn%20%282%29%7D%7Bt_%7B1%2F2%7D%7D)
Given that:
= 5730 years
Then:
![k = \dfrac{In (2)}{5730}](https://tex.z-dn.net/?f=k%20%3D%20%5Cdfrac%7BIn%20%282%29%7D%7B5730%7D)
![k = \dfrac{0.6931472}{5730}](https://tex.z-dn.net/?f=k%20%3D%20%5Cdfrac%7B0.6931472%7D%7B5730%7D)
k = 1.20968 × 10⁻⁴
However; the expression to find the value of x is:
![x= x_oe^{-kt}](https://tex.z-dn.net/?f=x%3D%20x_oe%5E%7B-kt%7D)
![4.6 \times 10^{-13} = 1.3 \times 10^{-12} \times e^{(-1.20968\times 10^{-4} \times t)}](https://tex.z-dn.net/?f=4.6%20%5Ctimes%2010%5E%7B-13%7D%20%3D%201.3%20%5Ctimes%2010%5E%7B-12%7D%20%5Ctimes%20e%5E%7B%28-1.20968%5Ctimes%2010%5E%7B-4%7D%20%5Ctimes%20t%29%7D)
![\dfrac{4.6 \times 10^{-13} }{1.3 \times 10^{-12}}= e^{(-1.20968\times 10^{-4} \times t)}](https://tex.z-dn.net/?f=%5Cdfrac%7B4.6%20%5Ctimes%2010%5E%7B-13%7D%20%7D%7B1.3%20%5Ctimes%2010%5E%7B-12%7D%7D%3D%20%20e%5E%7B%28-1.20968%5Ctimes%2010%5E%7B-4%7D%20%5Ctimes%20t%29%7D)
![0.353846= e^{(-1.20968\times 10^{-4} \times t)}](https://tex.z-dn.net/?f=0.353846%3D%20%20e%5E%7B%28-1.20968%5Ctimes%2010%5E%7B-4%7D%20%5Ctimes%20t%29%7D)
(-1.20968 × 10⁻⁴ × t) = In(0.353846)
(-1.20968 × 10⁻⁴ × t) = -1.03889
![t = \dfrac{-1.03889}{-1.20968 \times 10^{-4}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B-1.03889%7D%7B-1.20968%20%5Ctimes%2010%5E%7B-4%7D%7D)
t = 8588 years
Short Answer f(x) down 5 units, left 2 units and right side up from g(x)
Step OneFind out what -g(x+2) is.
There are two steps to this. The first is to deal with the minus sign
(g(x)) = - x^2 + 5. Be very careful what you do next.
Put brackets around both terms on the right.
g(x) = (-x^2 + 5) Now put the minus sign in front of g(x) and another one in front of the brackets.
-g(x) = - (-x^2 + 5) Remove the brackets.
-g(x) = x^2 - 5
<em>Result</em>
So far g(x) moves down 5 units and opens upward.
Step TwoThe second step is to see what the x + 2 does.
-g(x + 2) = (x + 2)^2 - 5
The final result is that the graph opens upward, moves left 2 spaces and down 5.
There is a graph enclosed to show you the key steps.
The red graph is g(x) = x^2 - 5
The blue graph is g(x+2) = (x+2)^2 - 5
Hello:<span>
the equation is : y = ax+b
the slope is a : a×(-3/4) = -1......(
perpendicular to a line : </span>
3x+4y-22=0 : another equation is : y = (-3/4)x +22/4 with the slope : (-3/4))
<span>
a =4/3 </span>
<span>an equation is : y - 4 = (4/3)(x-2)</span>
<span>
</span>
Answer:
6*6=36 sq cm
Step-by-step explanation:
The base is a square therefore the area is length * width
Definition of square also means all sides are equal therefore it would be 6*6
Answer:
x=2
Step-by-step explanation:
Step 1: Factor left side of equation.
(3x+1)(x−2)=0
Step 2: Set factors equal to 0.
3x+1=0 or x−2=0