Answer:
43.15
Step-by-step explanation:
Answer:
b) ![4x^2-12x+9=0](https://tex.z-dn.net/?f=4x%5E2-12x%2B9%3D0)
Step-by-step explanation:
We can use the discriminant
to determine how many real solutions a quadratic equation in the form
has.
- discriminant > 0 ⇒ 2 real solutions
- discriminant = 0 ⇒ 1 real solution
- discriminant < 0 ⇒ no real solutions
![5x^2+9x-4=0](https://tex.z-dn.net/?f=5x%5E2%2B9x-4%3D0)
![b^2-4ac=9^2-4(5)(-4)=161 > 0\implies \textsf{2 solutions}](https://tex.z-dn.net/?f=b%5E2-4ac%3D9%5E2-4%285%29%28-4%29%3D161%20%3E%200%5Cimplies%20%5Ctextsf%7B2%20solutions%7D)
![4x^2-12x+9=0](https://tex.z-dn.net/?f=4x%5E2-12x%2B9%3D0)
![b^2-4ac=(-12)^2-4(4)(9)=0 \implies \textsf{1 solution}](https://tex.z-dn.net/?f=b%5E2-4ac%3D%28-12%29%5E2-4%284%29%289%29%3D0%20%5Cimplies%20%5Ctextsf%7B1%20solution%7D)
![-9x^2+6x+1=0](https://tex.z-dn.net/?f=-9x%5E2%2B6x%2B1%3D0)
![b^2-4ac=6^2-4(-9)(1)=72 > 0 \implies \textsf{2 solutions}](https://tex.z-dn.net/?f=b%5E2-4ac%3D6%5E2-4%28-9%29%281%29%3D72%20%3E%200%20%5Cimplies%20%5Ctextsf%7B2%20solutions%7D)
![-2x^2-7=0](https://tex.z-dn.net/?f=-2x%5E2-7%3D0)
![b^2-4ac=0^2-4(-2)(-7)=-56 < 0 \implies \textsf{no solutions}](https://tex.z-dn.net/?f=b%5E2-4ac%3D0%5E2-4%28-2%29%28-7%29%3D-56%20%3C%200%20%5Cimplies%20%5Ctextsf%7Bno%20solutions%7D)
Answer:
They are right, the time calculated using the exponential decay equation is 1948.6 years.
Step-by-step explanation:
The time can be calculated using the exponential decay equation:
(1)
<u>Where</u>:
N(t): is the quantity of C-14 at time t
N₀: is the initial quantity of C-14
λ: is the decay constant
The decay constant is:
(2)
By entering equation (2) into (1) and solving for t, we have:
![t = \frac{t_{1/2}*ln(N_{t}/N_{0})}{ln(2)} = \frac{5730*ln(0.79)}{ln(2)} = 1948.6 y](https://tex.z-dn.net/?f=%20t%20%3D%20%5Cfrac%7Bt_%7B1%2F2%7D%2Aln%28N_%7Bt%7D%2FN_%7B0%7D%29%7D%7Bln%282%29%7D%20%3D%20%5Cfrac%7B5730%2Aln%280.79%29%7D%7Bln%282%29%7D%20%3D%201948.6%20y%20)
Therefore, the time of the scrolls estimated by the archeologists is right, since the time calculated using the exponential decay equation is 1948.6 years.
I hope it helps you!
Answer:
34 hundredhs
Step-by-step explanation:
27 plus 7= 34
Answer: Choice D
![x_n = f(x_{n-1})](https://tex.z-dn.net/?f=x_n%20%3D%20f%28x_%7Bn-1%7D%29)
This basically says "the nth term is found by computing math, aka evaluating some function, based on the (n-1)th term".
As an example, we could have a function that simply squares the input
Let's say we started at 5. It squares to 25 which in turns squares to 625, and so on. Each new term is based on the old term. Namely, we squared the old n-1 term to get the new nth term.