Answer:
The first derivative of
is
.
Step-by-step explanation:
Let
. we can determine its first derivative by Rule for the Square Root Function, Rule for Power Function, Rule of Chain and Rule for the Addition of Functions, Rule for the Subtraction of Functions, Rule for the Division of Functions:
![y' = \frac{1}{2\cdot \sqrt{\frac{1-x}{1+x} }}\cdot \frac{(-1)\cdot (1+x)-(1)\cdot (1-x)}{(1+x)^{2}}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B1%7D%7B2%5Ccdot%20%5Csqrt%7B%5Cfrac%7B1-x%7D%7B1%2Bx%7D%20%7D%7D%5Ccdot%20%5Cfrac%7B%28-1%29%5Ccdot%20%281%2Bx%29-%281%29%5Ccdot%20%281-x%29%7D%7B%281%2Bx%29%5E%7B2%7D%7D)
![y' = \frac{1}{2}\cdot \sqrt{\frac{1+x}{1-x} }\cdot \left[\frac{-1-x-1+x}{(1+x)^{2}} \right]](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%5Csqrt%7B%5Cfrac%7B1%2Bx%7D%7B1-x%7D%20%7D%5Ccdot%20%5Cleft%5B%5Cfrac%7B-1-x-1%2Bx%7D%7B%281%2Bx%29%5E%7B2%7D%7D%20%5Cright%5D)
![y' = \frac{1}{2}\cdot \sqrt{\frac{1+x}{1-x} } \cdot \left[-\frac{2}{(1+x)^{2}} \right]](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%5Csqrt%7B%5Cfrac%7B1%2Bx%7D%7B1-x%7D%20%7D%20%5Ccdot%20%5Cleft%5B-%5Cfrac%7B2%7D%7B%281%2Bx%29%5E%7B2%7D%7D%20%5Cright%5D)
![y' = -\frac{1}{(1-x)\cdot (1+x)^{3/2}}](https://tex.z-dn.net/?f=y%27%20%3D%20-%5Cfrac%7B1%7D%7B%281-x%29%5Ccdot%20%281%2Bx%29%5E%7B3%2F2%7D%7D)
The first derivative of
is
.
Answer: 2500 years
Step-by-step explanation:
I'm not quite sure if I'm doing this right myself but I'll give it a shot.
We use this formula to find half-life but we can just plug in the numbers we know to find <em>t</em>.
![A(t)=A_{0}(1/2)^t^/^h](https://tex.z-dn.net/?f=A%28t%29%3DA_%7B0%7D%281%2F2%29%5Et%5E%2F%5Eh)
We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For
let's just assume that there are 100 original atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. <em>h</em> is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.
![74=100(1/2)^t^/^5^7^3^0](https://tex.z-dn.net/?f=74%3D100%281%2F2%29%5Et%5E%2F%5E5%5E7%5E3%5E0)
Now, solve. First, divide by 100.
![0.74=(0.5)^t^/^5^7^3^0](https://tex.z-dn.net/?f=0.74%3D%280.5%29%5Et%5E%2F%5E5%5E7%5E3%5E0)
Take the log of everything
![log(0.74)=\frac{t}{5730} log(0.5)](https://tex.z-dn.net/?f=log%280.74%29%3D%5Cfrac%7Bt%7D%7B5730%7D%20log%280.5%29)
Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the <em>t</em> and get
![5730\frac{log(0.74)}{log(0.5)} =t](https://tex.z-dn.net/?f=5730%5Cfrac%7Blog%280.74%29%7D%7Blog%280.5%29%7D%20%3Dt)
Use your calculator to solve that giant mess for <em>t </em>and you'll get that <em>t</em> is roughly 2489.128182 years. Round that to the nearest hundred years, and you'll find the hopefully correct answer is 2500 years.
Really hope that all the equations that I wrote came out good and that that's right, this is definitely the longest answer I've ever written.
Answer:
24°
Step-by-step explanation:
Since m||n
55°=(x+31)°
55-31=x
24°=x
The graphical representation is give in image
Answer:
none
Step-by-step explanation:
i do not thinn it is any of these as 180 -120 =60 so uvt is 60 and t is 50. every triangles angles add up to 180 so 50 +60 = 110 and 180 -110 is 70. so i think the answer is 70 degrees and if i am wrong please correct me and explain how.