Answer:
![x_{n+1} = x_{n} - \frac{f(x_{n} )}{f^{'}(x_{n})}](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%20%3D%20x_%7Bn%7D%20-%20%5Cfrac%7Bf%28x_%7Bn%7D%20%29%7D%7Bf%5E%7B%27%7D%28x_%7Bn%7D%29%7D)
![x_{1} = -10](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20-10)
![x_{2} = -3.95](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20-3.95)
Step-by-step explanation:
Generally, the Newton-Raphson method can be used to find the solutions to polynomial equations of different orders. The formula for the solution is:
![x_{n+1} = x_{n} - \frac{f(x_{n} )}{f^{'}(x_{n})}](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%20%3D%20x_%7Bn%7D%20-%20%5Cfrac%7Bf%28x_%7Bn%7D%20%29%7D%7Bf%5E%7B%27%7D%28x_%7Bn%7D%29%7D)
We are given that:
f(x) =
; ![x_{0} = -21](https://tex.z-dn.net/?f=x_%7B0%7D%20%3D%20-21)
= df(x)/dx = 2x
Therefore, using the formula for Newton-Raphson method to determine
and ![x_{2}](https://tex.z-dn.net/?f=x_%7B2%7D)
![x_{1} = x_{0} - \frac{f(x_{0} )}{f^{'}(x_{0})}](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20x_%7B0%7D%20-%20%5Cfrac%7Bf%28x_%7B0%7D%20%29%7D%7Bf%5E%7B%27%7D%28x_%7B0%7D%29%7D)
![f(x_{0}) = x_{0} ^{2} + 21 = (-21)^{2} + 21 = 462](https://tex.z-dn.net/?f=f%28x_%7B0%7D%29%20%3D%20x_%7B0%7D%20%5E%7B2%7D%20%2B%2021%20%3D%20%28-21%29%5E%7B2%7D%20%2B%2021%20%3D%20462)
![f^{'}(x_{0}) = 2*(-21) = -42](https://tex.z-dn.net/?f=f%5E%7B%27%7D%28x_%7B0%7D%29%20%3D%202%2A%28-21%29%20%3D%20-42)
Therefore:
![x_{1} = -21 - \frac{462}{-42} = -21 + 11 = -10](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20-21%20-%20%5Cfrac%7B462%7D%7B-42%7D%20%3D%20-21%20%2B%2011%20%3D%20-10)
Similarly,
![x_{2} = x_{1} - \frac{f(x_{1} )}{f^{'}(x_{1})}](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20x_%7B1%7D%20-%20%5Cfrac%7Bf%28x_%7B1%7D%20%29%7D%7Bf%5E%7B%27%7D%28x_%7B1%7D%29%7D)
![f(x_{1}) = (-10)^{2} + 21 = 100+21 = 121](https://tex.z-dn.net/?f=f%28x_%7B1%7D%29%20%3D%20%28-10%29%5E%7B2%7D%20%2B%2021%20%3D%20100%2B21%20%3D%20121)
![f^{'}(x_{1}) = 2*(-10) = -20](https://tex.z-dn.net/?f=f%5E%7B%27%7D%28x_%7B1%7D%29%20%3D%202%2A%28-10%29%20%3D%20-20)
Therefore:
![x_{2} = -10 - \frac{121}{20} = -10+6.05 = -3.95](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20-10%20-%20%5Cfrac%7B121%7D%7B20%7D%20%3D%20-10%2B6.05%20%3D%20-3.95)
Answer:
3x6 = 729x when ever a number has an exponnet yo have to multiply the main number to itself as many times as it says.
So in this case you had to multiply 3 by itself(3) 6 times would be
(3x) x (3x) x (3x) x (3x) x (3x) x (3x) = 729x. And of course bring the variable.
x2 So when theres a varible that is by itself for example (x) you always add a 1 in front of it. so in this case x2 would be 1x2. 1 times itself(1) 2 times would be. (1x) x (1x) = 1x
729 smaller cubes would fit inside the larger cube.
<em>Show your work so your teacher can see your thinking. I know it looks a little bit confusing but trust me the more you do it the easier it gets.</em>
Answer:
The component on the left of original one would be
30 x cos45 =30 x sqrt2/2 =~21.21
The component on the right of original one would also be
30 x cos45 =30 x sqrt2/2 =~21.21