Answer:
2 sqr 6+4 or A
Step-by-step explanation:
Answer:
18 2/3
Step-by-step explanation:
Answer:
ur answer is 2/3 bc u divide both number by 2 and it would be 2/3
Step-by-step explanation:
Answer:
![x \approx 2.278863](https://tex.z-dn.net/?f=x%20%5Capprox%202.278863)
Step-by-step explanation:
Required
The positive root of ![3\sin(x) = x](https://tex.z-dn.net/?f=3%5Csin%28x%29%20%3D%20x)
Equate to 0
![0 = x -3\sin(x)](https://tex.z-dn.net/?f=0%20%3D%20x%20-3%5Csin%28x%29)
So, we have our function to be:
![h(x) = x -3\sin(x)](https://tex.z-dn.net/?f=h%28x%29%20%3D%20x%20-3%5Csin%28x%29)
Differentiate the above function:
![h'(x) = 1 -3\cos(x)](https://tex.z-dn.net/?f=h%27%28x%29%20%3D%201%20-3%5Ccos%28x%29)
Using Newton's method of approximation, we have:
![x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%20%3D%20x_n%20-%20%5Cfrac%7Bh%28x_n%29%7D%7Bh%27%28x_n%29%7D)
Plot the graph of
to get
--- see attachment for graph
From the attached graph, the first value of x is at 2.2; so:
![x_1 = 2.2](https://tex.z-dn.net/?f=x_1%20%3D%202.2)
So, we have:
![x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%20%3D%20x_n%20-%20%5Cfrac%7Bh%28x_n%29%7D%7Bh%27%28x_n%29%7D)
![x_{1+1} = x_1 - \frac{h(x_1)}{h'(x_1)}](https://tex.z-dn.net/?f=x_%7B1%2B1%7D%20%3D%20x_1%20-%20%5Cfrac%7Bh%28x_1%29%7D%7Bh%27%28x_1%29%7D)
![x_{2} = 2.2 - \frac{2.2 -3\sin(2.2)}{1 -3\cos(2.2)} = 2.28153641](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%202.2%20-%20%5Cfrac%7B2.2%20-3%5Csin%282.2%29%7D%7B1%20-3%5Ccos%282.2%29%7D%20%3D%202.28153641)
The process will be repeated until the digit in the 6th decimal place remains unchanged
![x_{3} = 2.28153641 - \frac{2.28153641 -3\sin(2.28153641)}{1 -3\cos(2.28153641)} = 2.2788654](https://tex.z-dn.net/?f=x_%7B3%7D%20%3D%202.28153641%20-%20%5Cfrac%7B2.28153641%20-3%5Csin%282.28153641%29%7D%7B1%20-3%5Ccos%282.28153641%29%7D%20%3D%202.2788654)
![x_{4} = 2.2788654 - \frac{2.2788654 -3\sin(2.2788654)}{1 -3\cos(2.2788654)} = 2.2788627](https://tex.z-dn.net/?f=x_%7B4%7D%20%3D%202.2788654%20-%20%5Cfrac%7B2.2788654%20-3%5Csin%282.2788654%29%7D%7B1%20-3%5Ccos%282.2788654%29%7D%20%3D%202.2788627)
![x_{5} = 2.2788627 - \frac{2.2788627-3\sin(2.2788627)}{1 -3\cos(2.2788627)} = 2.2788627](https://tex.z-dn.net/?f=x_%7B5%7D%20%3D%202.2788627%20-%20%5Cfrac%7B2.2788627-3%5Csin%282.2788627%29%7D%7B1%20-3%5Ccos%282.2788627%29%7D%20%3D%202.2788627)
Hence:
Answer:
6x
6x(x + 4)
Step-by-step explanation:
Both 6x^2 and 24x are divisible by 6x