Answer:
Just type this into a graphing calculator I would do it but im on the road right now. The graphing calculator will tell you exactly what the answer is.
Step-by-step explanation:
Answer:
The given function is
f(x)=cos 3x-7 x²+ 4x
f'(x)=-3 sin 3 x-14 x+4
When you will draw the graph of the function , you will find that root of the function lie between (-1,0).
Consider initial root as,
![x_{0}=0](https://tex.z-dn.net/?f=x_%7B0%7D%3D0)
Using Newton method to find the roots of the equation
![x_{n+1}=x_{n}-\frac{f{x_n}}{f'{x_{n}}}\\\\x_{1}=x_{0} - \frac{cos 3x_{0}-7 x_{0}^2+ 4x_{0}}{-3 sin 3 x_{0}-14 x_{0}+4}\\\\x_{1}=-\frac{\cos 0^{\circ}-0+0}{-3 \times 0-0+4}\\\\x_{1}=\frac{-1}{4}\\\\x_{1}= -0.25\\\\x_{2}=x_{1} - \frac{cos 3x_{1}-7 x_{1}^2+ 4x_{1}}{-3 sin 3 x_{1}-14 x_{1}+4}\\\\x_{2}=-0.25 -\frac{cos (-0.75)-7\times (0.0625)- 1}{-3 sin (-0.75)+3.50+4}\\\\x_{2}= -0.176054](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%3Dx_%7Bn%7D-%5Cfrac%7Bf%7Bx_n%7D%7D%7Bf%27%7Bx_%7Bn%7D%7D%7D%5C%5C%5C%5Cx_%7B1%7D%3Dx_%7B0%7D%20-%20%5Cfrac%7Bcos%203x_%7B0%7D-7%20x_%7B0%7D%5E2%2B%204x_%7B0%7D%7D%7B-3%20sin%203%20x_%7B0%7D-14%20x_%7B0%7D%2B4%7D%5C%5C%5C%5Cx_%7B1%7D%3D-%5Cfrac%7B%5Ccos%200%5E%7B%5Ccirc%7D-0%2B0%7D%7B-3%20%5Ctimes%200-0%2B4%7D%5C%5C%5C%5Cx_%7B1%7D%3D%5Cfrac%7B-1%7D%7B4%7D%5C%5C%5C%5Cx_%7B1%7D%3D%20-0.25%5C%5C%5C%5Cx_%7B2%7D%3Dx_%7B1%7D%20-%20%5Cfrac%7Bcos%203x_%7B1%7D-7%20x_%7B1%7D%5E2%2B%204x_%7B1%7D%7D%7B-3%20sin%203%20x_%7B1%7D-14%20x_%7B1%7D%2B4%7D%5C%5C%5C%5Cx_%7B2%7D%3D-0.25%20-%5Cfrac%7Bcos%20%28-0.75%29-7%5Ctimes%20%280.0625%29-%201%7D%7B-3%20sin%20%28-0.75%29%2B3.50%2B4%7D%5C%5C%5C%5Cx_%7B2%7D%3D%20-0.176054)
![x_{3}=x_{2} - \frac{cos 3x_{2}-7 x_{2}^2+ 4x_{2}}{-3 sin 3 x_{2}-14 x_{2}+4}\\\\x_{3}=-0.176054 -\frac{cos (3\times -0.176054)-7\times (-0.176054)^2+4 \times -0.176054}{-3 sin (-0.176054)-14 \times (-0.176054)+4}\\\\x_{3}= -0.1689](https://tex.z-dn.net/?f=x_%7B3%7D%3Dx_%7B2%7D%20-%20%5Cfrac%7Bcos%203x_%7B2%7D-7%20x_%7B2%7D%5E2%2B%204x_%7B2%7D%7D%7B-3%20sin%203%20x_%7B2%7D-14%20x_%7B2%7D%2B4%7D%5C%5C%5C%5Cx_%7B3%7D%3D-0.176054%20-%5Cfrac%7Bcos%20%283%5Ctimes%20-0.176054%29-7%5Ctimes%20%28-0.176054%29%5E2%2B4%20%5Ctimes%20-0.176054%7D%7B-3%20sin%20%28-0.176054%29-14%20%5Ctimes%20%28-0.176054%29%2B4%7D%5C%5C%5C%5Cx_%7B3%7D%3D%20-0.1689)
So, root of the equation is
=0.1688878
=0.1689(approx)
I believe it it will be the across the y axis
The missing numbers are 2,3,10,12,13
Answer:
6 x 5 x 5
Step-by-step explanation:
5 is the side length
5 * 5 to get the area of 1 square.
Multiply 6 because there are 6 total squares.
6 * 5 * 5