Answer:
![\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-%5Cfrac%7B8%7D%7B%5Csqrt%7B117%7D%20%7D%20%5C%5C%5Cfrac%7B7%7D%7B%5Csqrt%7B117%7D%20%7D%5C%5C%5Cfrac%7B2%7D%7B%5Csqrt%7B117%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We are required to find a unit vector in the direction of:
![\left[\begin{array}{c}-8\\7\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-8%5C%5C7%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Unit Vector, ![\hat{a}=\dfrac{\overrightarrow{a}}{|\overrightarrow{a}|}](https://tex.z-dn.net/?f=%5Chat%7Ba%7D%3D%5Cdfrac%7B%5Coverrightarrow%7Ba%7D%7D%7B%7C%5Coverrightarrow%7Ba%7D%7C%7D)
The Modulus of
=![\sqrt{(-8)^2+7^2+(-2)^2}=\sqrt{117}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-8%29%5E2%2B7%5E2%2B%28-2%29%5E2%7D%3D%5Csqrt%7B117%7D)
Therefore, the unit vector of the matrix is given as:
![\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-%5Cfrac%7B8%7D%7B%5Csqrt%7B117%7D%20%7D%20%5C%5C%5Cfrac%7B7%7D%7B%5Csqrt%7B117%7D%20%7D%5C%5C%5Cfrac%7B2%7D%7B%5Csqrt%7B117%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Answer:3
Step-by-step explanation:
Answer:
![\int_{-1}^{1}7(x^{3}-x)\:dx](https://tex.z-dn.net/?f=%5Cint_%7B-1%7D%5E%7B1%7D7%28x%5E%7B3%7D-x%29%5C%3Adx)
Step-by-step explanation:
1) The other curve is
then the common points of both curves are x-intercepts, the roots of ![y=7(x^{3}-x)](https://tex.z-dn.net/?f=y%3D7%28x%5E%7B3%7D-x%29)
![y=7(x^{3}-x)\Rightarrow 7(x^3-x)=0 \Rightarrow 7(x^{3}-x)=7x(x-1)(x-1)\Rightarrow \\S=\left ( 0,0 \right ),\left ( -1,0 \right ),\left ( 1,0 \right )](https://tex.z-dn.net/?f=y%3D7%28x%5E%7B3%7D-x%29%5CRightarrow%207%28x%5E3-x%29%3D0%20%5CRightarrow%207%28x%5E%7B3%7D-x%29%3D7x%28x-1%29%28x-1%29%5CRightarrow%20%5C%5CS%3D%5Cleft%20%28%200%2C0%20%5Cright%20%29%2C%5Cleft%20%28%20-1%2C0%20%5Cright%20%29%2C%5Cleft%20%28%201%2C0%20%5Cright%20%29)
2). Then those intersection points are the upper and the lower limits. Plugging in to this formula for they belong to the interval [-1,1]:
![\int_{a}^{b}|f(x)-g(x)dx](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%7Cf%28x%29-g%28x%29dx)
![\int_{a}^{b}|f(x)-g(x)dx \Rightarrow \int_{-1}^{1}|7(x^{3}-x)-0|dx \Rightarrow \int_{-1}^{1}7(x^{3}-x)\:dx](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%7Cf%28x%29-g%28x%29dx%20%5CRightarrow%20%5Cint_%7B-1%7D%5E%7B1%7D%7C7%28x%5E%7B3%7D-x%29-0%7Cdx%20%5CRightarrow%20%5Cint_%7B-1%7D%5E%7B1%7D7%28x%5E%7B3%7D-x%29%5C%3Adx)
Answer:
x = 2n - 4
Step-by-step explanation:
hope this helped have a great day
Oi :)
a= l*w
a=1.5 * 0.75
a= 1.125