Answer:
The angle between the two vectors is 84.813°.
Step-by-step explanation:
Statement is incomplete. Complete form is presented below:
<em>Let be (6,-3, 1) and (8, 9, -11) vector with same origin. Find the angle between the two vectors. </em>
Let 
and 
, the angle between the two vectors is determined from definition of dot product:
(1)
Where:
, 
- Vectors.
, 
- Norms of each vector.
Note: The norm of a vector in rectangular form can be determined by either the Pythagorean Theorem or definition of Dot Product.
If we know that 
and 
, then the angle between the two vectors is:
![\theta = \cos^{-1}\left[\frac{(6)\cdot (8) + (-3)\cdot (9) + (1)\cdot (-11)}{\sqrt{6^{2}+(-3)^{2}+1^{2}}\cdot \sqrt{8^{2}+9^{2}+(-11)^{2}}} \right]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B%286%29%5Ccdot%20%288%29%20%2B%20%28-3%29%5Ccdot%20%289%29%20%2B%20%281%29%5Ccdot%20%28-11%29%7D%7B%5Csqrt%7B6%5E%7B2%7D%2B%28-3%29%5E%7B2%7D%2B1%5E%7B2%7D%7D%5Ccdot%20%5Csqrt%7B8%5E%7B2%7D%2B9%5E%7B2%7D%2B%28-11%29%5E%7B2%7D%7D%7D%20%5Cright%5D)
The angle between the two vectors is 84.813°.
Answer:
1.
Step-by-step explanation:
1. 1.811/2=3.622 271/3=813
3.622*813=2,944.686
this is number one
2. 32x=729
divide both sides by 32
32x=729/32=
22.78125 approximate=22.8 or 23
Answer:
80 units cubed
Step-by-step explanation:
Volume=Base area x Height=16x5=80
Base area=8x2=16
Height=5
![\left[\begin{array}{ccc}22&18\end{array}\right]\times\left[\begin{array}{cccc}5&18&32&40\\25&40&38&12\end{array}\right]\\\\=\left[\begin{array}{cccc}22\cdot5+18\cdot25&22\cdot18+18\cdot40&22\cdot32+18\cdot38&22\cdot40+18\cdot12\end{array}\right]\\\\=\left[\begin{array}{cccc}560&1116&1388&1096\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D22%2618%5Cend%7Barray%7D%5Cright%5D%5Ctimes%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D5%2618%2632%2640%5C%5C25%2640%2638%2612%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D22%5Ccdot5%2B18%5Ccdot25%2622%5Ccdot18%2B18%5Ccdot40%2622%5Ccdot32%2B18%5Ccdot38%2622%5Ccdot40%2B18%5Ccdot12%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D560%261116%261388%261096%5Cend%7Barray%7D%5Cright%5D)
second question:
January: 32 · 22 + 38 · 18 = 704 + 684 = 1388
December: 18 · 22 + 40 · 18 = 396 + 720 = 1116
1388 - 1116 = 272
Answer: $272.
Hello :
<span>If f(x)=x/2-2 and g(x)=2x^2+x-3, find (f+g)(x)
</span>(f+g)(x)= f(x) +g(x) = x/2-2 +2x²+x-3 = x/2 +2x²+x-5
(f+g)(x)= (x+4x²-2x-10) /2
(f+g)(x)= (4x²+3x-10)/2 = 2x²+3/2 x -5
