Step-by-step explanation:
u.v=|u||v|cos60°
u.v=(2.5)(3.2)(1/2)
u.v=(8)(1/2)
u.v=4
Answer:
48/37
Step-by-step explanation:
Use the formula (y1 - y2)/(x1 - x2).
Plug in your x and y values to get (92 + 4)/(81 - 7).
Simplify down to get 96/74 and simplify again to get 48/37.
Your answer would be 13,122
You would multiply by -3 each time for this particular sequence.
Hope I helped!
9514 1404 393
Answer:
(a, b) = (-2, -1)
Step-by-step explanation:
The transpose of the given matrix is ...
![A^T=\left[\begin{array}{ccc}1&2&a\\2&1&2\\2&-2&b\end{array}\right]](https://tex.z-dn.net/?f=A%5ET%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%26a%5C%5C2%261%262%5C%5C2%26-2%26b%5Cend%7Barray%7D%5Cright%5D)
Then the [3,1] term of the product is ...
![(A\cdot A^T)_{31}=\left[\begin{array}{ccc}a&2&b\end{array}\right]\cdot\left[\begin{array}{ccc}1&2&2\end{array}\right]=a+2b+4](https://tex.z-dn.net/?f=%28A%5Ccdot%20A%5ET%29_%7B31%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%262%26b%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%262%5Cend%7Barray%7D%5Cright%5D%3Da%2B2b%2B4)
and the [3,2] term is ...
![(A\cdot A^T)_{32}=\left[\begin{array}{ccc}a&2&b\end{array}\right]\cdot\left[\begin{array}{ccc}2&1&-2\end{array}\right]=2a-2b+2](https://tex.z-dn.net/?f=%28A%5Ccdot%20A%5ET%29_%7B32%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%262%26b%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%26-2%5Cend%7Barray%7D%5Cright%5D%3D2a-2b%2B2)
Both of these terms in the product matrix are 0. We can solve the system of equations by adding these two terms:
(a +2b +4) +(2a -2b +2) = (0) +(0)
3a +6 = 0
a = -2
Substituting for 'a' in term [3,1] gives ...
-2 +2b +4 = 0
b = -1
The ordered pair (a, b) is (-2, -1).
= 
The 2 right triangles are similar and so the ratios of corresponding sides are equal
The corresponding sides are x and 2, 6 and 1.5, hence
= 