The magnitude and the direction of the <em>resulting</em> vector is 3 and 0°, respectively.
<h3>Procedure - Determination of a vector by subtraction</h3>
Let assume that angles are in standard position. According to the statement, we have following model for the direction of the <em>resulting</em> vector in terms of the vectors known in statement:
(1)
Where
is the resulting vector.
If we know that
,
and
, then we have the following expression:
![r\cdot (1, 0) = k \cdot \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)-3\cdot (0, 1)](https://tex.z-dn.net/?f=r%5Ccdot%20%281%2C%200%29%20%3D%20k%20%5Ccdot%20%5Cleft%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%20%5Cright%29-3%5Ccdot%20%280%2C%201%29)
![(r, 0) = \left(\frac{\sqrt{2}\cdot k}{2}, \frac{\sqrt{2}\cdot k}{2} - 3 \right)](https://tex.z-dn.net/?f=%28r%2C%200%29%20%3D%20%5Cleft%28%5Cfrac%7B%5Csqrt%7B2%7D%5Ccdot%20k%7D%7B2%7D%2C%20%5Cfrac%7B%5Csqrt%7B2%7D%5Ccdot%20k%7D%7B2%7D%20-%203%20%20%5Cright%29)
Then we have the following system of linear equations:
(2)
(3)
By (3):
![k = 3\sqrt{2}](https://tex.z-dn.net/?f=k%20%3D%203%5Csqrt%7B2%7D)
By (2):
![r = 3](https://tex.z-dn.net/?f=r%20%3D%203)
Hence, the magnitude and the direction of the <em>resulting</em> vector is 3 and 0°, respectively. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
To learn more on vectors, we kindly invite to check this verified question: brainly.com/question/13188123
2 2/19 feet because 19x=4
X=4/19
10x=10x4/9
40/19
Answer:
![\#\text{ of 8-onion bags: }4,\\\#\text{ of 3-onion bags: }3](https://tex.z-dn.net/?f=%5C%23%5Ctext%7B%20of%208-onion%20bags%3A%20%7D4%2C%5C%5C%5C%23%5Ctext%7B%20of%203-onion%20bags%3A%20%7D3)
Step-by-step explanation:
Let
be the number of bags with 8 onions and let
be the number of bags with 3 onions. We have the following system of equations:
![\begin{cases}a+b=7,\\8a+3b=41\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Da%2Bb%3D7%2C%5C%5C8a%2B3b%3D41%5Cend%7Bcases%7D)
Subtracting
from both sides of the first equation, we get
. Substitute this into the second equation:
![8(7-b)+3b=41,\\56-8b+3b=41,\\56-5b=41,\\-5b=-15,\\b=\boxed{3}](https://tex.z-dn.net/?f=8%287-b%29%2B3b%3D41%2C%5C%5C56-8b%2B3b%3D41%2C%5C%5C56-5b%3D41%2C%5C%5C-5b%3D-15%2C%5C%5Cb%3D%5Cboxed%7B3%7D)
Therefore, the number of 8-onion bags is:
![a=7-b,\\a=7-3,\\a=\boxed{4}](https://tex.z-dn.net/?f=a%3D7-b%2C%5C%5Ca%3D7-3%2C%5C%5Ca%3D%5Cboxed%7B4%7D)
Thus, the chef got 4 8-onion bags and 3 3-onion bags.
Answer:
4
Step-by-step explanation:
THE CORRECT ANSWER IS B