The answer to this question is 13.
Answer:
5.5
Step-by-step explanation:
Answer:
the kitten gained 21 ounces
Step-by-step explanation:
2 pounds = 32 ounces
so then i added 32 to 3 and got a total of 35 ounces
56-35=21
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°.
<h3>How to determine the magnitude and the direction of a resultant</h3>
Vectors are elements with two given characteristics: Magnitude and direction. A resultant is derived from the sum of vectors, the magnitude is the norm of a vector and the direction is the orientation of a vector. The resultant and its characteristics are described below:
<h3>Resultant</h3>
(1)
<h3>Magnitude</h3>
(2)
<h3>Direction</h3>
(3)
Where
is resultant angle, measured in degrees.
If we know that
,
,
,
,
and
, then the resultant, its magnitude and its direction:
<h3>Resultant</h3>
![\vec r = (-90\cdot \cos 40^{\circ}-60\cdot \sin 20^{\circ}+40\cdot \cos 30^{\circ}, 40\cdot \sin 30^{\circ}+60\cdot \cos 20^{\circ}-90\cdot \sin 40^{\circ})](https://tex.z-dn.net/?f=%5Cvec%20r%20%3D%20%28-90%5Ccdot%20%5Ccos%2040%5E%7B%5Ccirc%7D-60%5Ccdot%20%5Csin%2020%5E%7B%5Ccirc%7D%2B40%5Ccdot%20%5Ccos%2030%5E%7B%5Ccirc%7D%2C%2040%5Ccdot%20%5Csin%2030%5E%7B%5Ccirc%7D%2B60%5Ccdot%20%5Ccos%2020%5E%7B%5Ccirc%7D-90%5Ccdot%20%5Csin%2040%5E%7B%5Ccirc%7D%29)
![\vec r = (-54.824, 18.531)](https://tex.z-dn.net/?f=%5Cvec%20r%20%3D%20%28-54.824%2C%2018.531%29)
<h3>Magnitude</h3>
![\|\vec r\| = \sqrt{(-54.824)^{2}+18.531^{2}}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20r%5C%7C%20%3D%20%5Csqrt%7B%28-54.824%29%5E%7B2%7D%2B18.531%5E%7B2%7D%7D)
![\|\vec r\| \approx 57.871](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20r%5C%7C%20%5Capprox%2057.871)
<h3>Direction</h3>
![\theta = \tan^{-1} \left(\frac{18.531}{-54.824}\right)](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ctan%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B18.531%7D%7B-54.824%7D%5Cright%29)
![\theta \approx 198.676^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%5Capprox%20198.676%5E%7B%5Ccirc%7D)
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
To learn more on vectors, we kindly invite to check this verified question: brainly.com/question/13322477
Answer:
x = 13, y = 3
Step-by-step explanation:
3(5y - 2) - 4y = 27
15y - 6 - 4y = 27
11y = 33
y = 3
x = 15 - 2
x = 13