. The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (4, 8).
B is right option
4x + 2y = 32
5x + 2y = 36 subtracting
-x=-4
x=4
4(4)+2y=32
16+2y=32
2y=16
y=8
hope this helps
This can be solved a couple of ways. One way is to use the Pythagorean theorem to write equations for the magnitude from the components of the forces. That is what was done in the graph here.
Another way is to use the Law of Cosines, which lets you make direct use of the angle between the vectors.
.. 13 = a^2 +b^2 -2ab*cos(90°)
.. 19 = a^2 +b^2 -2ab*cos(120°)
Subtracting the first equation from the second, we have
.. 6 = -2ab*cos(120°)
.. ab = 6
Substituting this into the first equation, we have
.. 13 = a^2 +(6/a)^2
.. a^4 -13a^2 +36 = 0
.. (a^2 -9)(a^2 -4) = 0
.. a = ±3 or ±2
The magnitudes of the two forces are 2N and 3N, in no particular order.
We know, sum of all the angles in a triangle is equal to 180 degree
So, 90 + 2x + 3x = 180
5x = 180-90
x = 90/5
x = 18
∠ANB = 2x = 2(18) = 36
∠BNC = 3x = 3(18) = 54
Hope this helps!
The number -5 would go to the left of a number scale. Typically because all negatives move to the left of zero on the number scale.