Answer:
C
Step-by-step explanation:
We can solve simultaneous equations using substitution method, elimination method or graphical method. But for this purpose, we will be using the elimination method.
3x+4y=8 Equation 1
2x+y=42 Equation 2
Multiply Equation 1 by 2 and equation 2 by 3, so as to get the same coefficient for x
2(3x+4y=8)= 6x+8y=16 Equation 3
3(2x+y=42)= 6x+3y=126 Equation 4
Subtract equation 4 from 3, to eliminate x
6x-6x=0
8y-3y= 5y
16-126= -110
We now have 5y=-110
Divide both sides by 5,
y= -110/5
= -22
Substituting for y in equation 2
2x+(-22)= 42
2x= 42+22
2x=64
x= 64/2
= 32
(x, y)
(32, -22)
Actually, when you know 2 sides and an included angle, you use the Law of Cosines. (and we don't know if theta is an included angle).
Solving for side c
c^2 = a^2 + b^2 -2ab * cos(C)
c^2 = 36 + 16 - 2*6*4 * cos(60)
c^2 = 52 -48*.5
c^2 = 28
c = 5.2915
Using the Law of Sines
side c / sin(C) = side b / sin (B)
5.2915 / sin(60) = 4 / sin (B)
sin(B) = sin(60) * 4 / 5.2915
sin(B) = 0.86603 * 4 / 5.2915
<span><span>sin(B) = 3.46412
</span>
/ 5.2915
</span>
<span><span><span>sin(B) = 0.6546571451
</span>
</span>
</span>
Angle B = 40.894 Degrees
sin (A) / side a = sin (B) / side b
sin (A) = 6 * sin (40.894) / 4
sin (A) = 6 * 0.65466 / 4
sin (A) = .98199
angle A = 79.109 Degrees
angle C = 60 Degrees
I have concluded the answer is x=6.8
As we know :
Length of arc = Radius × Angle made by Arc at center [ in radians ]
or
