Which number sentence illustrates the commutative property of addition?
1 answer:
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Answer:
Magnitude = 220.49pounds
Direction = 16.7°
Step-by-step explanation:
Find attached the diagram obtained from the given information.
From the diagram, 25° is in the first quadrant with all positive values: x = cos25°, y = sin35°
Force for the x and y component: Fx, Fy
250(sin25, cos25) = (250sin25, 250cos25)
= [250(0.4226), 250(0.9063)]
= (105.65, 226.575)
The 250° is in the 2nd quadrant with values: x = cos250°, y = sin250°
Force for the x and y component: (Fx, Fy)
45(sin250, cos250) = (45sin250, 45cos250) = [45(-0.9397), 45(-0.3420]
= (−42.2865, -15.39)
The resultant forces for x and y components = sum of Fx in the 1st and 2nd force and, sum of Fy in the 1st and 2nd force
sum of Fx in the 1st and 2nd force = 105.65 + (−42.2865) = 63.3635
sum of Fy in the 1st and 2nd force = 226.575 + (-15.39) = 211.185
Magnitude = √[(ΣFx)² + (ΣFy)²]
= √[(63.3635)² + (211.185)²]
= √(4014.9331 + 44599.1042)
= √(48614.0373)
= 220.49pounds
Direction = arctan (ΣFx/ΣFy)
= arctan (63.3635/211.185)
= arctan(0.30)
= 16.7°
