-8d – 5d + 70 = 72
-13d + 70 = 72
-70 -70
_______________
-13d 2
___ = ___
-13 -13
d = -0.15 (<em>rounded</em>)
Answer:
Magnitude: 121.35 pounds
Direction: 21.64°
Explanation:
1) Decompose each force into its x - y components.
2) Force 1, F1: 140 pounds at angle of 30°
x-component: F1,x
F1, x = F1 *cos(30°) = 140 pounds * cos(30°) = 121.24 pounds
y-component: F1,y
F1,y = F1 * sin(30°) = 140 pounds * sin(30°) = 70 pounds.
3) Force 2, F2: 75 poounds at 150°
x-component: F2,x
F2,x = F2 * cos(150°) = 75 pounds * cos(150°) = - 64.95 pounds
y-component: F2,y
F2,y = F2 * sin(150°) = 75 pounds * sin(150°) = 37.5 pounds
4) Resultant Force, Fr
x-component: Fr,x
Fr,x = F1,x + F2,x = 121.24 pounds - 64.95 pounds = 56.29 pounds
y-component: Fr,y
Fr,y = F1,y + F2,y = 70 pounds + 37.5 pounds = 107.5 pounds
4.1) magnitude
|Fr| = √ [ (56.29 pouns)^2 + (107.5 pounds)^2 ] = 121.35 pounds.
4.2) direction
tan(α) = Fr,y / Fr,3 = 56.29 pounds / 107.5 pouns = 0.5236
=> α = arctan(0.5236) = 27.64 °
Answer:
m=75
percentage= 32
part= 24
whole= 75
Step-by-step explanation:
To get m, you divide 18 by .24(since it's the decimal form of 24%) and you get 75.
The part/whole part I'm not exactly sure about but since it's 24% of 75, I'm guessing the part is 24 and the whole is 75 and that's the entire thing we are working with here.
To get the percentage, we use the 24/75 fraction. We have to get the demonator to 100 but since 75 can't be multiplied by anything to get to 100, we have to simplfy the fraction so the demonator can go into 100. I divided the fraction by 3 since that would get the fraction to 8/25. 25 can go into 100 if we multiply by 4 so that's what you do. The ending fraction would be 32/100 after multiplying the numerator and demonator by 4(8/24). So the percentage would be 32% or 32/100.
I have never done this is my life but it is similar to what I have done so please correct me if I am wrong. I hope this helped you and I am incredibly sorry if it is wrong.
