Answer: ![R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}](https://tex.z-dn.net/?f=R%3D20.84%5C%20lb%5Cquad%2022.57%5E%7B%5Ccirc%7D%2C15.43%5E%7B%5Ccirc%7D)
Step-by-step explanation:
Given
Two forces of 9 and 13 lbs acts
angle to each other
The resultant of the two forces is given by
![\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}](https://tex.z-dn.net/?f=%5CRightarrow%20R%3D%5Csqrt%7Ba%5E2%2Bb%5E2%2B2ab%5Ccos%20%5Ctheta%7D)
Insert the values
![\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb](https://tex.z-dn.net/?f=%5CRightarrow%20R%3D%5Csqrt%7B9%5E2%2B13%5E2%2B2%289%29%2813%29%5Ccos%2038%5E%7B%5Ccirc%7D%7D%5C%5C%5CRightarrow%20R%3D%5Csqrt%7B81%2B169%2B184.394%7D%5C%5C%5CRightarrow%20R%3D%5Csqrt%7B434.394%7D%5C%5C%5CRightarrow%20R%3D20.84%5C%20lb)
Resultant makes an angle of
![\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Calpha%3D%5Ctan%5E%7B-1%7D%5Cleft%28%20%5Cdfrac%7Bb%5Csin%20%5Ctheta%7D%7Ba%2Bb%5Ccos%20%5Ctheta%7D%5Cright%29%5C%5C%5C%5C%5Ctext%7BConsidering%209%20lb%20force%20along%20the%20x-axis%7D%5C%5C%5C%5C%5CRightarrow%20%5Calpha%20%3D%5Ctan%5E%7B-1%7D%5Cleft%28%20%5Cdfrac%7B13%5Csin%2038%5E%7B%5Ccirc%7D%7D%7B9%2B13%5Ccos%2038%5E%7B%5Ccirc%7D%7D%5Cright%29%5C%5C%5C%5C%5CRightarrow%20%5Calpha%20%3D%5Ctan%5E%7B-1%7D%28%5Cdfrac%7B8%7D%7B19.244%7D%29%5C%5C%5C%5C%5CRightarrow%20%5Calpha%3D22.57%5E%7B%5Ccirc%7D)
So, the resultant makes an angle of
with 9 lb force
Angle made with 13 lb force is ![38^{\circ}-22.57^{\circ}=15.43^{\circ}](https://tex.z-dn.net/?f=38%5E%7B%5Ccirc%7D-22.57%5E%7B%5Ccirc%7D%3D15.43%5E%7B%5Ccirc%7D)
Answer:
222 minuets
Step-by-step explanation:
Step-by-step explanation:
So you need to figure out how much it can print in 1 minute. You can find that out by dividing 480 by 4. You get 120 which you then multiple by 10.
So the answer is 1,200
Because the ratio of women to children is 10:1, double the ratio of men to women so the women are both 10:
Men to women becomes 8:10
Now total the 3 ratios: 8 for men, 10, for women and 9 for children:
8 + 10 + 9 = 27
Divide total people by that number:
270/27 = 10
Multiply 10 by each ratio:
Men = 8 * 10 = 80
Women = 10 * 10 = 100
Children = 9 *10 = 90
There is 80 men.