Perimeter is
2 • width+ 2•length=
2• (4x-4)+2•(2x+5)=
Distribute multiplication in parentheses
8x-8+4x+10=
Combine like terms
12x+2
Answer:
104 ft total
Step-by-step explanation:
52 times 2 equals 104
The correct answer is X=6
If there are 4 trucks then the first truck weighs x
then x+2tons
then x+4tons
then x+6tons = 32tons
so 4x+12=32
-12 -12
/4 /4
x=5
so plug it back in
truck 1= 5tons or 10,000lbs
truck 2= 7tons or 14,000lbs
truck 3= 9tons or 18,000lbs
<span>truck 4= 11tons or 22,000lbs</span>
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)