$\mathbf{u}=\langle 70 \cos 230^{\circ}, 70 \sin 230^{\circ} \rangle\\\\\mathbf{v}=\langle 60\cos 140^{\circ}, 60 \sin 140^{\circ} \rangle\\\\\mathbf{w}=\langle 80 \cos 30^{\circ}, 80 \sin 30^{\circ} \rangle\\\\\\\therefore \mathbf{u}+\mathbf{v}+\mathbf{w}=\langle 70 \cos 230^{\circ}+60 \cos 140^{\circ}+80 \cos 30^{\circ}, 70 \sin 230^{\circ}+60 \sin 140^{\circ}+80 \sin 30^{\circ} \rangle\\\\ \approx \langle -21.675, 24.944 \rangle$

$\implies |\mathbf{u}+\mathbf{v}+\mathbf{w}| \approx \sqrt{(-21.675)^2 + (24.944)^2} \approx 33.046$

Direction: The vector is in the second quadrant, so the direction is about $180^{\circ}-\arctan \left(\frac{24.944}{-21.675} \right) \approx 131^{\circ}$

8 0

1 year ago

Upon renewing your cell phone, you have two options:

Margaret [11]

first put both options into equation format. option 1: 360+75m and option 2: 24(30). solve the easier problem first which is 24 multiplied by 30 which equals 720. so now you know what should be on the side of the equal sign so that they both have eqaul solutions. 360+75m =720. subtract 360 from both sides so that equation turns to 75m=360, then divide both sides by 75 and get 4.8. it would take 4.8 months

7 0

3 years ago