MS 101 Alg & Trig test six • 10 July 2015 Name:

1. Solve 4 (tan x) − 1 = 0 for x in degrees
2. Solve 4 cos²x − 1 = 0 for x in degrees
3. A ball is thrown at 609 cm/s perpendicular to the direction of RipStik traveling at 346 cm/s as seen in the diagram. V⃑_ground = v⃑_ball + w⃑_ripstik
   
   1. __________ î + _________ ĵ Write the resultant vector of V⃑_ground in unit vector form.
   2. __________ Calculate the direction angle θ for V⃑_ground in degrees.
   3. __________ Calculate the magnitude for V⃑_ground.
4. 1. ____________ The force vector for Jaeger Striker Eureka's right lead helicopter is given by $\stackrel{\rightharpoonup }{F}$ = -120î + 140ĵ. Calculate the angle to the vertical θ in degrees.
   2. ____________ Calculate the magnitude of the vector $\stackrel{\rightharpoonup }{F}$ = -120î + 140ĵ.
5. For the vector $\stackrel{\rightharpoonup }{u}$ = 260 î + 150 ĵ
   1. magnitude = __________ Calculate the magnitude.
   2. θ = __________ Calculate the direction angle in degrees.
6. A vector with a magnitude of 100 is at a direction angle of 67° to the horizontal. Write the vector in î, ĵ component form.
   
   $\stackrel{\rightharpoonup }{v}$ = ________ î + ________ ĵ
7. A vector u⃑ with a magnitude of 40 and a direction angle of 30° is added to a vector v⃑ with a magnitude of 50 and a direction angle of 60°. Determine the magnitude and direction angle in degrees for the vector u⃑ + v⃑.
   
   1. magnitude u⃑ + v⃑ = __________ Calculate the magnitude.
   2. θ = __________ Calculate the direction angle for u⃑ + v⃑ in degrees.
8. 
   Do NOT try at home: Child towing a RipStik with a bicycle __________ Shana is towing Marlin with a force of 100 Newtons at an angle of 30° to the horizontal for a distance of 20 meters. Calculate the energy (work done) using the dot product.
9. __________ Shana is towing Marlin with a force of 100 Newtons at an angle of 30° to the horizontal. The length of the lever arm d for the torque is 0.8 meters (the distance from the nose of the RipStik to the rear wheel). Calculate the torque on the RipStik using the cross product.
   
10. Given a matrix $A=\left[\begin{array}{ccc}3& -5& 0\\ -7& 1& 4\end{array}\right]$ and a matrix $B=\left[\begin{array}{ccc}5& 5& 7\\ -7& 2& 8\end{array}\right]$
    1. Calculate $A+B=\left[\begin{array}{ccc}\mathrm{\_\_\_}& \mathrm{\_\_\_}& \mathrm{\_\_\_}\\ \mathrm{\_\_\_}& \mathrm{\_\_\_}& \mathrm{\_\_\_}\end{array}\right]$
    2. Calculate $5A=\left[\begin{array}{ccc}\mathrm{\_\_\_}& \mathrm{\_\_\_}& \mathrm{\_\_\_}\\ \mathrm{\_\_\_}& \mathrm{\_\_\_}& \mathrm{\_\_\_}\end{array}\right]$