Review3Notes.notebook
March 18, 2016
C)
B)
A)
D)
F)
E)
exact answer
exact answer
exact answer
I)
H)
G)
2 decimal places
2 decimal places
2 decimal places
J)
2 decimal places
2 decimal places
2 decimal places
Solve this triangle. If there is no solution, write “No Solution”. If there is more than one answer, use subscripts to label your answers into two groups, one for Triangle1 and the other for Triangle2. Round all answers to 2 decimal places.
K) An airplane travels due east for 128 miles, and then turns 35° to the left. After the turn, it flies another 45 miles. How far from the starting point is the airplane, and how far to the left will it need to turn to point back to where it started? Round your answer to 2 decimal places.
L)
You are trying to throw a rope over a bar, and tie the two ends of the rope to two different points on the floor. The two points on the floor are 29 feet apart, and from one point, the angle of elevation to the bar is 74°. From the other point, on the far side of the bar, the angle of elevation is 82°. How long will the rope need to be to reach from one point, to the bar, to the other point? Round your answer to one decimal place.
M)
A very bad bicyclist is weaving back and forth in simple harmonic motion. He completes one full cycle of weaving once every 3 seconds. The distance between the furthest point to the left and the furthest point to the right is 30 inches. Find an equation of the form that describes this motion.
N)
and If is parallel to and O)
P)
, resolve into two vectors and , where is perpendicular to . Round your answers to 3 decimal places.
If a 1700 lb car rolls 1000 feet down an 8° slope, how many foot­pounds of work has gravity done in moving the car? (That’s how much kinetic energy it will have picked up, so in physics, you could use this information to figure out how fast the car would be going by that point!) Round to one decimal place.
Vector is 8 units long, and vector is 5 units long. If what is the angle between the two vectors? Round your answer to the nearest degree.
Q)
If an airplane that flies at 110 mph wants to travel due north, and there is a 15 mph wind from due North­West, what heading must the pilot fly? How fast will they end up travelling? Round your angle to the nearest degree, and the speed to the nearest mph.
R)
If the vector is points 3 units straight up along the z axis, and the vector , determine the cross product S)
Find a unit vector that points in the opposite direction of the vector <8, ­3, 5>
T)
Use DeMoivre’s Theorem to evaluate U)
Find ALL the 5th roots of 32 (in polar form).
V)
Sketch the graph of W)
Sketch the graph of X)
Sketch the graph of Y)
Sketch the graph of Z)
Sketch the graph of AA)
Sketch the graph of BB)
Sketch the graph of CC)
Convert this equation to polar coordinates: DD)
Convert this equation to rectangular coordinates: 1
Review3Notes.notebook
O)
March 18, 2016
If a 1700 lb car rolls 1000 feet down an 8° slope, how many foot­pounds of work has gravity done in moving the car? (That’s how much kinetic energy it will have picked up, so in physics, you could use this information to figure out how fast the car would be going by that point!) Round to one decimal place.
K) An airplane travels due east for 128 miles, and then turns 35° to the left. After the turn, it flies another 45 miles. How far from the starting point is the airplane, and how far to the left will it need to turn to point back to where it started? Round your answer to 2 decimal places.
2
Review3Notes.notebook
L)
J)
March 18, 2016
You are trying to throw a rope over a bar, and tie the two ends of the rope to two different points on the floor. The two points on the floor are 29 feet apart, and from one point, the angle of elevation to the bar is 74°. From the other point, on the far side of the bar, the angle of elevation is 82°. How long will the rope need to be to reach from one point, to the bar, to the other point? Round your answer to one decimal place.
Solve this triangle. If there is no solution, write “No Solution”. If there is more than one answer, use subscripts to label your answers into two groups, one for Triangle1 and the other for Triangle2. Round all answers to 2 decimal places.
3
Review3Notes.notebook
Q)
P)
March 18, 2016
If an airplane that flies at 110 mph wants to travel due north, and there is a 15 mph wind from due North­West, what heading must the pilot fly? How fast will they end up travelling? Round your angle to the nearest degree, and the speed to the nearest mph.
Vector is 8 units long, and vector is 5 units long. If what is the angle between the two vectors? Round your answer to the nearest degree.
4
Review3Notes.notebook
U)
T)
March 18, 2016
Find ALL the 5th roots of 32 (in polar form).
Use DeMoivre’s Theorem to evaluate 5
Review3Notes.notebook
S)
March 18, 2016
Find a unit vector that points in the opposite direction of the vector <8, ­3, 5>
BB)
Sketch the graph of 6
Review3Notes.notebook
DD)
M)
March 18, 2016
Convert this equation to rectangular coordinates: A very bad bicyclist is weaving back and forth in simple harmonic motion. He completes one full cycle of weaving once every 3 seconds. The distance between the furthest point to the left and the furthest point to the right is 30 inches. Find an equation of the form that describes this motion.
7
Review3Notes.notebook
N)
If March 18, 2016
and is parallel to and CC)
, resolve into two vectors and , where is perpendicular to . Round your answers to 3 decimal places.
Convert this equation to polar coordinates: 8
Review3Notes.notebook
R)
If the vector is March 18, 2016
points 3 units straight up along the z axis, and the vector , determine the cross product 9