Divide. Simplify, if possible.
÷ 
A. 
B. 
C. 
D. 
Answer: A
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If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the velocity vector.r(t) = (cot t)i + (csc t)j
A. v = (csc2 t)i + (cot t csc t)j B. v = (-sec2 t)i - (tan t sec t)j C. v = (sec2 t)i + (tan t sec t)j D. v = (-csc2 t)i - (cot t csc t)j
Find the length of the third side of the right triangle.Round to the nearest tenth, if necessary.
A. 151.5 cm B. 4.2 cm C. 12.3 cm D. 2.6 cm
Use the dot product to determine whether the vectors are parallel, orthogonal, or neither.v = 
j, w = 2i
A. orthogonal B. parallel C. neither
Solve the problem.The earth, Jupiter, Saturn, and Neptune all revolve around the sun. The earth takes 1 year, Jupiter approximately 12 years, Saturn approximately 30 years, and Neptune approximately 165 years to make a complete revolution. How often will Jupiter, Saturn, and Neptune appear in the same direction in the night sky as seen from earth?[Hint: Find the LCM of 12, 30, and 165]
A. Every 660 years B. Every 3300 years C. Every 1980 years D. Every 330 years