Suppose r(t)=costi+sintj+3tk represents the position of a particle on a helix, where z is the height of the particle above the ground.

a. What is t when the particle has height 16?
b. What is the velocity of the particle when its height is 16?
c. When the particle has height 16, it leaves the helix and moves along the tangent line at the constant velocity found in part b. Find a vector parametric equation for the position of the particle (in terms of the original parameter t) as it moves along this tangent line.

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Aswimming pool measures 22ft by 12ft and is 4ft deep. if the pool is being filled at 2.5 cubic ft per minute, how long will it take to fill the pool?

Look at the figure below: triangle abc is a right triangle with angle abc equal to 90 degrees. the length of ac is 5 units and the length of ab is 4 units. d is a point above c. triangle adc is a right triangle with angle dac equal to 90 degrees and dc parallel to ab. what is the length, in units, of segment cd?