Time And Distances

The movement of two submarines are being followed by a tracking system, and the positions of the submarines are modelled by points. The position of Sub A at time t is (2t+2, 2t+1) and the position of Sub B at time t is (4-t, t+5) (distance in Kilometers) 1.How would I go about eliminating t from each pair of coordinates, and from this realise each Sub travels in a straight line? 2. How would I go about finding the distance between the Subs at each of the times t=0 and t=2? 3. If d is the distance between the pods at time t, how would I go about finding an expression for d squared in terms of t? And how would I go about completing the square for this expression, and show that the m... click for more

Two problems

(1) Given function: f(x) = (x^2)*[e^(12x)] (a) Find its horizontal asymptotes. (b) Find its critical numbers. (c) Find its inflection points. (2) Given function: f(x) = (x^3) / [(x^2) - 16] (a) Find its critical numbers. (b) Find its inflection points.

Star polygons

5/3 and 5/4 are the two they give. Can you find the other 5 regular star polygons with fewer than 10 vertices?

Geometry / algebra problem.

(See attached file for full problem description with diagram) --- The 7y-2 should be in parenthesis (7y-2) and the same thing for 4x+1, i.e. (4x+1). I have tried solving this problem several times I need values for x and y. can you please explain. It is a paralellogram. Thank you soo much. ---

2 problems

(See attached file for full problem descriptions with diagrams) --- 1. Given: A is the midpoint of OX, AB is parallel to XY; BC is parallel to YZ Prove: AC is parallel to XZ. 2. Given: lines PQ, RS, and TU are each perpendicular bisectors to UQ; R is the of line PT. Prove: R is equidistant from U and Q. ---