You need to find the dimensions of a cylindrical can (much like a soda or soup can) so that its volume is 81 cubic inches. The sides of the can costs 50 cents per square inch, the bottom costs 65 cents per square inch and the top of the can costs 85 cents per square inch. Find the dimensions of the can that minimizes the cost. What is the minimum cost? How do you know that your answer gives a minimum?

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Simplify 6sin θsec θ. choices a) 6 tan θ b) 6 cos θ c) 6 cot θ d) 6

Tom can paint the fence in 12 hours, but if he works together with a friend they can finish the job in 8 hours. how long would it take for his friend to paint this fence alone?