Find the curve of shortest length between points (R0, 0, Z0) and (R1, Φ1, Z1) on the conical surface r = z tanα, where (r, φ, z) are cylindrical coordinates and α, the opening (half) angle of the cone, is a constant. Recall that the increment of length ds in cylindrical coordinates is given by ds2 = dr2 + r 2 dφ2 + dz2

Line cd passes through points c(1, 3) and d(4, –3). if the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b? –5 –2 1 5

What is not true about kl and mn? what is mn? (show your work)

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size.it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?