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

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

answer: the first graph

step-by-step explanation: