Consider S(d) = 0.159 + 0.118 log(d). S is the slope of a beach and D is the average diameter (in mm) of the sand particles on the beach. Suppose a particular beach rises 9 metres for every 100 metres inland. What size would you expect to find on that beach?
2006-08-27 11:22:14 · 3 answers · asked by ? 1 in Science & Mathematics ➔ Mathematics
S = 9/100 = .09
.09 = .159 + .118 log(d)
Subract .159 from each side
-.069 = .118 log(d)
Divide both sides by .118
-.584745762712 = log(d)
Apply base 10 to each side (since the log is base 10)
10^(-.584745762712) = 10^log(d)
.260168214997 = d
2006-08-27 11:31:08 · answer #1 · answered by MsMath 7 · 0⤊ 0⤋
slope = rise/run = 9/100 = 0.09 = S(d)
0.159 + .0118 log(d) = 0.09
Subtract 0.159 from each side
0.118 log(d) = 0.09 - 0.159 = -0.069
divide each side by 0.118
log(d) = -0.069/0.118 = -0.5847
take the inverse log of each side (10^x)
d = 10^(-0.5847) = 0.2602
2006-08-27 11:33:39 · answer #2 · answered by gtn 3 · 0⤊ 0⤋
S(d) = 0.159 + 0.118 log(d)
log(d) = (S - 0.159) / 0.118
S = 9/100 = 0.09
log(d) = (0.09 - 0.159) / 0.118
log(d) = -0.58475
d = 0.26 mm.
2006-08-27 11:30:46 · answer #3 · answered by bpiguy 7 · 0⤊ 0⤋