1.) Find the three geometric means between 16 and 1/322.) Find the two geometric means between 1 and 0.0013.) Two geometric means between 3/4 and 81/1284.) Find the geometric mean between of √15 and √20To whoever will answer to this. Thank you
Answer (1)
Answer:Here are the solutions with the final answers:## Problem 1: Find the three geometric means between 16 and 1/32Given: a = 16, b = 1/32, and n = 3.The formula for the nth geometric mean is:Gk = a (b/a)^(k/(n+1))Calculate b/a:b/a = (1/32) / 16 = 1/512Now, calculate each geometric mean:G1 = 16 (1/512)^(1/4) = √2G2 = 16 (1/512)^(2/4) = 1/√2G3 = 16 (1/512)^(3/4) = 1/8The three geometric means are √2, 1/√2, and 1/8.## Problem 2: Find the two geometric means between 1 and 0.001Given: a = 1, b = 0.001, and n = 2.The geometric means are:Gk = a (b/a)^(k/(n+1))Calculate b/a:b/a = 0.001 / 1 = 0.001Now, calculate each geometric mean:G1 = 1 (0.001)^(1/3) = 0.1G2 = 1 (0.001)^(2/3) = 0.01The two geometric means are 0.1 and 0.01.## Problem 3: Find the two geometric means between 3/4 and 81/128Given: a = 3/4, b = 81/128, and n = 2.The geometric means are:Gk = a (b/a)^(k/(n+1))Calculate b/a:b/a = (81/128) / (3/4) = 27/32Now, calculate each geometric mean:G1 = (3/4) (27/32)^(1/3) = 9/8∛4G2 = (3/4) (27/32)^(2/3) = 27/32The two geometric means are 9/8∛4 and 27/32.
