1)Find the largest integer n for which 12^n evenly divides 20! .

2)Suppose that a, b, and c are real numbers for which

a^2*b^2=28

b^2*c^2=21

a^2*c^2=27

Multiple questions deleted - Melody.

DragonXlayer Sep 25, 2020

#4**+1 **

From first equation b^2 = 28/a^2

From third equation c^2 = 27/a^2 Sub these into equation 2

28*27 / a^{4 }=21

a = +- sqrt 6 =+-2.45

Sub this into the first equation to find b

then b = +- 2.16

then c = +- 2.12

Since a < b < c a = -2.45 b = -2.16 c = +- 2.12

3b then equal 3 * -2.16 = -6.48

ElectricPavlov Sep 25, 2020