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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.

 Sep 25, 2020
edited by DragonXlayer  Sep 25, 2020
edited by Melody  Sep 26, 2020
 #1
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1) The largest n is n = 7.

 

2) 3b = 56.

 Sep 25, 2020
 #2
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okay thanks

DragonXlayer  Sep 25, 2020
edited by DragonXlayer  Sep 25, 2020
 #3
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Sorry, can't tell you what the actual answer is, but the guest is most likely incorrect.

Weiart000  Sep 25, 2020
 #4
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From first equation    b^2 = 28/a^2

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

 

28*27 / a4   =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

 Sep 25, 2020
edited by ElectricPavlov  Sep 25, 2020

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