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Let a, b and c be positive numbers satisfying ab = 11.25; ac = 20; and bc = 36. What is the value of c?

 Nov 3, 2019
 #1
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a = 5/2,  b = 9/2,  c = 8,

 

So, c = 8

 Nov 3, 2019
 #2
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Without the workings, this is fucking useless! 

Guest Nov 3, 2019
 #6
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Note that most 'Answerers' are less inclined to provide methods of finding an answer to 'guest' posters and may just post  an answer.....

    Ever thought of signing up as a registered user?    ~EP

ElectricPavlov  Nov 3, 2019
 #5
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b=11.25/a     (from first equation)

 

c=36/b = 36a/11.25

 

ac=20

a  * [36a / 11.25] = 20

solve for a =15/6

 

c= 36a/11.25 = 36(15/6) /11.25 = 8

 Nov 3, 2019
 #7
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Cool!! Thankx EP!

Guest Nov 3, 2019
 #10
avatar+105370 
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ab  =  11.25       ⇒  b  =  11.25 / a       (1)

ac  = 20   ⇒  c  = 20  / a        (2)

bc  = 36         (3)

 

Sub (1)  and (2)   into (3)

 

(11.25 /a ) (20 / a)  = 36

 

225/ a^2  =  36       rearrange as

 

a^2  =  225/36       take the positive root

 

a  =  15 / 6    =   5 / 2

 

So....using (2).....

 

c =  20 / ( 5/2)   =   8

 

 

cool cool cool

 Nov 3, 2019
 #11
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Really cool! Thanks CPhill!  Man Im glad I found this math site

What do you mean by positive root.

Guest Nov 3, 2019
 #12
avatar+105370 
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225 / 36     has two   roots  : (-15/6)     and  (15/6)   

 

If we square both of these.....we get   225 /36

 

But.....since    "a"  is positive....we need   15 / 6    =   5   / 2

 

Does that make sense  ???

 

 

 

cool cool cool

CPhill  Nov 3, 2019
 #13
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Oh yea! I remember the 2 roots thing from quadratic equations but I didnt know that one was a minus number. I remember some them had two plus numbers. How do you know which one to use if they are both plus numbers?

Guest Nov 3, 2019
 #14
avatar+105370 
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The only way that we can get two  positive roots is if we have something like this :

 

(x  - a)^2   =   0             take both roots

 

x  - a   =  0    [  both roots of   0   are  -0   and  + 0   =  0   ]

 

x  = a           (assuming that  a  >  0  )

 

 

cool cool cool

CPhill  Nov 3, 2019
edited by CPhill  Nov 3, 2019
 #15
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I put numbers in there to see what you mean but I only understand this a little. I will work on it some more later when I have time. 

Thanks CPhill with your help I’ll pass the quiz tomorrow and maybe I’ll pass the class.  

Guest Nov 3, 2019

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