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Could somebody help me w/ a step-by-step walkthrough of this unit that we're learning in school. Our math teacher doesn't teach us anything, and I want actual help from somebody who can help us properly as this year is necessary for my good grades to get into a good college.



Given that xy = 3/2 and both x and y are nonnegative real numbers, find the minimum value of 10x + 3y/5.


Thanks so much, as I really need and geniunly want to understand this topic. 

 Feb 26, 2019

xy = 3/2      implies that   y = 3 / [ 2x]


So....plugging this into  the second function  and get that


10x + (3/5)(3/[2x]) =


10x + 9 / (10x)


If you haven't had Calculus....we can find the  minimum of this curve :  https://www.desmos.com/calculator/nbecr6spbo


The minimum value occurs at x = 3/10    and the minimum is  y = 6


If you have had Calculus....let the function be


y =  10x + (9/10)x^(-1)       take the derivative and set to 0


y ' =  10 - (9/10)x^(-2)  = 0


10  =    (9/10)x^(-2)    rearrange as


x^2 = 9/100       take the positive root   (since x must be positive)


x = 3/10




Taking the second derivative we have


y " =  (18/10)x^(-3)


Putting 3/10 into this produces a positive.....this indicates a minimum at x = 3/10


And y =  10(3/10) + (9/10)/ (3/10) =  


3 + (9/10) (10/3) =


3 + 9/3 =


6  !!!




cool cool cool

 Feb 26, 2019
edited by CPhill  Feb 26, 2019

u good bro

 Feb 26, 2019

Chris you have answered the question for this person but it is highly unlikely that you have taught them anything.

You can not teach a person if you do not intereract with them.  


I was about to answer when I saw you answering.

But my initial response would have been


Have you done any calculus yet?

And can you make y the subject for me (with the first expression) and then plug that y value into the second expression.

Get back to me when you have done that and we will continue furthed.    laugh


I had an extremely frustrated teacher write a comprehsive message to me recently saying that we were destryoying his teaching world by supplying full cheat answers to his students.

I could understand his frustration.  This forum has become best known as a cheat site. Sad but true.

 Feb 26, 2019

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