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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.

Question:

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

#1
+111331
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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  !!!

Feb 26, 2019
edited by CPhill  Feb 26, 2019
#2
+194
+1

u good bro

Feb 26, 2019
#3
+109527
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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.

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.

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