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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.

Guest Feb 26, 2019

#1**+2 **

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 !!!

CPhill Feb 26, 2019

#3**-1 **

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.

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.

Melody Feb 26, 2019