Finals question.

[Watt2x]

The formula is:

L= sqrt(x^2+1600) + sqrt(x^2-160x+10000)

So far I got the derivative, which is:

L'= (2x) / (2*sqrt(x^2=1600)) + (2x-160) / (2*sqrt(x^2-160+10000))

I know that I need to solve this equation (finding the optimum) by saying = 0, like so:

(2x) / (2*sqrt(x^2=1600)) + (2x-160) / (2*sqrt(x^2-160+10000)) = 0






And I know the answer should be x = 32, but how do you solve this equation? (step by step please).

Extra info:
The question is called bushalte on page 5.
http://static.examenblad.nl/9336111/d/ex2011/ha-1025-a-11-1-o.pdf
Its in Dutch but I'll give you gist of it. Its about find the optimum length of footpath between two apartments to connect too one bus stop.

Thanks in advance,

 

[Deleted member 4993]

The formula is:

L= sqrt(x^2+1600) + sqrt(x^2-160x+10000)

So far I got the derivative, which is:

L'= (2x) / (2*sqrt(x^2+1600)) + (2x-160) / (2*sqrt(x^2-160+10000))

I know that I need to solve this equation (finding the optimum) by saying = 0, like so:

(2x) / (2*sqrt(x^2+1600)) + (2x-160) / (2*sqrt(x^2-160+10000)) = 0

x/√(x² + 1600) = (80-x)/√(x² - 160x + 10000)

Now square both sides and continue.....

And I know the answer should be x = 32, but how do you solve this equation? (step by step please).

Extra info:
The question is called bushalte on page 5.
http://static.examenblad.nl/9336111/d/ex2011/ha-1025-a-11-1-o.pdf
Its in Dutch but I'll give you gist of it. Its about find the optimum length of footpath between two apartments to connect too one bus stop.

Thanks in advance,

If this is a problem from your finals - are you supposed to get external help??!!

 

[Watt2x]

As per Subhotosh:
x / [SQRT(x^2 + 1600)] = (80 - x) / SQRT[(x^2 - 160x + 10000)]

Are you able to square both sides?

If so, then your next step is criss-cross multiplication.

Hint: at one point, the (x^4)'s and (x^3)'s will cancel out.

32 is correct as solution; the other solution (to be disregarded) is -160.

Don't think we should give more help than this, being from your finals.

Wouldn't it be odd that I have the answer to my finals.. Its from the finals of a previous year, and students are encouraged to study them.
But they don't offer much help as to how some things come to be. And I don't have external help because I signed up for the state exams this year, and not for school.

But thank you for these hints they made it quite clear.

 

[Deleted member 4993]

Wouldn't it be odd that I have the answer to my finals.. Its from the finals of a previous year, and students are encouraged to study them.
But they don't offer much help as to how some things come to be. And I don't have external help because I signed up for the state exams this year, and not for school.

But thank you for these hints they made it quite clear.

Odd - but not impossible, thanks to internet ......

 

[Watt2x]

I did do a internet course but they wouldn't give you the answer because you could only fill in the answer.

But yes Mr. Khan, internet courses are the future.. I'll give you that.

 

[Watt2x]

Yup, I get it now.

I finished of the exercise by using the ABC method.

Thanks for the help.