Two factories are located at the coordinates (-x, 0) and

arneguet9k

arneguet9k

Answered question

2021-12-02

Two factories are located at the coordinates (-x, 0) and (x, 0) and their power supply is at (0, h). Find y such that the total length of power line from the power supply to the factories is a minimum.

Answer & Explanation

Parminquale

Parminquale

Beginner2021-12-03Added 17 answers

If we call the entire length L, the equation to the right of the equal sign can be used to represent the length
L=(hy)+2x2+y2 
Consider the y-related derivative. h and x are constants; keep that in mind.
dL dy =1+2(2y2x2+y2) 
Simplify 
dL dy =1+2yx2+y2 
Derivative should be set to zero.
0=1+2yx2+y2 
Add 1 to both sides 
2yx2+y2=1 
Multiply both sides by x2+y2 
2y=x2+y2 
Square both sides. 
(2y)2=(x2+y2)2 
Squaring both sides 
4y2=x2+y2 
Subtract y2 form both sides 
3y2=x2 
Divide both sides by 3 
y2=x23 
Take the square root of both sides. Since it is a length we are only interested in the positive square root. 
y=x3 
Answer: 
y=x3

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?