Question
Asked Jul 25, 2019
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Find the point P on the line y = 5x that is closest to the point (52,0).  What is the least distance between P and (52,0)?

Let D be the distance between the two points. What is the objective function in terms of one number, x?

D =       

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Expert Answer

Step 1

Given:

The equation of the line is y = 5x.

(52,0) is the closest point to the point P which line on the line y= 5x.

Step 2

Calculation:

Let P(x,5x) and the other point be (52,0).

Compute the distance between the points P(x,5x) and (52,0) as follows.

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D (x-52)(5x - 0) D (x-52)25x2 D2 (x-52)25x2

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Step 3

Now, derivative the above obtained distance equation ...

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(D)=-52)+(25x") d d d (х-52)* +- dx dD 2D | 2 ( x-52)+ 50x dx dD D =x-52+ 25x dx

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