Installing an electric power line underwater costs $90,000 permile and running it along land costs $48,000 per mile. Supposepoint A is at coordinates (in miles) (0,3), point B is at (x,0),and point C is at coordinates (20,0). To run the wire from point Ato point B, the power line must be run underwater. To run the powerline from point B to point C, the power line runs along land. Thetotal cost to run the power line from point A to point B to point C is $1,500,000. Where is point B?

Freddy Friedman 2022-07-31 Answered
Installing an electric power line underwater costs $90,000 permile and running it along land costs $48,000 per mile. Supposepoint A is at coordinates (in miles) (0,3), point B is at (x,0),and point C is at coordinates (20,0). To run the wire from point Ato point B, the power line must be run underwater. To run the powerline from point B to point C, the power line runs along land. Thetotal cost to run the power line from point A to point B to point C is $1,500,000. Where is point B?
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Answers (2)

Helena Howard
Answered 2022-08-01 Author has 12 answers
$1,500,000 = (x/y)*$90,000 + a*$48,000
because A and B have a distance in the x and y direction betweenthem, while B and C only have distance in the x direction betweenthem, a distance that could be either (x-20) or (20-x) depending onwhere its located (we are going to call this a for now.
now we solve for x assuming a=(x-20)..... so x is greater than20
$1,500,000 = (x/y)*$90,000 + (x-20)*$48,000
$1,500,000 = x*((1/y)*$90,000 + $48,000) -(20)$48,000.................... distribute the $48000 and take outthe x form the rest of the terms.
x = ($1,500,000+(20)$48000) / ((1/y)*$90,000 + $48,000)
now plug in 3 for y
and you get x = 31.54 or round it to 32
now we try it with a = (20-x)
$1,500,000 = (x/y)*$90,000 + (20-x)*$48,000
$1,500,000 = x*((1/y)*$90,000 - $48,000) +(20)$48,000.................... distribute the $48000 and take outthe x form the rest of the terms.
x = ($1,500,000-(20)$48000) / ((1/y)*$90,000 + $48,000)
now plug in 3 for y
and you get x = -30
so you get two answers B = (32,0) and (-30,0)
so i guess your answer will depend on whether B or C are fartherform A, but they both work....
you can try to plug the answers in and see that you get $1,500,000in both (just remember that the equation depends on where you wantpoint B to be with relation to point C)
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Carpanedam7
Answered 2022-08-02 Author has 3 answers
The distance formula is as follows:
d = ( x ) 2 + ( y ) 2 = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2
Using this formula, we can calculate the distances between thepoints.
The distance between point A&B is:
( x 0 ) 2 + ( 0 3 ) 2 = x 2 + 9
Between B&C:
( 20 x ) 2 = 20 x
So we know that 90 , 000 ( x 2 + 9 ) + 48 , 000 ( 20 x ) = 1 , 500 , 000
90 , 00 ( x 2 + 9 ) + 960 , 000 48 , 000 x = 1 , 500 , 000
90 , 000 ( x 2 + 9 ) = 540 , 000 + 48 , 000 x
x 2 + 9 = 6 + 8 15 x
x 2 + 9 = 64 225 x 2 + 32 5 x + 36
0 = 161 225 x 2 + 32 5 x + 36
0 = 161 225 x 2 + 32 5 x + 27
Now if we use the quadratic equation
x = b ± b 2 4 a c 2 a , we get
32 5 ± ( 32 5 ) 2 4 ( 161 225 ) ( 27 ) 2 ( 161 225 )
720 161 ± ( 225 322 2956 25 )
b(x)=-3.13 (-3.13,0)
or b(x)=12.1 (12.1,0)
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