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
Answered question
2022-07-31
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?
Answer & Explanation
Helena Howard
Beginner2022-08-01Added 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)
Carpanedam7
Beginner2022-08-02Added 3 answers
The distance formula is as follows:
Using this formula, we can calculate the distances between thepoints. The distance between point A&B is: