You are working for a power plant that is located on a highway from east to west. Please help me find the answers to 1-4

Question

The town of Cortez is located 50 miles east of the power plant and 6 miles north of the freeway. The town of Joplin is located 43 miles east of the power plant and 10 miles south of the freeway. To connect power to the Two towns the power plant wants to build one junction station along the freeway then run power out to the tow cities from the junction station. The picture below shows the general layout where x is the length of power line run along the freeway( the length from the power plant to the junction at point P) your boss has asked you to determine where the junction station should be built

1. find a formula for the length of the power line needed to run from the junction at point P out to Cortez as a function of X. Your answer should be a function in terms of X NOT a numerical value of cable needed
2. Find a formula for the length of power line needed to run from the junction at point P out to Joplin as a function of X. Your answer should be a function of X NOT a numerical value for the amount of cable needed.
3. Find a formula for total length of cable needed for running all three length of cable. Your answer should be a function in terms of X NOT a numerical value for the total amount of cable needed
4. Use technology (calculator,Desmos, or other graphing software) to fund the value of x that minimizes the total length of cable needed. the value of X is NOT the total amount of cable needed it is JUST the length of the power line from the power plant to the junction at point P.

Answer 1

Hi Micha!

I've attached a video response to your questions.

Thanks!

- Aaron