Calculus
posted by Kokos .
Two posts, one 12 feet high and the other 28 feet high, stand 30 feet apart. They are to be stayed by two wires, attached to single stake, running from ground level to the top of each post. Where should the stake be placed to use the least wire?

If we place the origin (0,0) at the base of the 12' stake, then the 28' stake has its base at (30,0).
If the length of wire used is
L = sqrt(x^2 + 12^2) + sqrt((x30)^2 + 28^2)
= sqrt(x^2 + 144) + sqrt(x^2  60x + 1684)
dL/dx = x/(sqrt(x^2 + 144) + (x30)/sqrt(x^2  60x + 1684)
dL/dx = 0 when x=9
so, place the stake between the poles, 9' from the short pole, and 21' from the tall pole.
Respond to this Question
Similar Questions

Calculus
Two posts, one 12 feet high and the other 28 feet high, stand 30 feet apart. They are to be stayed by two wires, attached to single stake, running from ground level to the top of each post. Where should the stake be placed to use the … 
3rd grade math
A rectangle measures 30 feet by 20 feet and has a post at each corner. If posts are placed 2 feet apart. How many posts will there be in all? 
college/ precal
a square fence 9 feet high enclosing a radio tower is 3 feet from the tower on all 4 sides. guy wires used to hold the tower in position are attached to the tower 30 feet above the ground and 13 feet from the fence on all 4 sides. … 
calculus
2 posts one is 10m high and other is 15m higs stand 30m apart they are to be stayed by transmission wire attached to a single stake at the ground level, the wire running to the top of the post , where should stake place to used least … 
Geometry
I have two post that meet the ground perpendicular and the ground is level. One post is 40 feet high, the other is 25 feet high. If I draw a hypotenuse from the top of one post to the base of the other post and another hypotenuse from … 
math
Trahen is building a fence that is 6 feet high and 18 feet wide to put around his garden. He has two sizes of boards that he can use. One is 2 feet by 6 feet and the other is 4 feet by 6 feet. Trahen can put the boards either horizontally … 
Math! Helppppp
Two poles are place 15 feet apart. One pole is 8 ft high and the other pole is 16 ft high. The top of each pole is attached to the base of the other by cable which run in a straight line. Find the slopes of the lines defined by the … 
Algebra
Scott set up a volleyball net in his backyard. one of the poles, which forms a right angle with the ground, is 6 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 8 feet from the bottom of the pole. … 
Calculus
A statue 10 feet high is standing on a base 13 feet high. If an observer's eye is 5 feet above the ground, how far should he stand from the base in order that the angle between his lines of sight to the top and bottom of the statue … 
math
a post 47 m high is supported by two equal wires attached to its top and to two points on a level ground, each of it is 18 m from the food of the post. Find the length of each wire