a. two poles of heights m and n are separated by a horizontal distance d. a rope is stretched from the top…

a. two poles of heights m and n are separated by a horizontal distance d. a rope is stretched from the top of one pole to the ground and then to the top of the other pole. show that the configuration that requires the least amount of rope occurs when θ1 = θ2. b. fermats principle states that when light travels between two points in the same medium (at a constant speed), it travels on the path that minimizes the travel time. show that even when light from a source a reflects off a source and is received at point b, the angle of incidence equals the angle of reflection, or θ1 = θ2. a. let x represent the distance from the base of the first pole to the point where the rope contacts the ground. write an expression for the length of the rope from the top of the first pole to the ground l1 using only d, m, n, and x. l1 = √(m² + x²) write an expression for the length of the rope from the top of the second pole to the ground l2 - using only d, m, n, and x. l2 =

a. two poles of heights m and n are separated by a horizontal distance d. a rope is stretched from the top of one pole to the ground and then to the top of the other pole. show that the configuration that requires the least amount of rope occurs when θ1 = θ2. b. fermats principle states that when light travels between two points in the same medium (at a constant speed), it travels on the path that minimizes the travel time. show that even when light from a source a reflects off a source and is received at point b, the angle of incidence equals the angle of reflection, or θ1 = θ2. a. let x represent the distance from the base of the first pole to the point where the rope contacts the ground. write an expression for the length of the rope from the top of the first pole to the ground l1 using only d, m, n, and x. l1 = √(m² + x²) write an expression for the length of the rope from the top of the second pole to the ground l2 - using only d, m, n, and x. l2 =

Answer

Explanation:

Step1: Apply Pythagorean theorem for $L_2$

The horizontal distance from the point on the ground to the second - pole is $d - x$, and the height of the second - pole is $n$. By the Pythagorean theorem, which states that for a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $c=\sqrt{a^{2}+b^{2}}$. Here, $a = n$ and $b=d - x$. $L_2=\sqrt{n^{2}+(d - x)^{2}}$

Answer:

$\sqrt{n^{2}+(d - x)^{2}}$