The Height $h$ From Ground Level to a Hanging Cable Suspended Between Two

question 42

Essay

The height $h$ from ground level to a hanging cable suspended between two utility poles can be described by the function $h ( x ) = \frac { a } { 2 } \left( e ^ { x / a } + e ^ { - x / a } \right)$ , where $x$ is the horizontal distance in feet, measured from the origin, and $a$ is the lowest point of the hanging cable.
(a) Find the height of a cable, correct to two decimal places, $10$ feet to the right of its origin and its lowest point
$10$ feet above ground level.
(b) Find the height of a cable, correct to two decimal places, $25$ feet to the left of its origin and its lowest point
$35$ feet above ground level.

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