Chapter 4.3, Problem 62PS

Solution

a.

How tall is the arch at its highest point?

  $=630ft$

Given information:

The modeled function $y=757.7-63.85\left(e^{x/127.7}+e^{-x/127.7}\right)$

Concept Used:

Use the function and make the graph, from the graph can get highest point.

Calculation:

As per the given problem

Note the equation $y=757.7-63.85\left(e^{x/127.7}+e^{-x/127.7}\right)$

Now draw the graph

  

Now from the graph the highest point is about $630ft$.

Conclusion:

Hence, the highest point $630ft$

b.

How far apart are the ends of the arch?

  $=630ft$

Given information:

The modeled function $y=757.7-63.85\left(e^{x/127.7}+e^{-x/127.7}\right)$

Concept Used:

Use the function and make the graph, from the graph can get highest point.

Calculation:

As per the given problem

Note the equation $y=757.7-63.85\left(e^{x/127.7}+e^{-x/127.7}\right)$

Now draw the graph

  

Note that from the graph $x\approx 314.981$ is the distance from the center to one of the x intercept

Now double it to find how far apart the ends of the arch are

  $2\left(314.981\right)\approx 630ft$

Now from the graph the highest point is about $630ft$.

Conclusion:

Hence, the ends of the arch $630ft$