Chapter 9, Problem 25PT

(A)

To determine

To find: The transverse axis is horizontal.

Answer to Problem 25PT

The transverse axis is horizontal $\frac{x^2}{1.1025}-\frac{y^2}{7.8975}=1$ .

Explanation of Solution

Given information:

The given function is primary station are $6km$ and the speed of sound $0.35\raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ .

Calculation:

Calculate the function

The difference of the explosion’s distance from two station.

  $0.35*6=2.1km$

The distance of any point on hyperbola two foci is equal to the value of $2a$ .

  $\begin{array}{l}2a=2.1\\ a=1.05\end{array}$

The distance between two foci will be equal to 2c.

  $\begin{array}{c}2c=6\\ c=3\end{array}$

Use the relation between $a,bandc$ the value of b follows,

  $\begin{array}{c}{c}^2=a^2+b^2\\ {\left(3\right)}^2={\left(1.05\right)}^2+b^2\\ b^2=9-1.1025\\ =7.8975\end{array}$

Use the equation hyperbola.

  $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

Substitute the value of $a=1.05and{b}^2=7.8975$ .

  $\begin{array}{c}\frac{x^2}{{1.05}^2}-\frac{y^2}{{\left(7.8975\right)}^2}=1\\ \frac{x^2}{1.1025}-\frac{y^2}{7.8975}=1\end{array}$

Therefore, the transverse axis is horizontal $\frac{x^2}{1.1025}-\frac{y^2}{7.8975}=1$ .

(G)

To determine

To graph: for the ranger station in the drawing.

Explanation of Solution

Given information:

The given function is primary station are $6km$ and the speed of sound $0.35\raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ .

Graph:

The sketch of the equation $\frac{x^2}{1.1025}-\frac{y^2}{7.8975}=1$ is as follows figure (1): Figure (1)

Therefore, the two stations will be at point $\left(-3,0\right)and\left(3,0\right)$ .