Question

a plane is going to fly 300 miles at a planned speed of 530 mph. the flight will have an average headwind of w miles per hour the entire time, meaning the plane is flying directly against the wind. the time t in hours, of the flight is a function of the speed of the w, in mph, and can be modeled by

$t(w)=\frac{300}{530 - w}$

here is the graph of $y = t(w)$

2 what does $t(110)$ mean in this situation?

(a) the total time together

(b) at what value of w does the graph have a vertical asymptote?

a -530
b 530
c -110
d -300
e 110
f 300

(c) explain how you know and what this asymptote means in the situation.

the is a vertical asymptote because its close to the line but never crosss

Explanation:

Step1: <Find the vertical asymptote>

For a rational function \(T(w)=\frac{300}{530 - w}\), the vertical asymptote occurs when the denominator is equal to \(0\). So we set \(530 - w=0\).

Step2: <Solve the equation>

Solving \(530 - w = 0\) for \(w\), we add \(w\) to both sides of the equation: \(530=w\).

Answer:

B. \(530\)