Q. 119 From a parking lot, youwant to w... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 119 (page 397)

From a parking lot, you
want to walk to a house on the beach. The house is located
1500 feet down a paved path that parallels the ocean, which
is 500 feet away. See the illustration. Along the path you can
walk 300 feet per minute, but in the sand on the beach you
can only walk 100 feet per minute.
The time T to get from the parking lot to the beach
house can be expressed as a function of the angle u shown in
the illustration and is
$T (胃) = 5 - \frac{5}{3 \tan 胃} + \frac{5}{\sin 胃}, 0 < 胃 < \frac{蟺}{2}$
Calculate the time T if you walk directly from the parking lot
to the house.

Short Answer

Expert verified

The time taken is 15.8 minutes.

Step by step solution

Step 1. Given Information

Expression to calculate time

$T (胃) = 5 - \frac{5}{3 \tan 胃} + \frac{5}{\sin 胃}, 0 < 胃 < \frac{蟺}{2}$

Speed = 300 feet per minute

Horizontal distance = 1500 feet

Vertical distance = 500 feet

Step 2. Calc ulation

$F r o m t h e f i g u r e \tan 胃 = \frac{y}{x} \tan 胃 = \frac{500}{1500} \tan 胃 = \frac{1}{3} N o w w e w i l l c a l c u l a t e S i n 胃 f r o m t h e f i g u r e S i n 胃 = \frac{y}{r} w h e r e, r = \sqrt{x^{2} + y^{2}} t h e r e f o r e, \sin 胃 = \frac{y}{\sqrt{x^{2} + y^{2}}} a n d \sqrt{x^{2} + y^{2}} = \sqrt{3^{2} + 1^{2}} = \sqrt{10} \sin 胃 = \frac{1}{\sqrt{10}} s u b s t i t u t i n g t h i s i n t h e e q u a t i o n f o r t i m e w e g e t T (胃) = 5 - \frac{5}{3 \tan 胃} + \frac{5}{\sin 胃}, 0 < 胃 < \frac{蟺}{2} T (胃) = 5 - \frac{5}{3 脳 \frac{1}{3}} + \frac{5}{\frac{1}{\sqrt{10}}} = 5 - 5 + 5 \sqrt{10} = 15.8 m i n u t e s$