/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 92 Bridge Clearance A one-lane high... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 92 (page 412)

Bridge Clearance A one-lane highway runs through a tunnel in the shape of one-half a sine curve cycle. The opening is 28 feet wide at road level and is 15 feet tall at its highest point.

(a) Find an equation for the sine curve that fits the opening. Place the origin at the left end of the sine curve.
(b) If the road is 14 feet wide with 7 -foot shoulders on each side, what is the height of the tunnel at the edge of the road?

Short Answer

Expert verified

(a) The required sin functiony=15sin蟺28t

(b) The height of the tunnel at the edge of road is 152units

Step by step solution

01

Step 1.(a) Find an equation for the sine curve that fits the opening. Place the origin at the left end of the sine curve. 

The equation for the sine curve that fits the opening can be found out if we consider the curve with left end as the origin and half cycle as the half curve of sine function above the x-axis as follows-:


Now, the half-curve begins at x=0and ends at x=28, so the period of the function will be T=56as the full cycle will end at x=56. Therefore,

蝇=2蟺T=2蟺56=蟺28

Also, the amplitude of the function will beA=15because the maximum value of this sine function atx=0is 15 units.
Since the sine function is of the form y=Asin(蝇t), we get the required sine function as-:

localid="1646480248236" y=15sin蟺28t

02

Step 2.(b) If the road is 14 feet wide with 7 -foot shoulders on each side, what is the height of the tunnel at the edge of the road? 

If the road is 14 feet wide, the road will be 7 feet away from the origin point from where the sine curve starts.
So, we need to find the value of function atx=7to find the height of tunnel at the edge of road which is-:

y=15sin蟺28(7)=15sin蟺4=1512=152

Hence,the height of the tunnel at the edge of road is152units

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the exact value of: sin40掳+sin130掳+sin220掳+sin310掳

According to the Old Farmer鈥檚 Almanac,

in Miami, Florida, the number of hours of sunlight on the

summer solstice of 2011 was 13.75, and the number of hours.

(a)

Find a sinusoidal function of the form

y=Asin(蝇x-蠒)+Bthat models the data.

of sunlight on the winter solstice was 10.55.

(b)

Use the function found in part (a) to predict the number

of hours of sunlight on April 1, the 91st day of the year.

(c) Draw a graph of the function found in part (a).

(d)

Look up the number of hours of sunlight for April 1

in the Old Farmer鈥檚 Almanac, and compare the actual

hours of daylight to the results found in part (b).

The mean distance of the moon from Earth is 2.39脳105 miles. Assuming that the orbit of the moon around Earth is circular and that 1 revolution takes 27.3 days, find the linear speed of the moon. Express your answer in miles per hour.

What is the range of the tangent function?

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)=5-53tan胃+5sin胃,0<胃<蟺2

Calculate the time T if you walk directly from the parking lot

to the house.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.