Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 10.8, Problem 38E

a.

To determine

Write the system of second degree inequalities.

a.

Expert Solution
Check Mark

Answer to Problem 38E

  x2≤−9(y−4)y≥0

Explanation of Solution

Given information:

The transport and road laboratory proposes a parabolic speed bumps 4  inches in height and 1 foot  in width.

The vertex of speed bump at (0,4) .

Calculation:

Consider the vertex of speed bump at (0,4) ,

The equation of parabolic bump will be,

  x2=−4b(y−4)width=12  inches (∴1foot=12inch)

Therefore both end of the bump are 6  inches from the axis of parabola, means x=0 .

The coordinate of end point of speed bump are, (6,0),(−6,0)

Substitute (6,0) in x2=−4b(y−4) we get,

  62=−4b(0−4)b=36/16b=9/4

Substitute b=9/4 in x2=−4b(y−4) we get,

  x2=−494(y−4)x2=−9(y−4)

Now take a test point (0,3)

  0=−9(3−4)=9

  left  hand  side≤right  hand  sidex2≤−9(y−4)y≥0

Hence, system of second degree inequalities is,

  x2≤−9(y−4)y≥0

b.

To determine

Graph the system of second degree inequalities.

b.

Expert Solution
Check Mark

Answer to Problem 38E

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.8, Problem 38E , additional homework tip 1

Explanation of Solution

Given information:

The transport and road laboratory proposes a parabolic speed bumps 4  inches in height and 1 foot  in width.

The vertex of speed bump at (0,4) .

Calculation:

Graph will be,

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.8, Problem 38E , additional homework tip 2

c.

To determine

Write the system of second degree inequalities if height decreases by 3inches .

c.

Expert Solution
Check Mark

Answer to Problem 38E

  x2≤−12(y−3)y≥0

Explanation of Solution

Given information:

The transport and road laboratory proposes parabolic speed bumps 4  inches in height and 1 foot  in width.

The vertex of speed bump at (0,4) .

Calculation:

The height of speed bump is decreases by 3inches .

  x2=−4b(y−3)   at(6,0),(−6,0)62=−4b(0−3)b=36/12b=3

The equation of speed bump is,

  x2=−4×3(y−3) x2=−12(y−3)now  put  (0,2)x2=−12(y−3)0=−12(2−3)=12left  hand  side  ≤right  hand  sidex2≤−12(y−3)y≥0

Hence, the system of second degree inequalities if height decreases by 3inches are,

  x2≤−12(y−3)y≥0

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Chapter 10.8, Problem 37E
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Chapter 10.8, Problem 39E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFUCh. 10.1 - Prob. 2CFUCh. 10.1 - Prob. 3CFUCh. 10.1 - Prob. 4CFUCh. 10.1 - Prob. 5CFUCh. 10.1 - Prob. 6CFUCh. 10.1 - Prob. 7CFUCh. 10.1 - Prob. 8CFUCh. 10.1 - Prob. 9CFUCh. 10.1 - Prob. 10CFU
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