PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
10th Edition
ISBN: 9780136174318
Author: Demana
Publisher: PEARSON
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Chapter P.2, Problem 64E
Solution

a.

The coordinate of the points one-third and two-thirds of the way from a=2 to b=8 .

  4,  6

Given:

The numbers, a=2 to b=8 .

Calculation:

Note that the distance between the points a and b on the number line is

  8−2=6

One third of this distance is, 13×6=2 .

So, the point that is one-third from a must be 2 units right of the point a . And the point that is two-thirds on the way must be 4 units right side of a .

Thus, the point that is one-third of the way is 4 and the number that is two-thirds is 6.

b.

The coordinate of the points one-third and two-thirds of the way from a=−3 to b=7 .

  13,  113

Given:

The numbers, a=−3 to b=7 .

Calculation:

Note that the distance between the points a and b on the number line is

  7−−3=10

One third of this distance is, 13×10=103 .

So, the point that is one-third from a must be 103 units right of the point a . And the point that is two-thirds on the way must be 203 units right side of a .

So, the point on the number line that is one-third from a is

  −3+103=−9+103=13

And the number that is two-thirds from a is

  −3+203=−9+203=113

Thus, the point that is one-third of the way is 13 and the number that is two-thirds is 113 .

c.

The coordinate of the points one-third and two-thirds of the way from a to b .

  2a+b3,  a+2b3

Given:

The numbers, a and b .

Calculation:

Note that the distance between the points a and b on the number line is

  b−a

One third of this distance is, 13×b−a=b−a3 .

So, the point that is one-third from a must be b−a3 units right of the point a . And the point that is two-thirds on the way must be 2b−a3 units right side of a .

So, the point on the number line that is one-third from a is

  a+b−a3=3a+b−a3=2a+b3

And the number that is two-thirds from a is

  a+2b−a3=3a+2b−2a3=a+2b3

Thus, the point that is one-third of the way is 2a+b3 and the number that is two-thirds is a+2b3 .

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Chapter P.2, Problem 63E
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Chapter P.2, Problem 65E

Chapter P Solutions

PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)

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