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Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
3. Section 9.3
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Exercise 101 Page 519

Practice makes perfect
a The ratio of the areas A and B is the square of the linear scale factor between A and B.

(Linear scale factor)^2=(2/5)^2
PowQuot

(a/b)^m=a^m/b^m

(Linear scale factor)^2=2^2/5^2
CalcPow

Calculate power

(Linear scale factor)^2=4/25

The ratio of the areas of A and B is 425.

b The ratio of the perimeters of A and B is another way of expressing the linear scale factor.

The perimeter of A and B is 14:1 [0.4em] ⇕ Linear scale factor=14/1

Like in Part A, to find the ratio of the areas we have to square the linear scale factor.

(Linear scale factor)^2=(14/1)^2
PowQuot

(a/b)^m=a^m/b^m

(Linear scale factor)^2=14^2/1^2
CalcPow

Calculate power

(Linear scale factor)^2=196/1

The ratio of the areas of A and B is 196:1.

c As already discussed in Parts A and B, we know that the area of A is 81 times that of B. With this information, we can write the following equation.
Ratio of areas=81 ⇕ (Linear scale factor)^2=81 By solving for the linear scale factor we can determine the ratio of the perimeters.

(Linear scale factor)^2=81
SqrtEqn

sqrt(LHS)=sqrt(RHS)

Linear scale factor=± 9

(linear scale factor) > 0

Linear scale factor= 9

The linear scale factor is 9, which means the perimeter of A is 9 times greater than the perimeter of B.

Subchapter links expand_more
arrow_right 9.3.1 Average Rate of Change and Projectile Motion p.511-514
78
Average Rate of Change and Projectile Motion 79 (Page 512)
Average Rate of Change and Projectile Motion 80 (Page 512)
Average Rate of Change and Projectile Motion 81 (Page 512)
Average Rate of Change and Projectile Motion 82 (Page 513)
Average Rate of Change and Projectile Motion 83 (Page 513)
Average Rate of Change and Projectile Motion 84 (Page 513)
Average Rate of Change and Projectile Motion 85 (Page 513)
Average Rate of Change and Projectile Motion 86 (Page 513)
Average Rate of Change and Projectile Motion 87 (Page 514)
Average Rate of Change and Projectile Motion 88 (Page 514)
Average Rate of Change and Projectile Motion 89 (Page 514)
Average Rate of Change and Projectile Motion 90 (Page 514)
Average Rate of Change and Projectile Motion 91 (Page 514)
arrow_right 9.3.2 Comparing the Growth of Functions p.518-519
Comparing the Growth of Functions 95 (Page 518)
96
Comparing the Growth of Functions 97 (Page 518)
98
Comparing the Growth of Functions 99 (Page 519)
100
Comparing the Growth of Functions 101 (Page 519)
arrow_right 9.3.3 Piecewise-Defined Functions p.522-523
107
108
Piecewise-Defined Functions 109 (Page 522)
Piecewise-Defined Functions 110 (Page 522)
Piecewise-Defined Functions 111 (Page 522)
Piecewise-Defined Functions 112 (Page 523)
Piecewise-Defined Functions 113 (Page 523)
arrow_right 9.3.4 Combining Functions p.526-527
Combining Functions 118 (Page 526)
119
Combining Functions 120 (Page 526)
Combining Functions 121 (Page 526)
Combining Functions 122 (Page 527)
Combining Functions 123 (Page 527)
Combining Functions 124 (Page 527)