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birt gs1 128,
birt ean 128,
birt ean 128,
birt ean 128,
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birt gs1 128,
birt gs1 128,
birt ean 128,
birt ean 128,
birt gs1 128,
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birt ean 128,
birt ean 128,
birt gs1 128,
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birt ean 128,
birt ean 128,
birt ean 128,
birt gs1 128,
birt ean 128,
birt gs1 128,
birt gs1 128,
birt gs1 128,
birt gs1 128,
birt gs1 128,
birt ean 128,
birt gs1 128,
birt ean 128,
birt ean 128,
birt ean 128,
birt ean 128,
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birt gs1 128,
birt gs1 128,
birt ean 128,
birt ean 128,
birt gs1 128,
birt ean 128,
birt ean 128,
birt gs1 128,
birt ean 128,
birt ean 128,
birt ean 128,
birt ean 128,
birt gs1 128,
birt ean 128,
birt gs1 128,
birt ean 128,
birt ean 128,
birt ean 128,
birt ean 128,
birt ean 128,
birt ean 128,
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birt ean 128,
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At the same time in localities near each other, the rays of the sun strike the ground at equal angles; hence, /B > /B in Fig. 7-21. Since the tree and the pole make right angles with the ground, /C > /C . Hence, h 15 nABC , nA B C , so 2 and h 45 ft. 6

of prompting for the numerator and denominator, it reads a fraction type as 2 2 / 7 .

Fig. 7-21

9.19 Implement a conversion operator in the Rat ional class to convert to float type. 9.20 Implement a conversion operator in the Rational class to round to in t type. 9.21 Implement pre-decrement and post-decrement operator in the Rat ional class. 9.22 Implement an exponentiation operator for the Rat ional class with prototype: Rational operator&&(const Rational&, const unsigned&);

For example, if x represents the fraction 2/5, then x&&4 would return the Rat ional that represents the fraction 16/625.

7.24 Proving a similar-triangle problem stated in words Prove that two isosceles triangles are similar if a base angle of one is congruent to a base angle of the other.

9.23 Implement an exponentiation operator for the Rat i onal class with prototype: Rational operator&&(const Rational&, const irk&);

Given: Isosceles nABC (AB AC) Isosceles nA B C (A B A C ) /B > /B To Prove: nABC , nA B C Plan: Prove /C > /C and use Principle 3. PROOF:

For example, if x represents the fraction 2/5, then xscsc - 4 would return the Rat ional that represents the fraction 625/16. (See Problem 9.22.)

Reasons Given Base angles of an isosceles triangle are congruent. Things > to > things are > to each other. Two triangles are similar if two angles of one triangle are congruent to two angles of the other.

n = 10 (not a prime number) n = 13 (prime number)

9.24 Implement addition for the Vet t or class (Problem 9.14) by overloading the + operator. 9.25 Implement subtraction for the vet tor class (Problem 9.14) by overloading the - operator. 9.26 Implement scalar multiplication for the Vector class (Problem 9.14) by overloading the * operator. If t is a double and v is a vector, then t *V would return the Vet tor obtained by multiplying each element of v by t. 9.27 Implement an inner product (i.e., the dot product ) for the Vet tor class (Problem 9.14) by overloading the * operator. If v and w are vectors, then V*W would return the double

Given: Parallelogram ABCD AE AF To Prove: BC BF Plan: Prove (AEF ,nBCF) PROOF:

9.28 Implement a norm function for the Vector class (Problem 9.14). If v.norm() would return the square root of V*V (see Problem 9.27).

9.29 Modify the Vector class (Problem 9.14) so that its objects are all three-dimensional (physi-

Statements 1. 2. 3. 4. 5. 6. ABCD is a parallelogram. ED i BC /DEC > /ECB /EFA > /BFC nAEF , nBCF AE BC AF BF 1. 2. 3. 4. 5.

cal) vectors with subscripts ranging from 1 to 3. Include vector addition (Problem 9.24), vector subtraction (Problem 9.25), scalar multiplication (Problem 9.26), the inner product (Problem 9.27), the norm function (Problem 9.28), and a cross-product function: v x w = (v2w3 - v3w2, v3w1- VlW3, VlW.2 - v2w1)

Reasons Given Opposite sides of a parallelogram are parallel. Alternate interior angles of parallel lines are congruent. Vertical angles are congruent. Two triangles are similar if two angles of one triangle are congruent to two angles of the other. 6. Corresponding sides of similar triangles are in proportion.

9.30 Implement an overloaded assignment operator = for the Time class (see Problem 8.19). 9.31 Implement overloaded stream insertion operator < < the Time class (see Problem 8.19).

PRINCIPLE 1: PRINCIPLE 2: PRINCIPLE 3:

9.32 Implement overloaded pre-increment operator ++ and pre-decrement operator - - for the Time class (see Problem 8.19), where increment means to add one second. 9.33 Implement an overloaded operator + = for the Time class (see Problem 8.19) that adds one