Concept explainers
(a)
To Find: The expression for the sum of the cube of the number line.
(a)
Answer to Problem 39PPS
The expression for the sum of the cube of the number and the three is
Explanation of Solution
Consider that the number
Thus, the expression for the sum of the cube of the number and the three is
(b)
To Find: The table that includes the value of the expression for the 10 different values of
(b)
Answer to Problem 39PPS
The required table is shown in Table 1
Explanation of Solution
Consider the given expression is
The table for the value is shown in Table 1
Table 1
|
|
-4 | -61 |
-3 | -24 |
-2 | -5 |
-1 | 2 |
0 | 3 |
1 | 4 |
2 | 11 |
3 | 30 |
4 | 67 |
5 | 128 |
(c)
To Find: The conjecture about the values of the n when the value of the expression is even.
(c)
Answer to Problem 39PPS
The conjecture is if
Explanation of Solution
Consider the given expression is
From the table 1 it is clear that the expression
Thus, the conjecture is if
(d)
To Find: The indirect proof of the conjecture.
(d)
Answer to Problem 39PPS
The assumption is false.
Explanation of Solution
Calculation:
Consider that for the direct proof it must be assumed temporarily that the conclusion is false. It is observed by assuming that it is logically impossible to prove that the assumption is false as the original conclusion is true. For part (d) as the value fo
Consider the expression as
Consider the indirect proof that he n is even then,
Consider that for kto be the integer
Thus, the assumption is false.
Chapter 5 Solutions
Geometry, Student Edition
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