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Yuri [45]
2 years ago
6

Use the equation to answer the question. X^3=729. What

Mathematics
1 answer:
vaieri [72.5K]2 years ago
8 0

Answer:

A

Step-by-step explanation:

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What number falls between 7 and 8 on the number line.
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the answer is 7.5

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Which of the following is a composite number? <br><br> A. 63<br> B. 19<br> C. 1<br> D. 0
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Attachment Mathswatch!!
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y=3x+1

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Mathematical induction of 3k-1 ≥ 4k ( 3k = k power of 3 )
tresset_1 [31]

For making mathematical induction, we need:

  • a base case

An n_0 for which the relation holds true

  • the induction step

if its true for n_i, then, is true for n_{i+1}

<h3>base case</h3>

the relationship is not true for 1 or 2

1^3-1 = 0 < 4*1

2^3-1 = 8 -1 = 7 < 4*2 = 8

but, is true for 3

3^3-1 = 27 -1 = 26 > 4*3 = 12

<h3>induction step</h3>

lets say that the relationship is true for n, this is

n^3 -1 \ge 4 n

lets add 4 on each side, this is

n^3 -1 + 4 \ge 4 n + 4

n^3 + 3 \ge 4 (n + 1)

now

(n+1)^3 = n^3 +3 n^2 + 3 n + 1

(n+1)^3 \ge n^3 + 3 n

if n \ge 1 then 3 n \ge 3 , so

(n+1)^3 \ge n^3 + 3 n \ge n^3 + 3

(n+1)^3 \ge  n^3 + 3 \ge 4 (n + 1)

(n+1)^3  \ge 4 (n + 1)

and this is what we were looking for!

So, for any natural equal or greater than 3, the relationship is true.

4 0
3 years ago
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