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Feliz [49]
3 years ago
11

What is the solution set for |z+4|>15

Mathematics
1 answer:
Contact [7]3 years ago
5 0

Answer:

z + 4 = 15 \\ z + 4 - 4 = 15 \\ z = 15 - 4 \\ z = 11

z>11

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How to convert base two to base three​
sladkih [1.3K]

Consider this example: say we want to convert <em>x</em> = 11 0101 1001₂ to base 3.

The binary expansion of <em>x</em> is

<em>x</em> = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰

which in base 10 reduces to

<em>x</em> = 512 + 256 + 64 + 16 + 8 + 1 = 857

Recall the first several powers of 3:

3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729

Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.

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857 = 1×729 + 128 = 1×3⁶ + 128

• How many times does 81 go into 128? Also 1 time, so

128 = 1×81 + 47 = 1×3⁴ + 47

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47 = 1×27 + 20 = 1×3³ + 20

• How many times does 9 go into 20? 2 times,

20 = 18 + 2 = 2×9 + 2 = 2×3² + 2

• How many times does 1 go into 2? Also 2 times,

2 = 2 + 1 = 2×1 + 0 = 2×3⁰

So we found

857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰

which is the ternary expansion of <em>x</em>,

<em>x</em> = 1 011 202₃

6 0
2 years ago
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