Question

compare the functions f(x)=2x³ and g(x)=2ˣ by completing parts (a) and (b). (a) fill in the table below. note that the table is already filled in for x = 5. (the aleks calculator can be used to make computations easier.) x | f(x)=2x³ | g(x)=2ˣ 5 | 250 | 32 6 | | 11 | | 12 | | 13 | | (b) for x ≥ 12, the table suggests that f(x) is select less than g(x).

Explanation:

Step1: Calculate \( f(6) \) and \( g(6) \)

For \( f(x) = 2x^3 \), substitute \( x = 6 \): \( f(6)=2\times6^3 = 2\times216 = 432 \).
For \( g(x) = 2^x \), substitute \( x = 6 \): \( g(6)=2^6 = 64 \).

Step2: Calculate \( f(11) \) and \( g(11) \)

For \( f(x) = 2x^3 \), substitute \( x = 11 \): \( f(11)=2\times11^3 = 2\times1331 = 2662 \).
For \( g(x) = 2^x \), substitute \( x = 11 \): \( g(11)=2^{11} = 2048 \).

Step3: Calculate \( f(12) \) and \( g(12) \)

For \( f(x) = 2x^3 \), substitute \( x = 12 \): \( f(12)=2\times12^3 = 2\times1728 = 3456 \).
For \( g(x) = 2^x \), substitute \( x = 12 \): \( g(12)=2^{12} = 4096 \).

Step4: Calculate \( f(13) \) and \( g(13) \)

For \( f(x) = 2x^3 \), substitute \( x = 13 \): \( f(13)=2\times13^3 = 2\times2197 = 4394 \).
For \( g(x) = 2^x \), substitute \( x = 13 \): \( g(13)=2^{13} = 8192 \).

Table Filling:

| \( x \) | \( f(x)=2x^3 \) | \( g(x)=2^x \) |
|--------|----------------|---------------|
| 5 | 250 | 32 |
| 6 | 432 | 64 |
| 11 | 2662 | 2048 |
| 12 | 3456 | 4096 |
| 13 | 4394 | 8192 |

Step5: Analyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzey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yzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyze

Answer:

Step1: Calculate \( f(6) \) and \( g(6) \)

For \( f(x) = 2x^3 \), substitute \( x = 6 \): \( f(6)=2\times6^3 = 2\times216 = 432 \).
For \( g(x) = 2^x \), substitute \( x = 6 \): \( g(6)=2^6 = 64 \).

Step2: Calculate \( f(11) \) and \( g(11) \)

For \( f(x) = 2x^3 \), substitute \( x = 11 \): \( f(11)=2\times11^3 = 2\times1331 = 2662 \).
For \( g(x) = 2^x \), substitute \( x = 11 \): \( g(11)=2^{11} = 2048 \).

Step3: Calculate \( f(12) \) and \( g(12) \)

For \( f(x) = 2x^3 \), substitute \( x = 12 \): \( f(12)=2\times12^3 = 2\times1728 = 3456 \).
For \( g(x) = 2^x \), substitute \( x = 12 \): \( g(12)=2^{12} = 4096 \).

Step4: Calculate \( f(13) \) and \( g(13) \)

For \( f(x) = 2x^3 \), substitute \( x = 13 \): \( f(13)=2\times13^3 = 2\times2197 = 4394 \).
For \( g(x) = 2^x \), substitute \( x = 13 \): \( g(13)=2^{13} = 8192 \).

Table Filling:

\( x \)	\( f(x)=2x^3 \)	\( g(x)=2^x \)
6	432	64
11	2662	2048
12	3456	4096
13	4394	8192

Step5: Analyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzeyzey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