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2 years ago

What is the largest integer $n$ such that $7^n$ divides $1000!$ ?

Mathematics

1 answer:

stiks02 [169]2 years ago

6 0

Answer:

The correct answer is

n = 3038

Step-by-step explanation:

Where we have;

We note that 1000! = An even number

Since Even × Even = even

Even × Odd = Even

Also, 7ⁿ is an Odd number since odd × odd = odd

Therefore 7ⁿ will divide 1000! with some fractions as follows;

1000! divided by 7ⁿ

When 7ⁿ = 1000!

log(7ⁿ) = log(1000!) = log(4.02×10²⁵⁶⁷)

n·log(7) = 2567.604

n = 2567.604/(log(7)) = 3038.23

Therefore, the largest integer n such that 7ⁿ divides 1000! = 3038

Which gives, 1000! ÷ 7³⁰³⁸ = 1.5733.

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Answer: All the real values except x ≠ 7 and the x for which f(x)≠-3

Step-by-step explanation:

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2 years ago

The two-way frequency table below shows the preferred communication method of employees at a company, based on years of employme

Anna35 [415]

Answer:

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Step-by-step explanation:

The proportion is the number of desired outcomes divided by the number of total outcomes.

The percentage is the proportion multiplied by 100.

In this question:

210 employees with 8 of more year.

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0.3048*100 = 30.48%

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2 years ago

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Vinil7 [7]

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2 years ago

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2 years ago

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lisabon 2012 [21]

Answer:

<em>Mrs. Adams will earn $3,120 of interest at the end of year 8.</em>

Step-by-step explanation:

<u>Simple Interest</u>

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2 years ago