Determine the largest positive integer N such that 1005! is divisible by 10N.

Answers

Answer 1

9514 1404 393

Answer:

  N = 250

Step-by-step explanation:

The way your question is written, the answer is a number of 2582 digits, much too large to show here. We assume you actually want N such that 10^N is the largest power of 10 that will divide 1005!.

__

That factor is limited by the number of factors of 2 and 5 in 1005!. Of those, there are far more factors of 2, so the actual limit is the number of factors of 5 in 1005!.

Every 5th number is divisible by 5, so there are 1005/5 = 201 numbers divisible by 5 in 1005!.

Every 5th one of those is divisible by another factor of 5, so an additional 201/5 ≈ 40.

Every 5th one of those is divisible by another factor of 5, so an additional 40/5 = 8.

Finally, every 5th one of those has yet another factor of 5, so an additional 8/5 ≈ 1.

Then the total number of factors of 5 in 1005! is 201 +40 +8 + 1 = 250.

That is, the number 1005! will end in 250 zeros. It will be divisible by 10^250.

  N = 250


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A glucose molecule is the smallest type of protein monomer of starch and cellulose largest of the carbohydrate polymers fundamental unit of genetic material.

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Step-by-step explanation:

Glucose is an organic molecule composed of carbon atoms, oxygen atoms, and hydrogen atoms.It has a molecular formula of [tex]C_6H_{12}O_6[/tex]It is a monosaccharide sugar, carbohydrateAn important source of an energy in living organisms.Glucose gives two different natural polymers named: starch and cellulose. This polymer is formed by linking small units of glucose molecules with each other. And this small unit which repeats in the structure of its polymer is known as a monomer.Glucose in the monomer in its natural polymer that was starch and cellulose.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

The probability of rolling the same number

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Answer:

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Step-by-step explanation:

I hope thats correct

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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12.

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[tex] \frac{x + 1}{x - 1} [/tex]

13.

[tex] \frac{ \frac{ {t}^{2} }{ \sqrt{ {t}^{2} + 1} } - \sqrt{ {t}^{2} + 1} }{ {t}^{2} } [/tex]

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Answers

Answer:

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9514 1404 393

Answer:

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Step-by-step explanation:

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_____

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Answers

Answer:

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Find the value of x if 3(4x+3)

Answers

You can’t actually find x with this equation.
3(4x+3)
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If it was something like this:
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add 6 to the difference between 9 and 7

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d) 9 - (7 + 6)

Answers

It is b!!!!!! (9-7)+6

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Answers

Answer:

{6, 8, 10, 12, 14, 16, 18, 20, ...}

Step-by-step explanation:

even natural numbers >/= 6.

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The set of even natural numbers greater than or equal to 6 is

What are the natural numbers?

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We know the natural numbers are:

{1, 2, 3, 4, 5, 6, 7,..........}

Now, the set of even natural numbers are:

{2, 4, 6, 8, 10...........}

Therefore, the set of even natural numbers greater than or equal to 6 is

{6, 8, 10, 12,..............}

Learn more about natural numbers here: https://brainly.com/question/8102087

#SPJ2

If k is an integer, what is
k + 1
/2
!
? Why?

Answers

If [tex]k\in\mathbb{Z}[/tex] than [tex]k+1\in\mathbb{Z}[/tex] however any [tex]\mathbb{Z}[/tex] divided by 2 is in [tex]\mathbb{Q}[/tex].

But it is not so simple.

If [tex]k[/tex] is odd then [tex]k+1[/tex] is even but when even number is divided by 2, you get an odd number which is in [tex]\mathbb{Z}[/tex].

However if [tex]k[/tex] is even then [tex]k+1[/tex] is odd and when we divide that by 2, you get a number like for example [tex]\frac{5}{2}[/tex] which is not in [tex]\mathbb{Z}[/tex] but rather inside [tex]\mathbb{Q}[/tex]. There are fortunately no irrational numbers.

There is also a problem with zero, zero is neither odd nor even but still an integer. If your [tex]k[/tex] happens to be -1, [tex]k+1=0[/tex], and zero divided by 2 is still just 0 which is in [tex]\mathbb{Z}[/tex].

So to sum up,

If [tex]k[/tex] is odd and not -1, then [tex]\frac{k+1}{2}\in\mathbb{Z}[/tex].

Or to put it in math [tex]\forall k\in\mathrm{odd}-\{-1\}\cup\{0\}\implies\frac{k+1}{2}\in\mathbb{Z}[/tex].

If [tex]k[/tex] is even or -1, then [tex]\frac{k+1}{2}\in\mathbb{Q}[/tex].

Or to put it in math [tex]\forall k\in\mathrm{even}\cup \{-1\}\implies\frac{k+1}{2}\in\mathbb{Q}[/tex].

Notes:

[tex]\mathbb{Z}[/tex] is a set of integers.

[tex]\mathbb{Q}[/tex] is a set of rational numbers.

[tex]\mathbb{Z}\subset\mathbb{Q}[/tex] means integers are a subset of rational numbers, that is, every integer is a also a fraction, however not every fraction is an integer.

Hope this helps :)

A 16-ft steel beam is to be cut into two pieces so
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Answers

Answer:

8.5 feet and 7.5 feet.

Step-by-step explanation:

Hope this helps :)

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