1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lina20 [59]
3 years ago
12

For positive integers $n$, let $f(n)$ return the smallest positive integer $k$ such that $\frac{1}{k}$ has exactly $n$ digits af

ter the decimal point. How many positive integer divisors does $f(2010)$ have?
Mathematics
1 answer:
disa [49]3 years ago
3 0

Answer:

There are a total of 2011 integer divisors.

Step-by-step explanation:

The only primes p such that 1/p has finite spaces after the coma are 2 and 5. If we divide a number with last digit odd we will obtain 1 extra digit after the decimal point and if we divide a number by 5 we will obtain 1 more digit if that number has a last digit in the decimal which is not a multiple of 5.

If we take powers of those primes we will obtian one more digit each time. In order to obtain more digits it is convinient to divide by a power of 2 instead of a power of 5, because the resulting number will be smaller.

If we want 2010 digits after the decimal point, we need to divide 1 by 2 a total of 2010 times, hence f(2010) = 2²⁰¹⁰, which has as positive integer divisors every power of 2 between 0 and 2010, hence there are a total of 2011 integer divisors of f(2010).

You might be interested in
Find the value of x and the value of y
marshall27 [118]
Right triangle 30 60 90
short leg = 1/2 hypo = 4√2 / 2 = 2√2
so x = 2√2

long leg = short leg times √3 = 2√2 * √3 = 2√6
so y = 2√6

answer C. 
x = 2√2 ; y = 2√6
5 0
3 years ago
Which two types of potential energies would be types of mechanical energies?
lisov135 [29]

Answer:

D) elastic and gravitational

Step-by-step explanation:4.elastic and gravitational

Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position).

4 0
3 years ago
Read 2 more answers
Write a method called removeinrange that accepts four parameters: an arraylist of integers, an element value, a starting index,
LiRa [457]
Yjhgujo yo8 t hi/ l h fylif .i yo.u/;i pb
[
 
7 0
3 years ago
Determine whether the given point (-6,2) is a solution of the equation y = -2x - 1
Basile [38]
Y-y1= m(x-x1)

y-2= -2(x+6)

y-2= -2x-12

y= -2x-10
Unless there is supposed to be a zero at the end of that 1, then the answer is no
3 0
3 years ago
Read 2 more answers
The members of a cooking club are making cakes, which they will sell at a street fair for $8 apiece. It cost $30 for a booth at
Olin [163]

They need to sell 5 pieces to cover their expenditures (have a profit of zero).

<h3>How many cakes will they have sold?</h3>

We know that the costs are:

  • $30 for the booth at the fair.
  • $2 for each piece of cake they sell.

And the revenue is:

  • $8 for each piece of cake.

So, the profit (the difference between the revenue and the cost) for selling x pieces is:

p(x) = $8*x - $2*x - $30

p(x) = $6*x - $30

We want to find the value of x such that p(x) = 0, then:

0 =  $6*x - $30

x = $30/$6 = 5

They need to sell 5 pieces to cover their expenditures (have a profit of zero).

If you want to learn more about profit:

brainly.com/question/23103804

#SPJ1

5 0
2 years ago
Other questions:
  • Kim's softball team is playing in the championship game. They are losing by a score of 17 to 6. There are 4 innings to go. Kim w
    6·2 answers
  • What is 4x^2 + 3xy -7xy + 2y^2
    8·1 answer
  • Together, John and Kevin have 72 pokemon cards. Kevin has 5 times as many cards as John. How many cards does each person have? S
    11·1 answer
  • Help asap pleaseeeee
    7·1 answer
  • What's the slope- intercept equation? 10x-3y= -6
    13·1 answer
  • Whats 2.48 divided by 0.4?
    14·1 answer
  • a vegetable farmer fills 2/3 of a crate with 5/7 of a pound of tomatoes. how many lbs can fit in one crate​
    12·2 answers
  • Which statement about parallel lines is true?
    15·1 answer
  • A basket contains four apples and five peaches. Three times, you randomly select a piece of fruit, return it to the basket, and
    9·1 answer
  • Solving right triangles geometry help please
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!