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ad-work [718]
3 years ago
5

Factor the following question.

Mathematics
1 answer:
Lerok [7]3 years ago
5 0
Factor the following:
125 w^3 - 8
125 w^3 - 8 = (5 w)^3 - 2^3:
(5 w)^3 - 2^3
Factor the difference of two cubes. (5 w)^3 - 2^3 = (5 w - 2) ((5 w)^2 + (5 w) 2 + 2^2):
(5 w - 2) ((5 w)^2 + 5 2 w + 2^2)
Multiply each exponent in 5 w by 2:
(5 w - 2) (5^2 w^2 + 5 2 w + 2^2)
5^2 = 25:
(5 w - 2) (25 w^2 + 5 2 w + 2^2)
5×2 = 10:
(5 w - 2) (25 w^2 + 10 w + 2^2)
2^2 = 4:
Answer:  (5 w - 2) (25 w^2 + 10 w + 4)
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If you write all the whole numbers from 1 to 500 in a row, what will be the 500th digit?
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Answer:

Option A.

Step-by-step explanation:

We need to find the 500th digit if we write all the whole numbers from 1 to 500 in a row.

Single digit numbers are : 1-9 = 9 number = 9 digits

Double digit numbers are : 10-99 = 90 number = 180 digits

Total digits form 1 to 99 = 9+180 = 189

Now,

500-189=311

It means we have write 311 more digits.

After 99 we have 3 digit number.

311 is not divisible by 3. The number immediate before 311 which is divisible by 3 is 309.

\frac{309}{2}=103

It means the required digit is 2nd digit of 104th number after 99.

104th number after 99 is 203 and second digit of 203 is 0.

Therefore, the correct option is A.

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Step-by-step explanation:

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Question 3(Multiple Choice Worth 5 points)
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