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xeze [42]
3 years ago
5

What is the least positive integer which when divided by 5 gives a remainder of 4, when divided by 6 gives a remainder of 5, whe

n divided by 7 gives a remainder of 6, when divided by 8 gives a remainder of 7, when divided by 9 gives a remainder of 8, and when divided by 10 gives a remainder of 9
Mathematics
1 answer:
docker41 [41]3 years ago
4 0

Answer:

  2519

Step-by-step explanation:

In each case, the remainder is 1 less than the divisor. This means the number of interest will be 1 less than the least common multiple of 5, 6, 7, 8, 9, 10.

The prime factors of these numbers are ...

  5 = 5

  6 = 2·3

  7 = 7

  8 = 2³

  9 = 3²

  10 = 2·5

The unique factors are 2, 3, 5, 7. When they are used to their highest powers, the resulting product is ...

  2³·3²·5·7 = 2520

The number of interest is 1 less than this, so is 2519.

2519 is the least positive integer that will give the required remainders.

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9) It helps to draw a picture.  Since one angle is 60°, the other angle is 120°.  When you draw the ddiagonal lines, you will see that you end up with a 30°-60°-90° triangle where √3 is the hypotenuse. The longest diagonal will be across from the 60° angle, which will be length a√3. The length of the hypotenuse is 2a. (Remember: a, a√3, 2a are lengths for this special triangle)
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10) Volume of a square pyramid = (1/3) B · h, where B is the area of the base
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Lateral edge is √194.




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