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Reika [66]
3 years ago
15

N is the sum of three consecutive primes and is also the product of two 2-digit primes, what is the least possible value of N

Mathematics
1 answer:
Nookie1986 [14]3 years ago
7 0

Hello from MrBillDoesMath!

Answer:   N = 143

Discussion:

This one took some trial and error! At first I listed all 2 digit primes, looked at the list, but didn't know how to proceed. So, I took the smallest 2 digit primes numbers:  11 and 13 and wondered if their product, 13*11 = 143, could be represented as the sum of  3 consecutive primes.   I went back to my list of primes,  added groups of three consecutive numbers that seemed to be in the right range to give the desired sum, and stumbled on  43, 47, and 53!

43 + 47 + 53 =  143 !


Therefore N = 143. It's the sum of 43, 47, and 53 as well as the product of 11 and 13.


Thank you,

MrB


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Problem 1

x = measure of angle N

2x = measure of angle M, twice as large as N

3(2x) = 6x = measure of angle O, three times as large as M

The three angles add to 180 which is true of any triangle.

M+N+O = 180

x+2x+6x = 180

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Use this x value to find that 2x = 2*20 = 40 and 6x = 6*20 = 120 to represent the measures of angles M and O in that order.

<h3>Answers:</h3>
  • Angle M = 40 degrees
  • Angle N = 20 degrees
  • Angle O =  120 degrees

====================================================

Problem 2

n = number of sides

S = sum of the interior angles of a polygon with n sides

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n-2 = 2700/180

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<h3>Answer: 17 sides</h3>

====================================================

Problem 3

x = smaller acute angle

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<h3>Answers:</h3>
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