Which value, when placed in the circle, would result in a system of equations with infinitely many solutions?
1 answer:
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The biggest remainder obtained by dividing 2015 by either 1, 2, 3,
4,...,1000 is the option;
(C) 671
<h3>How can the biggest remainder be found?</h3>The given number Maria divides is 2015
The divisors = 1, 2, 3, 4,..., 1000
Required:
The biggest remainder Maria noted down.
Solution:
From remainder theorem, we have;
p(x) = (x - a) × q·(x) + r(x)
Where;
r(x) = The remainder
q(x) = The quotient
(x - a) = The devisor
Which gives;
Therefore;
The remainder is largest when both and (x - a) are large
is largest when the quotient changes to the next lower
digit and the divisor is not a factor.
By using MS Excel, we have, at 672, the remainder is found as follows;
At 672, ≈ 0.999, which when multiplied by 672, gives
the biggest remainder of 671, which is the biggest remainder.
- The biggest remainder obtained by dividing 2015 by either 1, 2, 3, 4,...,1000 is <u>(C) 671</u>
Learn more about the remainder theorem here: