Rebecca needs 10 1/2 yards of fabric to make a quilt. She has one piece of fabric that is 2 1/2 yards and another piece of fabri
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The charity will receive $ 11
<h3><u>Solution:</u></h3>Ken earned $176 from his part-time job this summer
Amount earned = $ 176
He spent 25% of his money on games
Therefore,
Money spent on games = 176 - 25 % of 176
He is going to donate 1/4 of the remaining money to charity
Reamining amount = 176 - 132 = 44
Therefore,
Thus he gave $ 11 to charity
Two main facts are needed here:
1. The logarithm , regardless of the base of the logarithm, exists for
.
2. The square root exists for
.
(in both cases we're assuming real-valued functions only)
By (2) we know that exists if
, or
.
By (1), we know that exists if
, or
. But as long as the square root exists, it will always be positive, so this condition will always be met.
Ultimately, then, we only require , so the function has domain
.
To determine the range, we need to know that, in their respective domains, and
increase monotonically without bound. We also know that
at minimum, at which point the square root term vanishes, so the least value the function takes on is
. Then its range would be
.