The lenght of the library is 13 inches.The lenght of the actual library is 78 feet. Which scale leon use to create the scale dra
1 answer:
So the scale used was
1 inch = 6 feet
Step-by-step explanation:
Given
Length of library on drawing = 13 inches
Actual length of library = 78 feet
In order to find the scale we divide the actual length by the length of library on drawing.
So,
Scale =
So the scale used was
1 inch = 6 feet
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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
.