What is 2+2-4 x 40-60 and the answer is...........????
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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
.
Volume of a cylinder is 
, where r is the radius and h is the height.
This comes from the area of a circle being
. A cylinder is the area of the base circle multiplied by its height.
Using this formula, the volume of the given cylinder is
This comes from the area of a circle being
Using this formula, the volume of the given cylinder is