A cylinder has a height of 7 millimeters and a diameter of 6 millimeters. What is its volume?
1 answer:
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Domain, on an "even root" context, means, an even root cannot have a negative radicand, since say for example 
so... you end up with an "imaginary value"
so... for the case of 20-6x
"x", the domain, or INPUT
can afford to have any value, so long it doesn't make the radicand negative
to check for that, let us make the expression to 0, and see what is "x" then
now, if "x" is 10/3, let's see
now, 0 is not negative, so the radicand is golden
BUT, if "x" has a value higher than 10/3, the radicand turns negative
for example
so.. that's not a good value for "x"
thus, the domain, or values "x" can safely take on, are all real numbers from 10/3 onwards, or to infinity if you wish
so... you end up with an "imaginary value"
so... for the case of 20-6x
"x", the domain, or INPUT
can afford to have any value, so long it doesn't make the radicand negative
to check for that, let us make the expression to 0, and see what is "x" then
now, if "x" is 10/3, let's see
now, 0 is not negative, so the radicand is golden
BUT, if "x" has a value higher than 10/3, the radicand turns negative
for example
so.. that's not a good value for "x"
thus, the domain, or values "x" can safely take on, are all real numbers from 10/3 onwards, or to infinity if you wish
We have the following expression
This is equivalent to
Since
we have that
Therefore, the answer is the second option from top to bottom.