Mr. Roseanne will buy 12 1/2 pounds beef for for a cookout. The price for the first 3 pounds of beef is $4.99 per pound. After t
1 answer:
Answer:
As per the statement:
Mr. Roseanne will buy pounds beef for for a cookout.
⇒ Weight of the beef he buy = pounds.
It is given that:
The price for the first 3 pounds of beef is $4.99 per pound.
then;
the price for 3 pounds he will pay=
After that, the price is $4.49 per pound.
Remaining weight of beef left = pounds.
then;
the price of pounds he will pay =
now, total money he will pay for the pounds beef =
Therefore, $57.625 will Mr. Roseanne pay for the beef
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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
.