Which of the following is equivalent to (5 /k) + ((k + 3) /(k + 5)) ?
2 answers:
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9514 1404 393
Answer:
(x +3)² +(y -4)² = 145
Step-by-step explanation:
The center of the circle is the midpoint of the given segment PQ. If we call that point A, then ...
A = (P +Q)/2
A = ((-12, -4) +(6, 12))/2 = (-12+6, -4+12)/2 = (-6, 8)/2
A = (-3, 4)
The equation of the circle for some radius r is ...
(x -(-3))² +(y -4)² = r² . . . . . . where (-3, 4) is the center of the circle
The value of r² can be found by substituting either of the points on the circle. If we use Q, then we have ...
(6 +3)² +(12 -4)² = r² = 9² +8²
r² = 81 +64 = 145
Then the equation of the circle is ...
(x +3)² +(y -4)² = 145
As for the domain, the only restriction comes from the logarithm. The argument of a logarith must be strictly positive, so we have
As for the range, we have:
- The range of
are all real numbers
- If we change to
we're translating the function horizontally, so the range remains the same
- If we change to
we're stretching the function horizontally, so the range doesn't change
- If we change to
we're translating the function 1 unit up, but the range is already all the real numbers, so it doesn't change.