Find the equation for the circle with a diameter whose endpoints are (-5, -3) and (3,2).
1 answer:
Answer:
(x +1)^2 +(y +0.5)^2 = 22.25
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so is ...
(h, k) = ((-5, -3) +(3, 2))/2 = (-5+3, -3+2)/2 = (-1, -1/2)
The circle formula is then ...
(x -h)^2 +(y -k)^2 = r^2
(x -(-1))^2 +(y -(-1/2))^2 = r^2
We can find r^2 by substituting one of the points for (x, y).
(3 +1)^2 +(2 +1/2)^2 = r^2 = 16 +6.25 = 22.25
Then the circle equation is ...
(x +1)^2 +(y +0.5)^2 = 22.25
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Answer:
Part 1) The measure of angle A is
Part 2) The length side of a is equal to
Part 3) The length side of b is equal to
Step-by-step explanation:
step 1
Find the measure of angle A
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
substitute the given values
step 2
Find the length of side a
Applying the law of sines
substitute the given values
step 3
Find the length of side b
Applying the law of sines
substitute the given values
Answer:
a. The critcal points are at
b. Then, is a maximum and
is a minimum
c. The absolute minimum is at and the absolute maximum is at
Step-by-step explanation:
(a)
Remember that you need to find the points where
Therefore you have to solve this equation.
From that equation you can factor out and you would get
And from that you would have , so
.
And you would also have .
You can factor that equation as
Therefore .
So the critcal points are at
b.
Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since
Then, is a maximum and
is a minimum
c.
The absolute minimum is at and the absolute maximum is at