Which point does not lie on the circle centered at (3, 2) with radius 5?
1 answer:
The complete question in the attached figure
we know that
the equation of a circle is
(x-h)²+(y-k)²=r²
where
(h,k) is the center
and
r is the radius
so
(x-h)²+(y-k)²=r²------> (x-3)²+(y-2)²=5²
case A) point (0,6)
for x=0 and y=6
(0-3)²+(6-2)²=5²------> 9+16=5²-----> 25=25
<span>the point lie on the circle
</span>case B) point (3,-3)
for x=3 and y=-3
(3-3)²+(-3-2)²=5²------> 0+25=5²-----> 25=25
the point lie on the circle
case C) point (-2,2)
for x=-2 and y=2
(-2-3)²+(2-2)²=5²------> 25+0=5²-----> 25=25
the point lie on the circle
case D) point (3,0)
for x=3 and y=0
(3-3)²+(0-2)²=5²------> 0+4=5²-----> 4 is not 25
the point not lie on the circle
the answer is
point (3,0) not lie on the circle
we know that
the equation of a circle is
(x-h)²+(y-k)²=r²
where
(h,k) is the center
and
r is the radius
so
(x-h)²+(y-k)²=r²------> (x-3)²+(y-2)²=5²
case A) point (0,6)
for x=0 and y=6
(0-3)²+(6-2)²=5²------> 9+16=5²-----> 25=25
<span>the point lie on the circle
</span>case B) point (3,-3)
for x=3 and y=-3
(3-3)²+(-3-2)²=5²------> 0+25=5²-----> 25=25
the point lie on the circle
case C) point (-2,2)
for x=-2 and y=2
(-2-3)²+(2-2)²=5²------> 25+0=5²-----> 25=25
the point lie on the circle
case D) point (3,0)
for x=3 and y=0
(3-3)²+(0-2)²=5²------> 0+4=5²-----> 4 is not 25
the point not lie on the circle
the answer is
point (3,0) not lie on the circle
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Part a: Option D 18 feet per second
Part b: increasing
Solution:
Height
Part a: To find the average rate of change for h(t) between t = 0 and t = 2.
Substitute t = 0 in h(t).
h(0) = 3
Substitute t = 2 in h(t).
h(2) = 39
Average rate of change formula:
Here, a = 0 and b = 2.
= 18
Average rate of change = 18 feet per second
Option D is the correct answer.
Part b:
This means height of the ball is increasing for 0 < x < 2.