Answer:
Yes, point B will lie inside the circle.
Step-by-step explanation:
Let the distance between point C and point A be the radius of our given circle.
We have been given that a circle with center C(4, -2) passes through the point A(1, 3).
Since we know that a point will lie inside circle if the distance between the point and center of circle is less than radius of circle.
Let us find distance between points C and A using distance formula.
![\text{Radius}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}](https://tex.z-dn.net/?f=%5Ctext%7BRadius%7D%3D%5Csqrt%7B%28x_2-x_1%29%5E%7B2%7D%2B%28y_2-y_1%29%5E%7B2%7D%7D)
![\text{Radius}=\sqrt{(4-1)^{2}+(-2-3)^{2}}](https://tex.z-dn.net/?f=%5Ctext%7BRadius%7D%3D%5Csqrt%7B%284-1%29%5E%7B2%7D%2B%28-2-3%29%5E%7B2%7D%7D)
![\text{Radius}=\sqrt{(3)^{2}+(-5)^{2}}](https://tex.z-dn.net/?f=%5Ctext%7BRadius%7D%3D%5Csqrt%7B%283%29%5E%7B2%7D%2B%28-5%29%5E%7B2%7D%7D)
![\text{Radius}=\sqrt{9+25}](https://tex.z-dn.net/?f=%5Ctext%7BRadius%7D%3D%5Csqrt%7B9%2B25%7D)
![\text{Radius}=\sqrt{34}](https://tex.z-dn.net/?f=%5Ctext%7BRadius%7D%3D%5Csqrt%7B34%7D)
Radius of our circle is
. Now let us find distance between center of our circle and point B.
![\text{Distance between C and B}=\sqrt{(4-8)^{2}+(-2--2)^{2}}](https://tex.z-dn.net/?f=%5Ctext%7BDistance%20between%20C%20and%20B%7D%3D%5Csqrt%7B%284-8%29%5E%7B2%7D%2B%28-2--2%29%5E%7B2%7D%7D)
![\text{Distance between C and B}=\sqrt{(-4)^{2}+(-2+2)^{2}}](https://tex.z-dn.net/?f=%5Ctext%7BDistance%20between%20C%20and%20B%7D%3D%5Csqrt%7B%28-4%29%5E%7B2%7D%2B%28-2%2B2%29%5E%7B2%7D%7D)
![\text{Distance between C and B}=\sqrt{16+(0)^{2}}](https://tex.z-dn.net/?f=%5Ctext%7BDistance%20between%20C%20and%20B%7D%3D%5Csqrt%7B16%2B%280%29%5E%7B2%7D%7D)
![\text{Distance between C and B}=\sqrt{16}](https://tex.z-dn.net/?f=%5Ctext%7BDistance%20between%20C%20and%20B%7D%3D%5Csqrt%7B16%7D)
We can see that distance of point B from center of our given circle is less than distance between point A and center of circle, therefore point B will lie inside the circle.
It would be 23/40, because you have to simply 0.575/1000.
The next answer to the next step is simplify y
Answer:
296.25 more miles.
Step-by-step explanation:
If you subtract 350, 105.5, and 200.25 from 952, you get 296.25.
Answer:
A) 2.8 m
Step-by-step explanation:
The formula for the volume of a right rectangular prism is:
Volume = Length × breadth × height
We can just put in the values that we know to find the height.
110.1 = 7.8 × 5.1 × height
height = 110.1 ÷ 7.8 ÷ 5.1
height ≈ 2.8 (rounded to nearest tenth)
Thus, the answer is Option A.