a sphere has center (0,0,0) and a radius of 5. which of the following points lies on the sphere?
(0,-3,4)
(5,5,-5)
(2,3,0)
(1,-1,3)
The equation of a sphere with center (0,0,0) and radius 5 is x^2 + y^2 + z^2 = 5^2 = 25.
We can test each point to see which one satisfies this equation:
(0,-3,4): 0^2 + (-3)^2 + 4^2 = 0 + 9 + 16 = 25. This point lies on the sphere.
(5,5,-5): 5^2 + 5^2 + (-5)^2 = 25 + 25 + 25 = 75. This point does not lie on the sphere.
(2,3,0): 2^2 + 3^2 + 0^2 = 4 + 9 + 0 = 13. This point does not lie on the sphere.
(1,-1,3): 1^2 + (-1)^2 + 3^2 = 1 + 1 + 9 = 11. This point does not lie on the sphere.
The point (0, -3, 4) lies on the sphere.