Hi Dr Taylor,
I am a bit stuck on this one. I'm pretty sure I have parts 1,3 & 4 correct, but part 2 has me stumped.
According to my calculations,part 2 should have a centre at (2,2,1) with a radius of 0.5.
(x-2)^2 +(y-2)^2 + (z-1)^2 = 1/4
From what I can see none of the available spheres match that description. I have gone over my work several times but can't see where to go from here.
Any pointers would be greatly appreciated.
You completed the square correctly; the left hand side of the equation is indeed
(x-2)^2 +(y-2)^2 + (z-1)^2; this means that you added 4+4+1=9 to the left side so you must add 9 to the right side of the equation as well. This gives -35/4+9=-35/4+36/4=1/4--which is what you got, so you were correct that the radius-squared of the sphere is 1/4, hence the radius is 1/2. This means that you are looking for a sphere with radius 1/2, hence diameter 1, centered at (2,2,1). At this point, I have to agree with you that none of the sphere images looks very much like the sphere with radius 1/2 centered at (2,2,1), however, both D and F seem like they should have radius 1/2. F seems like it's center is (2,0,0), while D seems like it has a center (x,y,z) where y looks close to 2, z looks close to 1 and x is positive, so I choose D, which turns out to be the correct answer.
No comments:
Post a Comment