Find an equation of the largest sphere with center (8, 2, 9) that is contained in the first octant.

1 answer:

8 0

The point (8,2,9) is in the first octant.
The closest distance from the coordinate planes is the value y=2, which will therefore be the maximum radius of the required sphere.

The standard equation of a sphere with radius r and centre (u,v,w) is given by
(x-u)^2+(y-v)^2+(z-w)^2=r^2

Substituting r=2, u=8, v=2, w=9, we get the equation of the required sphere
(x-8)^2+(y-2)^2+(w-9)^2=2^2

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Based on the work shown on the right, check all of the possible solutions of the equation.

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Solve 3x^2 + 17x - 6 = 0.

Based on the work shown to the left, which of these values are possible solutions of the equation? Check all of the boxes that apply

A X=-6

B X=6

C X=-1/3

D X=1/3

E X=0

Answer:

A and D

Step-by-step explanation:

Note that such question requires using completing the square method of solving equations. By using the values X= -6 and X= 1/3 we arrive at a solution.