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Law Incorporation [45]
2 years ago
11

Write down an (in)equality which describes the solid ball of radius 3 centered at (7,1,−1). It should have a form like x2+y2+(z−

2)2−4>=0, where you use one of the following symbols ≤,<,=,≥,>.
Mathematics
1 answer:
masya89 [10]2 years ago
6 0

Answer:

(x-7)^2+(y-1)^2+(z+1)^2-9\le 0

Step-by-step explanation:

A ball is the solid inside a surface which is a sphere.

The equation of a sphere has the form:

(x-h)^2+(y-k)^2+(z-s)^2= r^2

Where (h,k,s) is the center and r is the radius.

When we plug the given center (7,1,-1) and radius 3 we get:

(x-7)^2+(y-1)^2+(z+1)^2= 3^2

Then we turn this into an inequality: Since the ball is inside the surface we must use the \le symbol.

(x-7)^2+(y-1)^2+(z+1)^2\le 9

Then we just subtract 9 from both sides to get:

(x-7)^2+(y-1)^2+(z+1)^2-9\le 0

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