Find an equation of the sphere that passes through the point (7, 1, −3) and has center (5, 6, 5).

The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is .

Step-by-step explanation:

Any sphere centered at in an Euclidean space with a radius is represented by the following formula:

If and , the radius of the sphere is obtained:

The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is .

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions