A person borrows rs 80000 at 12% per anum .the principal and interest are to be paid in 11 monthly installments doubling each installment from its previous one calculate first and last payment

We are given equation of sphere x^2 + y^2 + z^2 + 6x − 2y − 6z = 17.

We know , standard form of a sphere (x−a)^2+(y−b)^2+(x−c)^2=r^2.

Where centered at (a,b,c) ( a , b , c ) with radius r.

Let us convert given equation of sphere in standard form by completing the square.

Writing x, y and z terms seprately.

(x^2+6x) + (y^2-2y) + (z^2-6z) = 17.

We have coefficents of x, y and z are 6, -2 and -6.

First we will find half of those coefficents and then square them.

We get 6/2 =3, -2/2 =-1 and -6/2=-3.

Now, squaring we get

(3)^2 = 9,  (-1)^2 = 1 and (-3)^2 = 9.

Adding those numbers inside first, second and third parentheses and adding same numbers on right side.

(x^2+6x+9) + (y^2-2y+1) + (z^2-6z+9) = 17+9+1+9.

Now, finding perfect square of each, we get

(x+3)^2 + (y-1)^2 + (z-3)^2 = 36.

We could write 36 as 6^2.

So, final answer would be

(x+3)^2 + (y-1)^2 + (z-3)^2 = 6^2 is the standard form of a sphere equation.