The equation of a given circle in. general form is x^2+y^2+12y+27=0. write the equation in standard form, (x-h)^2+(y-k)^2=r^2, by completing the squares in the equation. show your work in the table.

Center (h, k) = (0, 6)

Radius, r = 3 units

Step-by-step explanation:

The given equation of the circle is:

STEP I: Move the constant term to the right hand side.

To do that we subtract 27 on both the sides, we get:

STEP II: Divide the co - effecient of 'x' by 2 and square it.

Here there is no 'x' term. Its co-effecient is 0.

STEP III: Add the result on both sides.

Since, we got 0 in the previous step, there would no change in the equation

STEP IV: We repeat the process for 'y'.

Here, the co-effecient of 'y' is: 12.

Dividing by 2 and squaring it will yield:

STEP V: Adding 36 to both the sides of the equation, it becomes:

We have arrived at perfect squares.

STEP VI: Write in the form of perfect squares.

STEP VII: Compare it with the standard form.

We get: The centre of the circle: (h, k) = (0, 6) and

the radius of the circle, r = 3 units.

Smallest number = 3500

Step-by-step explanation:

Rounding of numbers involve replacing numbers with simpler numbers. In order to round a number to the nearest thousand, the last 3 digits of the number should be considered. If the last 3 digits are less than 500, the number is rounded down(the thousand figure is unaffected), but if the last 3 digits are greater or equal to 500, the number is rounded up.

In this case, Yuri is thinking of a 4-digit whole number and he rounds his number to the nearest thousand. Since his answer is 4000, the smallest number yuri could be thinking of would be 3500 and the highest number he could be thinking of is 4499.

Thus, the smallest number Yuri could be thinking of is 3500