The center of a circle is at (-3, 1) and it’s radius is 9. what is the equation of the circle? (x - 3)^2 + (y + 1)^2 =81 (x - 3)^2 + (y + 1)^2 = 18 (x + 3)^2 + (y - 1)^2 =81 (x + 3)^2 + (y - 1)^2 =18

(x + 3)² + ( y - 1)² = 81

Step-by-step explanation:

To go in reverse, you need to remember that in the equation:

(x - a)² + (y - b)² = r²

a is the x coordinate of the centre and b is the y coordinate of the centre.

As -3 is the x coordinate, we can replace a with 3, and then replace  b with 1:

(x - -3)² + (y - 1)² = r²

The two negatives change to a positive:

(x + 3)² + ( y - 1)² = r²

If r is already given as 9, r² is simply 9²

(x + 3)² + ( y - 1)² = 9²

(x + 3)² + ( y - 1)² = 81

So the equation of the circle is (x + 3)² + ( y - 1)² = 81

so, converting firstly the mixed fractions to improper fractions and then "adding".

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places