In the figure, the area of the shaded region is 243π cm2. what is the value of x?

Answer

Find out the  value of x.

To  proof

Formula

As given

Radius  of the bigger circle = 18cm

Radius  of the smaller circle =x

As shown in the diagram

shaded area = Area of the bigger circle - Area of the smaller circle

than we have

243 = 324 - x²

324- 243 = x²

√81 = x

9cm = x

the value of x is 9cm .

Hence proved

Remember that the vertex form of a parabola is where is the vertex of the parabola.

Now, to find the vertex of the parabola, we are going to use the vertex formula:

For a quadratic of the form , the vertex is given by:

in other words, we find by evaluating the function at

We know form our quadratic that and , so let's use our formula to find :

Now we can evaluate our function at to find :

Now, we can rewrite our parabola in vertex form:

, , and

We can conclude that the correct answer is: y = 6(x + 1)2 – 16