Find the area of the shaded region.

Mathematics

1 answer:

slamgirl [31]2 years ago

7 0

Answer:

25,886 in²

Step-by-step explanation:

The given figure shows 2 circles centered at the same point. We need to find the area of the shaded region. If we observe carefully, the area in between two circles is the shaded region. So if we subtract the Area of smaller circle from the Area of larger circle we can calculate the Area of the shaded region.

Area of a circle = πr²

Radius of larger circle = OP = OQ = 93.4 inches

Radius of smaller circle = OR = OQ - RQ = 93.4 - 71.5 = 21.9 inches

Therefore, area of shaded region will be:

Area of Shaded Region = Area of larger circle - Area of smaller circle

Area of Shaded Region = π(93.4)² - π(21.9)²= 25,886 in²

Thus, the area of shaded region, rounded to nearest inch will be 25,886 in²

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Solving Quadratic Equations with Complex SolutionsThe discriminant: D=b^2-4acQuestion:5x^2-2x+1=0

fomenos

• The value of the discriminant ,D= -16

• The solution to the quadratic equation is

$x=\frac{1+2i}{5}\text{ or }\frac{1-2i}{5}$

Step - by - Step Explanation

What to find?

• The discriminant d= b² - 4ac

• The solution to the quadratic equation.

Given:

5x² - 2x + 1=0

Comparing the given equation with the general form of the quadratic equation ax² + bx + c=0

a=5 b=-2 and c=1

Uisng the quadratic formula to solve;

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

The discriminant D=b² - 4ac

Substitute the values into the discriminant formula and simplify.

D = (-2)² - 4(5)(1)

D = 4 - 20

D = -16

We can now proceed to find the solution of the quadratic equation by substituting into the quadratic formula;

$x=\frac{-(-2)\pm\sqrt[]{-16}}{2(5)}$

Note that:

√-1 = i

$x=\frac{2\pm\sqrt[]{16\times-1}}{10}$

$x=\frac{2\pm\sqrt[]{16}\times\sqrt[]{-1}}{10}$ $x=\frac{2\pm4i}{10}$ $x=\frac{2}{10}\pm\frac{4i}{10}$ $x=\frac{1}{5}\pm\frac{2}{5}i$ $x=\frac{1\pm2i}{5}$

That is;