A square has been circumscribed inside of a
circle as shown to the right. If the area of the
circles is 16 units, determine the area of the
square.

Area of Square ≈ 10.17

Step-by-step explanation:

It would be difficult to derive this answer in terms of π, so let us assume π to be 3.14 units;

Now given the area of this circle we can derive the radius through a simple " Area of Circle " formula πr^2 where r ⇒ radius;

Area of Circle ⇒ πr^2,

16 units^2 = πr^2,

16 = 3.14 * r^2,

5.09554140127... = r^2,

r = 2.25733059193, r ≈ 2.255,

diameter ⇒ ≈ 4.51

The diameter splits the square into two right triangles, such that Pythagorean Theorem can be applied. We don't know the length of either one of the legs to solve this, but as in a square all sides are ≅, we can say;

4.51^2 = x^2 + x^2 ⇒ x is one of the legs of the right triangles,

2x^2 = 4.51^2,

2x^2 = 20.3401,

x^2 = 10.17005,

x ≈ 3.19

Thus, the area of this Square is ≈ 3.19 * 3.19 ⇒ 10.17005;

Area of Square ≈ 10.17

its electric no smoke

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!