The circumference of acircle is about 53.38cm. The radius of the circle is 8.5cm

To calculate the area of a circle we need to know it's radius.

The formula for the circumference of a circle is:

C

=

2

π

r

Substituting

53.38

cm

for

C

and solving for

r

gives:

53.38

cm

=

2

π

r

53.38

cm

2

π

=

2

π

r

2

π

26.69

π

cm

=

2

π

r

2

π

26.69

π

cm

=

r

r

=

26.69

π

cm

The formula for the area of a circle is;

A

=

π

r

2

Substituting the radius we solved for above and calculating

A

gives:

A

=

π

(

26.69

π

cm

)

2

#A = pi(712.3561/pi^2"cm"^2)#

#A = color(red)(cancel(color(black)(pi)))(712.3561/pi^color(red)(cancel(color(black)(2)))"cm"^2)#

#A = 712.3561/pi"cm"^2#

Substituting

3.14

for

π

allows us to approximate the area as:

#A = 712.3561/3.14"cm"^2#

A

=

226.865

cm

2

Step-by-step explanation:

sounds & other waves originate from any vibrating object

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.