Fasttt
a square has a side that measures 5.5 units. what is the area of a circle with a circumference that equals the perimeter of the square? use 3.14 for π, and round your answer to the nearest hundredth.

38.47 units2
94.99 units2
153.86 units2
379.94 units2

answer:

38.47 units²

step-by-step explanation:

calculate the perimeter of the circle. 5.5 + 5.5 + 5.5 + 5.5 = 22 or 5.5 * 4 = 22.

the circumference of the circle is the same as the perimeter of the square.

now you have to solve for the radius to find the area.

c = circumference   or 22         r = radius         π = pi or 3.

round answer to nearest hundredth.

c = 2πr

22 = 2πr

divide 2π from both sides.

22/2π = r

22/6.   = r

3.   = r

now calculate the area.

a = area       r = radius or 3.50         π = pi or 3.

a =   πr²

a =   π * 3.50²

a =   π * 12.25

a = 38.47 units²

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!