Answer:
Part 7) Option C. The approximate perimeter of the patio is [tex]54\ ft[/tex]
Part 8) Option G. [tex]3\ floats[/tex]
Part 9) [tex]150.72\ minutes[/tex]
Step-by-step explanation:
Part 7) we know that
The perimeter of the figure is equal to the circumference of the larger half circle plus the circumference of the smaller half circle plus two times the length of 8 ft
step 1
Find the circumference of the larger half circle
The circumference of the larger half circle is
[tex]C=\pi r[/tex]
we have
[tex]r=8+2=10\ ft[/tex]
substitute
[tex]C=\pi(10)[/tex]
[tex]C=10\pi\ ft[/tex]
step 2
Find the circumference of the smaller half circle
The circumference of the smaller half circle is
[tex]C=\pi r[/tex]
we have
[tex]r=2\ ft[/tex]
substitute
[tex]C=\pi(2)[/tex]
[tex]C=2\pi\ ft[/tex]
step 3
Find the perimeter of the figure
[tex]10\pi\ ft+2\pi\ ft+2(8)\ ft=(12\pi+16)\ ft[/tex]
assume [tex]\pi=3.14[/tex]
so
[tex](12(3.14)+16)=53.68=54\ ft[/tex]
Part 8) we know tat
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=28.26\ ft^{2}[/tex]
assume [tex]\pi=3.14[/tex]
substitute the values and solve for r
[tex]28.26=(3.14)r^{2}[/tex]
[tex]r^{2}=28.26/(3.14)[/tex]
[tex]r^{2}=9[/tex]
[tex]r=3\ ft[/tex]
Find the diameter D
[tex]D=2r=2(3)=6\ ft[/tex]
Divide the width of the pool by the diameter of the floats
so
[tex]\frac{18}{6}=3\ floats[/tex]
Part 9)
step 1
Find the circumference of one coaster
The circumference of circle is
[tex]C=2\pi r[/tex]
we have
[tex]r=1.5\ in[/tex]
assume [tex]\pi=3.14[/tex]
substitute
[tex]C=2(3.14)(1.5)=9.42\ in[/tex]
step 2
Find the circumference of 48 coasters
so
[tex]48(9.42)=452.16\ in[/tex]
step 3
we know that
The laser cut woods at the rate of 3 inches per minute
By proportion find how many minutes will it take to cut out 48 coasters
[tex]\frac{3}{1}\frac{inches}{minute} =\frac{452.16}{x}\frac{inches}{minutes}\\ \\x=452.16/3\\ \\x=150.72\ minutes[/tex]
