Answer:
Part 2) Option b. 5.4
Part 3) Option c. 8
Part 4) Option a. 15
Part 5) Option d. 8.9
Step-by-step explanation:
Part 2) Find the value of x to the nearest tenth
we know that
x is the radius of the circle
Applying the Pythagoras Theorem
[tex]x^{2}=3.6^{2}+(8/2)^{2}[/tex]
[tex]x^{2}=28.96[/tex]
[tex]x=5.4\ units[/tex]
Part 3) Find the value of x
In this problem
x=8
Verify
step 1
Find the radius of the circle
Let
r -----> the radius of the circle
Applying the Pythagoras Theorem
[tex]r^{2}=8^{2}+(15/2)^{2}[/tex]
[tex]r^{2}=120.25[/tex]
[tex]r=\sqrt{120.25}[/tex]
step 2
Find the value of x
Applying the Pythagoras Theorem
[tex]r^{2}=x^{2}+(15/2)^{2}[/tex]
substitute
[tex]120.25=x^{2}+56.25[/tex]
[tex]x^{2}=120.25-56.25[/tex]
[tex]x^{2}=64[/tex]
[tex]x=8\ units[/tex]
Part 4) Find the value of x
In this problem
x=OP=15
Verify
step 1
Find the radius of the circle
Let
r -----> the radius of the circle
In the right triangle FPO
Applying the Pythagoras Theorem
[tex]r^{2}=15^{2}+(40/2)^{2}[/tex]
[tex]r^{2}=625[/tex]
[tex]r=25[/tex]
step 2
Find the value of x
In the right triangle RQO
Applying the Pythagoras Theorem
[tex]25^{2}=x^{2}+(40/2)^{2}[/tex]
[tex]625=x^{2}+400[/tex]
[tex]x^{2}=625-400[/tex]
[tex]x^{2}=225[/tex]
[tex]x=15\ units[/tex]
Part 5) Find the value of x
Applying the Pythagoras Theorem
[tex]6^{2}=4^{2}+(x/2)^{2}[/tex]
[tex]36=16+(x/2)^{2}[/tex]
[tex](x/2)^{2}=36-16[/tex]
[tex](x/2)^{2}=20[/tex]
[tex](x/2)=4.47[/tex]
[tex]x=8.9[/tex]
