We are given
v is inversely proportional to r^2
so, we can write our equation as
[tex]v=\frac{k}{r^2}[/tex]
where
k is proportionality constant
we have
r=2 and v=12
so, we can use it and find k
[tex]12=\frac{k}{2^2}[/tex]
[tex]k=48[/tex]
now, we can plug back k
[tex]v=\frac{48}{r^2}[/tex]
we can plug r=2.83
so, we can plug it and find v
[tex]v=\frac{48}{2.83^2}[/tex]
[tex]r=\frac{48}{8.0089}[/tex]
[tex]v=5.9933[/tex]
So, the approximate value of v is 6..........Answer
Answer:
The correct answer option is 6.
Step-by-step explanation:
We know that [tex]v[/tex] is inversely proportional to [tex]r^2[/tex] so we can write it as:
[tex]v[/tex] ∝ [tex]\frac{1}{r^2}[/tex]
To change the proportionality to equality, we need to have a constant k.
[tex]v = \frac{k}{r^2}[/tex]
When [tex]r=2[/tex]then [tex]v=12[/tex] so we can find the value of the constant [tex]k[/tex]:
[tex]12=\frac{k}{2^2}[/tex]
[tex]k=48[/tex]
Now that we know the value of [tex]k[/tex], we can find the value of [tex]v[/tex] when [tex]r=2.83[/tex]:
[tex]v=\frac{48}{2.83^2}[/tex]
[tex]v= 5.99[/tex] ≈ [tex]6[/tex]
