Question

V is inversely proportional to r^2 when r=2, v=12. The value of r is approximately 2.83 when v=

Answer 1

We are given

v is inversely proportional to r^2

so, we can write our equation as

$v=\frac{k}{r^2}$

where

k is proportionality constant

we have

r=2 and v=12

so, we can use it and find k

$12=\frac{k}{2^2}$

$k=48$

now, we can plug back k

$v=\frac{48}{r^2}$

we can plug r=2.83

so, we can plug it and find v

$v=\frac{48}{2.83^2}$

$r=\frac{48}{8.0089}$

$v=5.9933$

So, the approximate value of v is 6..........Answer

Answer 2

Answer:

The correct answer option is 6.

Step-by-step explanation:

We know that $v$ is inversely proportional to $r^2$ so we can write it as:

$v$ ∝ $\frac{1}{r^2}$

To change the proportionality to equality, we need to have a constant k.

$v = \frac{k}{r^2}$

When $r=2$then  $v=12$ so we can find the value of the constant $k$:

$12=\frac{k}{2^2}$

$k=48$

Now that we know the value of $k$, we can find the value of  $v$ when  $r=2.83$:

$v=\frac{48}{2.83^2}$

$v= 5.99$ ≈ $6$