Question

If p p and q q vary inversely and p is 17 when q is 4, determine q when p p is equal to 2.

Answer 1

Solving for q, we get q = 34. Therefore, when p is equal to 2, q is 34.

Step-by-step explanation:

This question involves the concept of inverse variation. Inverse variation is a relationship where the product of two variables is a constant. In this case, we are given that p and q vary inversely. We are also given that when p is 17, q is 4. To find q when p is equal to 2, we can set up the inverse variation equation:

p * q = k

Substituting the known values, we have:

17 * 4 = k

Solving for k, we find that k = 68. Then, we can substitute the value of k and p into the inverse variation equation to find q:

2 * q = 68

Solving for q, we get q = 34. Therefore, when p is equal to 2, q is 34.

Answer 2

`q = 34` when
`p = 2`.

Step-by-step explanation:

Variables
`p` and
`q` (
`p \\e 0`,
`q \\e 0`) are inversely proportional to one another if one variable- for example,
`p`- is proportional to the reciprocoal of the other variable-
`(1/q)`.

In other words, if
`p` and
`q` (
`p \\e 0`,
`q \\e 0`) are inversely proportional to one another, there would exist a constant
`k` (
`k \\e 0`) such that:

`\displaystyle p = k* \left((1)/(q)\right)`.

The value of
`k` is constant and is independent of
`p` and
`q`. Given that
`p = 17` when
`q = 4`, rearrange the equation above to find the value of
`k\!`:

`k = p\, q = 68`.

Rewrite the equation again to find
`q` in terms of
`k` (which doesn't change) and
`p` (which might change):

`\begin{aligned}q &= (k)/(p)\end{aligned}`.

Since
`k = 68`, given that
`p = 2`, the value of
`q` would be:

`\begin{aligned}q &= (k)/(p) \\ &= (68)/(2) = 34\end{aligned}`.