I went through and solved this problem plenty of times...and my answer always comes out to 5/6..however, that's not even one of the choices. One of the choices is 6/5 though...

maybe I'm doing somehting wrong

1. Find the missing value. Y is directly proportional to x and inversely proportional to the square of z. Y = 20 when x = 50 and z = 5. Find y when x = 3 and z = 6

y = kx/z^2

20 = k(50)/(25)
k = 10

Now use k to find y:

y = (10)(3)/36 = 30/36 = 5/6

Gotta go with your answer, guy.

Thanks.

...and I'm a girl

It's cool, that's the point

I go with 5/6 also.

To solve this problem, you need to use the concepts of direct and inverse proportionality.

Let's break down the information given:

1. Y is directly proportional to x: This means that as x increases, Y also increases proportionally.

2. Y is inversely proportional to the square of z: This means that as z increases, Y decreases proportionally, but the relationship is not linear. Instead, it is inversely related to the square of z, meaning that the decrease in Y is more significant as z increases.

Now let's find the missing value, Y, when x = 3 and z = 6.

Step 1: Set up the proportionality equation.

Y is directly proportional to x, so we can write this as Y = k * x, where k is the constant of proportionality.

Y is inversely proportional to the square of z, so we can write this as Y = k / (z^2), where k is the constant of proportionality.

Combining these two equations, we get Y = k * x / (z^2).

Step 2: Find the value of k.

We are given a specific value of Y, x, and z, which allows us to solve for k.

Using the values Y = 20, x = 50, and z = 5, we can substitute them into the equation Y = k * x / (z^2).

20 = k * 50 / (5^2)
20 = 10k / 25
20 * 25 = 10k
500 = 10k
k = 500 / 10
k = 50

Step 3: Find Y when x = 3 and z = 6.

Now that we have the value of k, we can substitute it back into the equation Y = k * x / (z^2).

Y = 50 * 3 / (6^2)
Y = 150 / 36
Y = 25 / 6

So, the value of Y when x = 3 and z = 6 is 25/6, which can also be written as 4 1/6. It seems that the choices given have inaccuracies, and your answer of 5/6 is indeed correct.

sorry; too mysterious