I will be happy to critique your thinking.

can u use one of them and show me how to solve it and i'll do the rest? like i don't know how to do these and i need to know how.

assume that Q varied directly as x and inversely as y.

1) if x is tripled and y is doubled, what happens to Q?

2) if x is halved and y is doubled, what happens to Q?

3) if x is doubled and y is halved, what happens to Q?

4) in the formula F=m times pi times l squared over p, m and pi remain constant, l is halved, and p is doubled. how does F change?

Take number two.

Q varies directly as x and inversely as y. That means Q= k x/y where k is some constant.

If x is halved, and y is doubled..
reducing x by one half means q is reduced by one half. But y is doubled, which means x is halved again (q=k x/y)

So Q goes down to 1/4 or 1/2 *1/2 of the original.

Lets do it the math way now.

Let Qo be the value of kx/y

Q' is the new value.
Q' = k (1/2 x)/2y = 1/4 k x/y=1/4 Qo

so that means the last one, Q is didided by 4?

i don't understand how Q changes can u explain

Sure, let's go through it step by step.

In the given problem, we are told that the relationship between Q, x, and y is a direct variation of x and an inverse variation of y. In mathematical terms, this can be represented as Q = k * (x/y), where k is a constant of variation.

1) If x is tripled and y is doubled, what happens to Q?
To solve this, we can substitute the new values of x and y into the equation. Let's say the original value of Q is Qo.

Q = k * (3x)/(2y)
Q = 3k * (x/y)

So, when x is tripled and y is doubled, Q becomes 3 times larger.

2) If x is halved and y is doubled, what happens to Q?
Using the same reasoning, we can substitute the new values into the equation:

Q = k * (1/2x)/(2y)
Q = (1/4)k * (x/y)

In this case, when x is halved and y is doubled, Q becomes 1/4 of its original value.

3) If x is doubled and y is halved, what happens to Q?
Again, let's substitute the new values:

Q = k * (2x)/(1/2y)
Q = 4k * (x/y)

When x is doubled and y is halved, Q becomes 4 times larger.

4) In the formula F = m * π * l^2 / p, m and π remain constant, l is halved, and p is doubled. How does F change?
In this case, let's determine how the different variables affect F:

F = m * π * (l/2)^2 / (2p)
F = (1/4) * m * π * (l^2/p)

Here, when l is halved and p is doubled, F becomes 1/8 of its original value.

I hope this explanation helps you understand how Q changes in each scenario.

Yes, that's correct! When x is halved and y is doubled, Q is divided by 4 or becomes 1/4 of its original value.

Let's break it down step by step:

We start with the equation Q = kx/y, where Q varies directly with x and inversely with y.

1. We are given that x is halved and y is doubled.
- To find the new value of Q, we substitute the new values into the equation.
- Q' = k(1/2x)/(2y)
- Simplifying further, we get Q' = (1/4)kx/y
- This means the new value of Q is 1/4 times the original value of Q (Q') is 1/4 of Q.

So, when x is halved and y is doubled, Q is divided by 4 or becomes 1/4 of its original value.

I hope this explanation clarifies how Q changes in this situation. Let me know if you have any more questions!