Create an abstract mathematical image that visually represents the concept of variables and their relationships. The image should include elements that symbolize the variables p, q, and r, as well as demonstrate the concept of a variable varying partly as another variable and partly as the square of another. The elements should be arranged in a way that signifies an equation. Please ensure the image contains no text.

P varies partly as q and partly as the square of r. When p=6,q=8 r=4 and when p=10,q=12 and r=5. find the formula connecting p,q and r

7 answers

p = mq + nr^2

so,
8m + 16n = 6
12m + 25n = 10

Now just solve for m,n

I don't understand the explanation

I don't understand

I understand not

So what is M and N now

I understand well

To find the formula connecting p, q, and r, we need to determine how p varies with q and r. Let's start by setting up the equation.

According to the problem statement, p varies partly as q and partly as the square of r. This can be represented as:

p = k * q * r^2

Where k is the constant of variation that we need to find.

Now let's use the first set of values given, where p=6, q=8, and r=4, to solve for k.

6 = k * 8 * 4^2
6 = 32k

Dividing both sides of the equation by 32, we get:

k = 6/32
k = 3/16

Now we have the value of k. Let's substitute it into the equation and use the second set of values given, where p=10, q=12, and r=5, to verify:

10 = (3/16) * 12 * 5^2
10 = (3/16) * 12 * 25
10 = 9 * 25
10 = 225

The equation checks out with the second set of values as well.

Therefore, the formula connecting p, q, and r is:

p = (3/16) * q * r^2