Inverse square law (biology)

Can I have help on this please ?

Okay, what do you understand by inverse square law?

I understand 1/distance squared but that isnt really helping me ,can give me a explanation around the question please

Okay, no worries.

Let's start with something is directly proportional to something, which means that there exists a formula such that y = kx between two variables x and y, where k is a constant (any number, e.g. 5 but but in these questions k is not important).

So let's take an example at a fairground where you get 5 points every time you hit a target with a bow and arrow. So if we say y is the number of points you get and x is the number of hits you make, then you know that y=5x.

Now proportionality is concerned with what happens when you double, halve, triple etc from one x value to another.

So for example, if you have 2 hits then you know you get 10 points. If you double your hits, your score doubles to 20. If you halve your hits, your score halves to 1. This is why it's directly proportional. The change that happens to the x is identical to the change that happens to y. Proportionality isn't concerned with what happens when you had 2 shots and you add one more, which would be going from 2 shots and 10 points to 3 shots and 15 points.


Now let's say in the above example, you didn't know what k was, I.e. You don't know how many points you get for each hit but you know that it's y = kx. Let's say it's not 5 as before.

One way to figure it out is by getting 6 shots, and the game tells you you got 60 points. Now double the shots hit, and it says you got 120 points. So what happens when we get 24 shots? Does it now matter what k is? No.

We know that it's directly proportional. So 120 = 12k from y = kx, where y = 120 and x = 12.

Now, when we double from 12 shots to 24, it is really saying y = 2*12*k. And we already know what 12k is, without having to know what k is. It is 120 from the previous paragraph.

So we know that y = 2*12*k = 2* 120 = 240.

This is what directly proportional is.

Proportional to the square means that it's y = k* x^2, so when you double x y quadruples. This is because if you crudely substitute x with 2x and square the whole thing, you end up with 4 * (old value).

Now, inverse proportional is just y = k/x. If x was number of missed and y was score and k was some number, and you had 5 misses to give a score of 6, then if you had 10 misses then your score would halve to give 3.

So when it's inverse square, y = k/x^2. And when you combine the two things above...

Thank so much for your time ,but may you use the knowledge you have provided and use it on one question above ,thank you

That would be against the ethos of offering help on this forum - do you have any questions about my explanation, or an idea as to how to apply it to the problem above?

Idea of how to apply what you have shown me

I'm afraid my last few paragraphs in the explanation give decent hints without giving it away or doing it for you. Happy to answer any specific questions you may have.

I just don't understand what k y and x would be in my questions and the answers I'm getting are far away from the one I should get as i'm trying to use the ones that have no empty boxes as a way to try and figure out the method

I just don't understand what k y and x would be in my questions and the answers I'm getting are far away from the one I should get as i'm trying to use the ones that have no empty boxes as a way to try and figure out the method

x is the independent variable you are changing (the distance) and y is the thing you are measuring (the light intensity) and k doesn't matter as I mentioned in the post somewhere

Edit: I see the table has been generous. Look at 35cm and 70cm - when you double he distance from 35 to 70, the light intensity is divided by 4 - does that give you a hint?

Thank you so would the first box be 240 and second box be 40cm