okay next video exposure maintenance formula sometimes called the density maintenance formula again i stole the numbers i'm about to use from your exposure lecture handout again you don't need them if you don't have it with you because i'm going to work through the entire problem but in the corner i do have the density maintenance formula in case you don't have it handy okay so first things first these are the variables that were supplied you used a 40 inch sid and a 40 mass and a 72 inch sid what would you need for your mass okay so the first thing that you want to do is identify your variables for the formula okay so one identify variables if you already watched the inverse square law video these steps are going to be quite similar okay so in this scenario our distance 1 squared is our 40 inch sid our mass is here so i'm just going to put mass 1 our distance 2 squared is 72 and we're solving for mass 2. that is our unknown okay second step is you want to plug those variables into the formula and the reason why i like to do that right away is just again i've said it before but the quicker that you get those moved into the format of the density maintenance formula the less of a chance there is for you to put them into the wrong spot later on so if i was setting this up now my mass 1 so 40 mass over mass 2 which is my unknown is equal to distance 1 which is 40 squared over distance 2 72 inches squared okay step three you're going to cross multiply and i'm just going to put arrows i like to put arrows for myself so i can easily see what's supposed to be tied together but the other thing that i like to do is put this formula into my cross multiplied style formula in which case that would be mass 1 times distance 2 squared is equal to mass 2 times distance 1 squared now if i move these numbers into that format that's going to be 40 times 72 squared is equal to our unknown variable times our distance one forty squared okay our next step that we want to do is isolate the unknown variable and what i mean by that is i want my x to be independent of the on the equal sign side so i don't want anything else hanging out with that x so what i'm going to do is divide out that 40 squared and again we're not actually doing any math here we're just setting up our math problem so that translates get you can get rid of this now and make it simpler simplify that down to x i like to put it on the left i think it looks cleaner you can do it either way x being equal to your 40. times 72 squared over 40 squared okay so this these are going to cancel each other out so i'm just rewriting this okay i'm going to plug these values in directly to my calculator to get my next step which is just solving so 40 times 72 squared leave your little brackets on a lot of scientific calculators require it but that is going to make your next step look like this it's going to be hundred and seven thousand three hundred and sixty for the top line and your bottom line forty squared is sixteen hundred okay so divide those two out x is going to equal 129.6 okay that means your final answer is going to be mass 2 is equal to 129.6 i like to leave my mass rounded to the nearest tenth space your instructor might like it there or rounded to a whole number you'll have to ask them but through these steps you've done it you've solved the density maintenance formula not too bad