Given these constructions, there is no maximal volume. The volume approaches infinity as the angle approaches 90 degrees.
In fact these formulae are unrelated
the lateral height of a cone is the length of a line segment from the apex of the cone along its side to its base.
try harder.
I’m a math grad student I don’t deserve to be humiliated like this
sorry, it was either you or me :V
I think? But I’m only at undergrad level in mathematics, so feel free to point out if I f@*$ed up. I was never particularly amazing at geometry.
this is entirely correct; very thorough too :3
also this should entirely be accessible to anyone who’s done just enough calculus to talk about maxima and minima of continuously differentiable functions, which means either high school or undergrad calc, depending on your educational path; don’t be so worried ;p
(incidentally you could have skipped from h=l/√3 straight to the answer by using arccos instead of arctan but arctan is a nicer function anyways so w/e)
Ok so I rly fucking need to clean my house. Do any other People With Depression™ have any tips or ways you motivate urself to clean? Because this feels like the hardest goddamn thing in the world even tho I know it’s not and I’m just continually frustrated with myself and have been for the past two weeks.
HOO BOY DO I HAVE DEPRESSION/EXECUTIVE DYSFUNCTION CLEANING TIPS
in no particular order (because I have depression and executive dysfunction):
1. If something sensory about cleaning bothers you, eliminate that before you start. For example, I wear gloves to do the dishes. If the sound of the vacuum bothers you, wear headphones and turn up the music. etc.
2. If you can, make a list of everything that needs to be done. Then acknowledge that you probably can’t do it all, and circle all the things that absolutely, no matter what, have to be done. Pick one (ONE! ONLY ONE! START WITH ONE!) of those things and break it down into smaller steps. Then even smaller steps. Seriously, if step one is “stand up” and step two is “walk to closet” and step 3 is “get mop”, that’s fine. It can be that small.
3. Take a break. “But I literally only started five minutes ago!” Don’t care. If you want a break, take a break. “At this point I’ve spent more time on breaks than I’ve spent on cleaning.” Ok, but you’ve spent more than zero time on cleaning, so you’ve accomplished more than you had at the beginning. “If I take a break it won’t get done!” If you burn out it won’t get done either. Take a break.
4. If nothing is working, try what I call bin cleaning/box cleaning. Take a big trash bag and a box. Pick up the first object you see. Step 1: Is it trash? Put it in the trash bag. Step 2: Will you use it in the next 2 days? No? Put it in the box. It’s a problem for Future You. If you’ll use it in the next 2 days, take time to put it away. Rinse and repeat.
5. Did you get distracted and forget what you were doing? Don’t worry about it. Just clean a thing. It doesn’t matter if it’s the thing you were cleaning before. You have to clean lots of things, so just pick a thing and clean it. Eventually you’ll get around to the thing you forgot.
6. If you have to do a thing you really hate, do a thing you like afterwards. I hate doing dishes, but folding laundry soothes me, so that’s a nice one to do afterwards. YMMV. If there are no cleaning things you like that you can do afterwards, see number 3.
7. Make it fun. Play loud music and dance while you’re cleaning. Wear something that makes you feel cute, or if you prefer, something comfy. Light your favorite candle. Whatever.
8. If it’s nice out, open a window. Seriously, it helps.
This is seriously so helpful, thank you.
Oh oh I got one for anyone struggling to sort through clutter (as someone who lives with a mother who hoards and spends more time staring at STUFF not knowing where to start than anything else):
9. Grab a box and pick an area of clutter. Keep telling yourself it doesn’t have to be pretty and then just FILL THE BOX. Fill it with random crap. Most clutter LOOKS worse than it is because of the chaos and disorganization. So just grab random crap and throw it into a box. Then put the box to the side and grab a new box. Fill that one too. Keep going until you can’t anymore. Then take one of the boxes you filled and go through it item by item. Having the stuff in boxes automatically breaks the work up into smaller pieces, and you can work through things one box at a time at your own pace.
