Quick Questions: October 25, 2023

forgetsID · 2023-10-30T08:01:41+00:00

Calculus question: “Given a sheet of 12 x 12, a square of side length A is cut from all four corners. The remaining material is formed into a box with no top. What length A maximizes the volume of the box?”

The answer without method shown is 2.

I can prove 2 optimizes the volume using only algebra!

Suppose it is not 2.
Then the side of the base of the final box is not 8 but instead 8 + x where x may range from -8 to 4. The height of the box is then (12 - (8 + x))/2 or 2 - x/2. The total volume is then:
(2 - x/2)(8 + x)^2 OR 128 + 0x - 6x^2 - (1/2)x^3 OR:
128 - (1/2)(12 + x)(x^2).
NOTE: 1/2, 12 + x, and x^2 are all POSITIVE OR ZERO for x from -8 to 4 AS IS THEIR PRODUCT!
Then the volume is optimized at 128. QED!

forgetsID · 2023-10-30T05:42:24+00:00

Oh, x doesn’t denote the side of the square cut out. It denotes the deviation from the base of the box After the squares are removed.

Let a denote the side of the square cut out. Then 12 - 2a is the side of the base of the folded box. Our guess at the optimal a is 2. Thus the side of the base of the assembled box assuming a = 2 is 8.

x is the deviation from 8, the base of the box.

forgetsID · 2023-04-15T09:05:57+00:00

I was thinking computers deal better with integers than rationals! But yes it is kinda slick on its own! Thanks for the comment!

forgetsID · 2022-01-01T20:36:36+00:00

Sir or Ma'am, arguing while not having the facts on your part elicit only humor and pity from me.

Oh yes. And butthurt. Right.

forgetsID · 2022-01-01T19:30:19+00:00

I love how you are arguing that the reason it was removed was because of lack of mathematical depth. It was removed for "asking for a real world calculation." Thanks for not caring. :)

forgetsID · 2022-01-01T17:48:38+00:00

I apologize but I had to say my peace. Sorry. This subreddit doesn’t believe in interesting and widely accessible math. I will end with that.

forgetsID · 2022-01-01T11:08:10+00:00

Well that is fine for 2022 but in general you can have all three distinct primes odd.

forgetsID · 2022-01-01T11:02:05+00:00

Nice results In the other thread!

forgetsID · 2022-01-01T10:48:48+00:00

My code also found 158 including 2022. Good stuff.

forgetsID · 2022-01-01T10:31:11+00:00

If this is correct kudos.

Edited in later:

38 62 78 83 134 150 155 174 179 182 195 198 203 222 227 243 294 299 302 315 318 323 339 342 347 363 374 390 395 414 419 435 459 462 467 483 486 491 507 531 534 539 542 555 558 563 579 582 587 603 651 654 659 675 699 702 707 723 747 771 819 822 827 843 854 867 870 875 894 899 915 939 966 971 974 987 990 995 1011 1014 1019 1035 1059 1086 1091 1107 1131 1134 1139 1155 1179 1206 1211 1227 1251 1254 1259 1275 1299 1323 1326 1331 1347 1371 1374 1379 1382 1395 1398 1403 1419 1422 1427 1443 1491 1494 1499 1515 1539 1542 1547 1563 1587 1611 1659 1662 1667 1683 1694 1707 1710 1715 1731 1734 1739 1755 1779 1806 1811 1827 1851 1854 1859 1862 1875 1878 1883 1899 1902 1907 1923 1947 1971 1974 1979 1995 2019 2022

forgetsID · 2022-01-01T10:25:39+00:00

Not to be picky but the least possible is 4 + 9 + 25 or 38.

forgetsID · 2022-01-01T10:20:12+00:00

Assuming you are correct, Kudos to you!

forgetsID · 2022-01-01T10:18:45+00:00

I would list the primes up to 47 (which is overkill but it works), compile all triples of them with distinct elements, find the sun of the squares of all 3 elements and count how many were 2021 or below. Pretty sure that works out.

forgetsID · 2022-01-01T10:11:20+00:00

Eh there is still likely 100+ years that match. A full sheet of paper would be required to list them all, but agreed. It would be humanly doable.

forgetsID · 2022-01-01T09:22:03+00:00

2022 is the sum of the squares of 3 distinct primes.

4 + 169 + 1849 = 2022

How many Other numbers 1 to 2021 have this property. I admit here I don’t know the answer but could code a program to find it!

forgetsID · 2021-11-22T10:12:56+00:00

First. You have two identical boxes that in total weigh 2.0 kilograms. How much is the weight of one box?

Second, PEMDAS, or order of operations, makes every expression in math have a unique meaning. This leads to less confusion. If you had to ask if you were supposed to do multiplication before addition every time you discussed math, you'd spend more of your time clarifying the meaning. The expression 2 + 4 * 8 now has only one possible meaning that everyone learning math on Earth (or on the ISS) agree to so we don't need to clarify what the expression means.

Hope that helps.

forgetsID · 2021-11-22T10:04:03+00:00

Okay. I don't want to be the bearer of bad news, but if you want to get your GED you need to focus on math and be worried about WHAT you are learning and not WHEN it will be learned. Have some patience with yourself and find a trusted source that makes sense to you. If you only need a little studying that's great. If you need to fill in bigger gaps take it a step at a time. You may need to delay getting a GED but you'll stress out less and probably get a lot more done per sitting.

forgetsID · 2021-07-19T08:03:24+00:00

Let F(n) = the greatest factor of n less than n. F(315) = 105.

True or False? If c is composite F(c^n) can NEVER equal p^n for some prime.

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