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help-10
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Angelic
04/08/2022 08:50:10
Oooh right
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Angelic
04/08/2022 08:50:19
I could’ve done that
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Angelic
04/08/2022 08:50:26
I completely forgot about that equation
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Angelic
04/08/2022 08:50:51
Well I appreciate the help ty very much @Ann
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Soundview
04/08/2022 09:32:44
Bob needs to bake the pizza in exactly 17 min. Bob have a sand clock that ends in 9 minute and 13 minute. Then how to bake the pizza in exact time? (math type: logical, grade level: grade 5)
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Soundview
04/08/2022 09:48:00
@Helpers
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whitefang
04/08/2022 09:48:18
you have 2 clocks, right ?
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Soundview
04/08/2022 09:49:57
yes
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whitefang
04/08/2022 09:51:44
i am not sure if thats the best way but probably you need to start the clocks first and later put the pizza in the oven
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whitefang
04/08/2022 09:52:47
try to make one of the two clocks to end in a more useful time than the ones you have right now
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Alexander42
04/08/2022 10:04:50
think about which times from now you can get using only the first clock and which times from now you can get using only the second clock. Then notice that you can put the pizza in the oven at a time measured by the first (or second) clock and take it out at a time measured by the second (or first) clock
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Math_Helper
04/08/2022 10:05:05
start both clocks at the same time, when 9 runs out flip it and you know that 9 minutes passed, then when 13 runs out flip 9 again, it will have ran for 4 minutes and will run for another 4 so 9+4+4=17
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Soundview
04/08/2022 10:10:42
ive come up to an idea. you start the clocks at same time and when the 9 min clock runs out, put pizza in the oven. and immediately after 13 min clock runs out, flip it. and after 13 min clock runs out, take pizza out
https://cdn.discordapp.c…7754/unknown.png
unknown.png
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Soundview
04/08/2022 10:11:54
.close
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kishblockpro
04/08/2022 11:13:38
how do i prove that 0.5 maximises x - x^2 ? i am aware this is probably the most stupid obvious insight ever and yet my idiot head has been banging against the wall
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ramonov
04/08/2022 11:16:40
complete the square to get vertex form or use calculus
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kishblockpro
04/08/2022 11:18:45
i dont understand
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kishblockpro
04/08/2022 11:19:01
complete what?
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ramonov
04/08/2022 11:19:13
the square
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ramonov
04/08/2022 11:19:22
look up completing the square
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kishblockpro
04/08/2022 11:19:42
i am talking about only decimal inputs btw
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ramonov
04/08/2022 11:19:47
what?
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kishblockpro
04/08/2022 11:19:52
you mean the quadratic formula?
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ramonov
04/08/2022 11:19:54
no
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ramonov
04/08/2022 11:19:58
i mean what i said
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kishblockpro
04/08/2022 11:20:09
ok
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ramonov
04/08/2022 11:20:43
completing the square is a method that can be used to convert a quadratic expression from general form to vertex form where you can easily identify extrema
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kishblockpro
04/08/2022 11:21:20
wait i think i did it
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kishblockpro
04/08/2022 11:21:25
but i didnt complete the square
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kishblockpro
04/08/2022 11:21:32
and since im stupid it mnight be wrong can you verify it?
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ramonov
04/08/2022 11:22:57
show what you did
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kishblockpro
04/08/2022 11:23:46
alright so if were only considering decimal inputs
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ramonov
04/08/2022 11:23:59
wdym by only considering decimal inputs
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kishblockpro
04/08/2022 11:24:16
the function x - x^2 for only decimal inputs how do i prove that 0.5 is the max output
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kishblockpro
04/08/2022 11:25:09
okay so i am trying to show that changing x any amount from that is going to result in something smaller
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ramonov
04/08/2022 11:25:19
also max output of 0.5 and max output at 0.5 mean different things
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kishblockpro
04/08/2022 11:25:33
shit yeah i meant at
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kishblockpro
04/08/2022 11:26:01
we need to say that changing x any amount will yeild this:
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kishblockpro
04/08/2022 11:26:21
x - y (y = amount of change) -(x - y)^2
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kishblockpro
04/08/2022 11:26:37
and we cant forget adding y to x
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kishblockpro
04/08/2022 11:26:48
x + y -(x + y)^2
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kishblockpro
04/08/2022 11:27:11
so since i already hypothesise/know that 0.5 is it, i can substitute 0.5
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kishblockpro
04/08/2022 11:27:39
0.5 + y -(0.5 + y)^2
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kishblockpro
04/08/2022 11:27:57
since the output at 0.5 is 0.25, i can set it like so
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kishblockpro
04/08/2022 11:28:14
0.5 + y -(0.5 + y)^2 < 0.25
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kishblockpro
04/08/2022 11:28:36
if we evaluate the expression on the left side
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kishblockpro
04/08/2022 11:28:47
0.25 - y^2 < 0.25
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kishblockpro
04/08/2022 11:28:49
which makes sense
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kishblockpro
04/08/2022 11:29:04
so now we should consider the case where we subtract y
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kishblockpro
04/08/2022 11:29:20
0.5 - y -(0.5-y)^2 < 0.25
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kishblockpro
04/08/2022 11:29:38
again evaluating we end up with 0.25 - y^2 < 0.25
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kishblockpro
04/08/2022 11:29:54
which is correct since inputting 0.4 and 0.6 in x-x^2 yeilded the same result
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kishblockpro
04/08/2022 11:30:14
so i can say that making any change to 0.5 as the input will result in something smaller than 0.25
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kishblockpro
04/08/2022 11:30:18
is this all correct?
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kishblockpro
04/08/2022 11:30:31
i am kind of worried thsi argument will still hold up for inputs that CAN be changed to output something larger
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ramonov
04/08/2022 11:31:33
you didn't square properly
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kishblockpro
04/08/2022 11:32:04
oopsies i didnt mean to do that
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kishblockpro
04/08/2022 11:32:11
substitute x wherever it is with 0.5
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kishblockpro
04/08/2022 11:32:49
ok wait lemme see if i did it correct
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kishblockpro
04/08/2022 11:33:54
no i think its correct
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kishblockpro
04/08/2022 11:33:57
lemme show the working
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kishblockpro
04/08/2022 11:34:52
1/2 - y -(1/2-y)^2 1/2 - y -(1/4 +y^2 - y) 1/2 - y - 1/4 - y^2 + y 1/2 - 1/4 - y^2 1/4 - y^2
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kishblockpro
04/08/2022 11:35:13
i may be missing something since i always make sillies but i think this is right
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ramonov
04/08/2022 11:36:06
seems ok
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ramonov
04/08/2022 11:36:17
i'd recommend using a variable other than y though
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ramonov
04/08/2022 11:36:23
like h
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kishblockpro
04/08/2022 11:36:24
i used epsilon
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ramonov
04/08/2022 11:36:27
or Delta x
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kishblockpro
04/08/2022 11:36:32
but i didnt want to say epsilon over and over
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kishblockpro
04/08/2022 11:36:39
since idk the symbol for it
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kishblockpro
04/08/2022 11:36:57
i saw someone use it for incremental changes when they were explaining derivatives so i just used it
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kishblockpro
04/08/2022 11:38:03
but would my solution be correct?
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ramonov
04/08/2022 11:38:07
it works
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kishblockpro
04/08/2022 11:38:38
are you sure it doesnt just do the same thing for values other than 1/2 when in reality they could be changed to output something larger
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ramonov
04/08/2022 11:39:13
well you could try and see what happens when you try another value
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kishblockpro
04/08/2022 11:39:13
whati wanted was a smooth proof showing a linear change and a peak or something but i just went muddy
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kishblockpro
04/08/2022 11:39:33
okay ill do that now
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kishblockpro
04/08/2022 11:39:47
3/2 - y should be able to get larger so lemme try that
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kishblockpro
04/08/2022 11:40:44
shit
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kishblockpro
04/08/2022 11:40:44
i meant
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kishblockpro
04/08/2022 11:40:45
2/3
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kishblockpro
04/08/2022 11:46:00
ok so its working out for 2/3
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kishblockpro
04/08/2022 11:46:04
its showing me that the inequality is false
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kishblockpro
04/08/2022 11:46:08
lets fucking gooo
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kishblockpro
04/08/2022 11:47:29
well actually my domain for the function x - x^2 is 0 to 2, but the real numbers between 1 and 2 would always return a negative number when inputted right(i am solving a bigger problem and this is one of the subparts i need to do[i think])
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kishblockpro
04/08/2022 11:48:28
yeah i think they would since a number greater than one squared would have the numerator increasing much faster than the denominator even if they were consecutive
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kishblockpro
04/08/2022 11:48:55
anyawys thanks for helping but do you have an elegant proof for it? you were talking about completing a square
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help-10
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220,517,274,845,577,200
ramonov
04/08/2022 11:51:13
look it up
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kishblockpro
04/08/2022 11:52:57
yes yes i looked it up and understand it now, you complete the sides and add the amount you splitted by squared to the other side
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kishblockpro
04/08/2022 11:53:07
but since im an idiot i dont understand how this would help me here...
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kishblockpro
04/08/2022 11:54:11
how would figuring out the roots of that polynomial help me is what im trying to say
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ramonov
04/08/2022 11:54:22
i didn't say anything about figuring out the roots
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kishblockpro
04/08/2022 11:54:27
hmm
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ramonov
04/08/2022 11:54:44
there's a difference between completing the square and solving an equation using completing the square
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help-10
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ramonov
04/08/2022 11:55:29
completing the square by itself refers to the part where you complete the square and balance the equation / maintain the value of the expression
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kishblockpro
04/08/2022 11:55:31
i guess i could use the two equivalent expressions
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ramonov
04/08/2022 11:55:41
$\cts$
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TeXit
04/08/2022 11:55:46
**ℝamonov**
https://cdn.discordapp.c…274845577216.png
220517274845577216.png
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ramonov
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false
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ramonov
04/08/2022 11:56:17
since the coefficient of the leading term in `x-x^2` is negative
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help-10
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220,517,274,845,577,200
ramonov
04/08/2022 11:56:24
you can consider factoring out -1 first
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