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help-10
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kat.
04/10/2022 06:42:00
phrasing into formula
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Ann
04/10/2022 06:42:18
have you heard of the _floor_ and _ceiling_ functions?
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kat.
04/10/2022 06:42:21
yess
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Ann
04/10/2022 06:42:24
okay
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Ann
04/10/2022 06:42:39
so now just to be clear, what unit do you want to measure time in? hours or minutes?
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Ann
04/10/2022 06:42:50
neither choice is less valid than the other but it'll affect what the formula will look like
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kat.
04/10/2022 06:43:17
im not sure but the problem says half an hr im assuming hr?
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kat.
04/10/2022 06:43:26
it didnt tell me what specific unit
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Ann
04/10/2022 06:43:43
kat, do you think that was a question with a right and a wrong answer?
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Ann
04/10/2022 06:43:57
because it wasn't.
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Ann
04/10/2022 06:44:06
i specifically said there was no wrong answer here.
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kat.
04/10/2022 06:44:15
i guess hour
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Ann
04/10/2022 06:44:22
if you want to go with measuring time in hours then just say hours lol
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Ann
04/10/2022 06:44:31
okay, hours it is
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kat.
04/10/2022 06:44:31
ok sorry i wasnt sure huhu
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Ann
04/10/2022 06:45:09
now the following _is_ a question with a right and a wrong answer: since we are rounding _up_, what rounding function do we use? floor or ceil?
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kat.
04/10/2022 06:45:26
ceil
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Ann
04/10/2022 06:45:36
correct
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kat.
04/10/2022 06:45:50
oh wait my friends used mins
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kat.
04/10/2022 06:45:53
can i change?
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Ann
04/10/2022 06:45:56
sure
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kat.
04/10/2022 06:46:01
ok ty!
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Ann
04/10/2022 06:46:03
we didn't really get to the part where the unit matters anyway
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Ann
04/10/2022 06:46:14
well, we were about to get there but you stopped just moments prior
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Ann
04/10/2022 06:46:16
but ok, minutes it is
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Ann
04/10/2022 06:46:30
now we need to find how many half-hours there are in **x** minutes
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Ann
04/10/2022 06:46:46
as i am sure you know there are 30 minutes in a half-hour, so...
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kat.
04/10/2022 06:46:51
yes
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Ann
04/10/2022 06:47:13
when you convert _x_ minutes into half-hours, what do you get?
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kat.
04/10/2022 06:47:36
30 60 90
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Ann
04/10/2022 06:47:47
....................
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Ann
04/10/2022 06:47:48
what
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kat.
04/10/2022 06:47:48
am i right?
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kat.
04/10/2022 06:47:50
oops
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kat.
04/10/2022 06:47:52
HAHAHA
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Ann
04/10/2022 06:47:54
no, that's nowhere near it
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kat.
04/10/2022 06:47:59
well
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Ann
04/10/2022 06:48:04
are you familiar with the concept of _unit conversion_ at all
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kat.
04/10/2022 06:48:24
no
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Ann
0413
Ann
false
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kat.
04/10/2022 06:48:31
sorry im so dumb rn
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Ann
04/10/2022 06:48:36
so you do not know how to do things such as convert lengths between feet and inches?
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kat.
04/10/2022 06:48:44
oh yea i meant yes
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kat.
04/10/2022 06:48:54
yes ik unit conversion my bad
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Ann
04/10/2022 06:48:57
so you _are_ familiar with this concept. ok
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kat.
04/10/2022 06:49:09
yes
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Ann
04/10/2022 06:49:14
so let's try to jog your memory a little
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Ann
04/10/2022 06:49:31
there are 12 inches in a foot. if you have a measurement listed in inches and you want to convert it to feet, what do you do?
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kat.
04/10/2022 06:50:38
do i divide it by 12
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kat.
04/10/2022 06:50:42
so 1 foot
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Ann
04/10/2022 06:51:11
"divide the number by 12" and "always say it's 1 foot no matter what" are very different things to do, don't you agree?
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kat.
04/10/2022 06:51:24
yes
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Ann
04/10/2022 06:51:32
"a measurement listed in inches" does NOT mean "a measurement that says 12 inches" despite the presence of the number 12 in the previous sentence...
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kat.
04/10/2022 06:51:48
okok
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Ann
04/10/2022 06:51:57
would recommend not latching onto the first number you see out of desperation to use something as the input to some arithmetic.
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Ann
04/10/2022 06:52:10
but other than that, yes, to convert a measurement from inches to feet you divide the number by 12.
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Ann
04/10/2022 06:52:14
now in the same token
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kat.
04/10/2022 06:52:18
okk
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Ann
04/10/2022 06:52:41
there are 30 minutes in a half-hour. if you have a length of time listed in minutes and you want to convert it to half-hours, what do you do?
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kat.
04/10/2022 06:53:43
30 = 1 half hr 60 = 2 half hrs so basically i divide it by 30
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Ann
04/10/2022 06:54:04
those two first sentences were entirely unnecessary
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Ann
04/10/2022 06:54:19
i was intending for you to follow purely by analogy with the foot/inch thing.
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kat.
04/10/2022 06:54:28
i meant divide by 30
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Ann
04/10/2022 06:54:31
two units, one of them a multiple of the other.
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Ann
04/10/2022 06:54:52
but yes, so to convert from minutes to half-hours you divide by 30.
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Ann
04/10/2022 06:55:12
and now, to bring in the "rounded up" thing
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Ann
04/10/2022 06:55:30
a parking time of _x_ minutes is counted as _ceil(x/30)_ half-hours.
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kat.
04/10/2022 06:56:07
okk
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kat.
04/10/2022 06:56:14
how do i say that in a piecewise function?
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kat.
04/10/2022 06:56:18
in a formula
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Ann
04/10/2022 06:56:28
is your teacher requiring you to write it as a piecewise function?
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kat.
04/10/2022 06:56:32
yes
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Ann
04/10/2022 06:56:35
that's strange.
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Ann
04/10/2022 06:56:52
i mean, you could _shoehorn_ a piecewise definition in, but there's no need to
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Ann
04/10/2022 06:57:01
the price for $x$ minutes of parking is simply $f(x) = 6 \ceil{x/30}$
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510,789,298,321,096,700
TeXit
04/10/2022 06:57:04
**Ann**
https://cdn.discordapp.c…144404037632.png
183668144404037632.png
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Ann
04/10/2022 06:57:13
this works regardless of whether x is less than 30 or greater than 30
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kat.
04/10/2022 06:57:32
she prefers me to put a piecewise function and conclude what the discontinuities mean
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Ann
04/10/2022 06:57:36
so just to be clear, despite this, your teacher is FORCING you to write down a PIECEWISE FORMULA for the function, and will REJECT OUTRIGHT any answer that doesn't write it like that
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Ann
04/10/2022 06:57:39
is that correct?
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Ann
04/10/2022 06:57:51
am i understanding you correctly?
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kat.
04/10/2022 06:57:54
yes
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Ann
04/10/2022 06:58:03
okay, then i guess we will have to do something stupid like this:
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kat.
04/10/2022 06:58:35
my friend put like 6 ; 0<x__<__30 so on
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help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 06:58:46
$f(x) = \begin{cases} 6 & 0 < x \leq 30 \\12 & 30 < x \leq 60 \\ 18 & 60 < x \leq 90 \\ 24 & 90 < x \leq 120 \\ \vdots & \vdots \end{cases}$
0
1
null
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null
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null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
605,972,482,284,978,200
kat.
04/10/2022 06:58:56
yeaa
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
510,789,298,321,096,700
TeXit
04/10/2022 06:58:58
**Ann**
https://cdn.discordapp.c…144404037632.png
183668144404037632.png
0
1
null
null
null
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1,800
help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 06:59:00
like this
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 06:59:08
and this despite your class knowing about the existence of the ceiling function
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 06:59:10
presumably
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
605,972,482,284,978,200
kat.
04/10/2022 06:59:12
ooo ok tysm i get it now
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 06:59:21
what is there to get? i didn't write anything new.
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
605,972,482,284,978,200
kat.
04/10/2022 06:59:36
i just didnt know how to form the piecewise function
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 06:59:40
all i did was transcribe the definition that you just said your friend wrote down, no?
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 07:00:04
i guess this one has the benefit of explicitly highlighting the first few points of discontinuity in the pricing function.
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 07:00:23
namely the ones at x=30, x=60, x=90, etc.
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
605,972,482,284,978,200
kat.
04/10/2022 07:00:29
yess
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
183,668,144,404,037,630
Ann
04/10/2022 07:00:32
every half hour the price jumps up by $6
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
605,972,482,284,978,200
kat.
04/10/2022 07:00:46
thank you so much for the help! sorry if i wasted any of your time
0
1
null
null
null
null
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1,800
help-10
369c5e0197634eb58022fd53b5caf61e
605,972,482,284,978,200
kat.
04/10/2022 07:00:49
ty!
0
1
null
null
null
null
null
1,800
help-10
369c5e0197634eb58022fd53b5caf61e
605,972,482,284,978,200
kat.
04/10/2022 07:02:23
.close
0
1
null
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null
null