if $\sin \theta = 0$ then $\cos \theta \neq 0$
#help-23
warm warren
flat frigateBOT
Annie Maqionde
warm warren
it is implied
warm warren
you may cancel it out; if you want to be absolutely rigorous, you may write a small note on why $cos(xy) \neq 0$(then tan is undefined, right, but tan is an integer here)
flat frigateBOT
Annie Maqionde
warm warren
While cancelling cos(a) we should say cos(a) =/ 0
yes it is good practise, but not necessary, to do so
graceful lichen
you may cancel it out; if you want to be absolutely rigorous, you may write a sm...
So for integers we can ignore it
To define both equations
Right?
warm warren
So for integers we can ignore it
well because if cos is zero, tan is undefined
graceful lichen
yes
warm warren
To define both equations
correct. so that $\tan(xy)$ is an integer
flat frigateBOT
Annie Maqionde
graceful lichen
so it is not necessary to say cos(a) is not zero if equations are defined on integers
warm warren
so it is not necessary to say cos(a) is not zero if equations are defined on int...
you may add a small point
graceful lichen
what it is
warm warren
**Annie Maqionde**
this one
graceful lichen
you may cancel it out; if you want to be absolutely rigorous, you may write a sm...
cos(xy)=/ 0 because it is equal to some integer already
warm warren
cos(xy)=/ 0 because it is equal to some integer already
no
$\cos(xy) \neq 0$ since if $\cos(xy) = 0$ then $\tan(xy)$ will be undefined. But as stated in question, $\tan(xy)$ is an integer. Therefore $\cos(xy)$ is not zero
flat frigateBOT
Annie Maqionde
warm warren
something along the lines of this
graceful lichen
I want to clear one thing only
from the step where we did xy=0
After sin(xy)=xy
graceful lichen
from the step where we did xy=0
here because tanx= sinx/cosx and sinx= 0 means tan 0 but here tan can't be zero it is fixed integer then this implies cos is 0 right?
warm warren
here because tanx= sinx/cosx and sinx= 0 means tan 0 but here tan can't be zero ...
since when is cos zero?
please reread our entire conversation again
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stuck tusk
The question is confusing when there comes 2^x and x too
safe radishBOT
The question is confusing when there comes 2^x and x too
desert pasture
The question is confusing when there comes 2^x and x too
What is $\log_{2}(2^x)$
flat frigateBOT
Wai
lone ocean
The question is confusing when there comes 2^x and x too
This is a graph question
Sketch approximate graphs
stuck tusk
This is a graph question
can't we do without graphically?
lone ocean
Usually it’s too much to handle both exponentials and x in the same expression
lone ocean
Is this a Jee question
stuck tusk
Jee Main level question
lone ocean
Yeah then graph
stuck tusk
can't we use hit & trial method?
brisk apex
stuck tusk
But how will you confirm that those are the only solutions
I think given that rhs is 6- x
And there's a condition of log too
lone ocean
Doing those is equivalent to solving it graphically right
lone ocean
You know graphical transformations?
stuck tusk
initially
i am 11th moving student
And our teachers haven't taught us graph
but yeah they showed exponential graph
honest perch
do you know the log graph
stuck tusk
Yeah
upbeat hatch
Do u know the fact that log function takes only positive values ?
stuck tusk
Yep
quantity and base should be positive
not the answer of logs but
and base shouldn't be 1
honest perch
you should know graph transformations probably
graph log_2(x) then shift it 5 units left
to get log_2(x+5)
stuck tusk
is there any animation graph website
honest perch
desmos
stuck tusk
like this?
fair hound
yeah x = 3 gives log2(8) = 3 which is true
that's why your first screenshot gives the line x = 3
on your second screenshot you see the intersection at x = 3, where it's equal
stuck tusk
ohh yes
fair hound
from log_2(x+5) = 6-x
you could also have written x+5 = 2^(6-x) by log properties
so 2^x (x+5) = 64, and since 2^x (x+5) is strictly increasing as the product of 2 strictly increasing functions, it will go through 64 only once
fair hound
from log_2(x+5) = 6-x
you could also have written x+5 = 2^(6-x) by log propertie...
I did here
stuck tusk
from log_2(x+5) = 6-x
you could also have written x+5 = 2^(6-x) by log propertie...
2^x (x + 5) = 64?
ohhh
Like multiplication
fair hound
your equation is log_2(x+5) = 6-x, so x+5 = 2^(6-x)
multiply by 2^x on both sides, you get 2^x (x+5) = 2^6 = 64
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stuck tusk
@fair hound
fair hound
yes
stuck tusk
Now what to do?
fair hound
2^x (x+5) is strictly increasing as the product of 2 strictly increasing functions, it will go through 64 only once
hence the answer is 1
fair hound
yes
stuck tusk
JEE Advanced level question
thorn dragon
JEE Advanced level question
hmm
fair hound
I would first simplify A
thorn dragon
is the qn saying 5 power raised to the power of 1/2 10 times?
fair hound
10 times
thorn dragon
yeah so 5 power 1/1024
fair hound
yes, you simplify A, you get 1/512, and then it asks for log_sqrt(3) (2+1)
stuck tusk
is the qn saying 5 power raised to the power of 1/2 10 times?
like
fair hound
which is 2
stuck tusk
,tex 1/2^10
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stuck tusk
,tex 1/2^(10)
thorn dragon
which is 2
yep
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thorn dragon
this qn isnt that hard eh
upbeat hatch
JEE Advanced level question
Lol this can't be jee adv level
stuck tusk
Lol this can't be jee adv level
I can but the section where this question belongs to is JEE advanced level (it is shown like that)
i guess this question comes in the category of atleast mains or conceptual level
upbeat hatch
i guess this question comes in the category of atleast mains or conceptual level
Logarithm usually won't have standalone qs without other concepts in jee mains or adv
So it could be for conceptual clarity
stuck tusk
Logarithm usually won't have standalone qs without other concepts in jee mains o...
I see that the some questions of logarithm which looks advanced but ain't is asked in jee advanced
alright thanks for the doubt have a good day
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Fact?
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blud got hacked
Ah
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karmic sleet
tryna understand remainder theorem
where is f(a) plugged? and why is x now -1
i can see how we get 16 if u yk..add to the other side to cancel out n stuff
manic patrol
here's an excerpt of my own writeup of the polynomial remainder theorem (technically it's part of my proof of the polynomial factor theorem, but this part is enough for the remainder theorem).
perhaps this will help you understand a little more about the polynomial remainder theorem.
crystal wigeon
tryna understand remainder theorem
where is f(a) plugged? and why is x now -1
...
if f(x)
x + 1 =0
x = -1 /
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✅ Original question: #help-23 message
karmic sleet
if f(x)
x + 1 =0
x = -1 /
i dont get it
crystal wigeon
i dont get it
you asked why is x = -1
if we put x value in function(x), we need to find value of x first, so we find it by putting 0 in rhs, so x + 1 = 0
karmic sleet
yeah cause...if the r is 7 that means a is 7 which means x-a should be x-7? no?
rugged cave
r = 7 means f(a) = 7, not a itself.
rugged cave
here's an excerpt of my own writeup of the polynomial remainder theorem (technic...
take a look here
crystal wigeon
yeah cause...if the r is 7 that means a is 7 which means x-a should be x-7? no?
when you put x value in polynomial f(x), then the value of polynomial will be equal to r.
rugged cave
here's an excerpt of my own writeup of the polynomial remainder theorem (technic...
again OP, may I know if you've read this?
specifically, this part right here.
karmic sleet
i did but it was still pretty confusing for me :')
karmic sleet
ig just...the principle of it? like
when f(x) is divided by (x-a) the remainder is f(a)
so f(a)=7
f(a) = (a-a)q(a)+7
and a-a=0 so
f(a) = 0q(a)+7...which is =7....
am i on the right track
rugged cave
please don't gif spam in help channels
karmic sleet
sorry
rugged cave
takes up half the screen, esp. when one of your helpers has a vision-related request
rugged cave
ig just...the principle of it? like
when f(x) is divided by (x-a) the remainde...
yeah that looks good
karmic sleet
ah gotcha, noted
rugged cave
in fact you've kinda stumbled upon the idea of the proof of the remainder theorem
karmic sleet
yeah that looks good
not sure where to go from there..im trying to keep f(a)=7 right? how do i find out what q is? and a?
rugged cave
I haven't actually looked at your original question, a moment
manic patrol
there seems to be insufficient information to solve the original question. you have one constraint to find two unknowns with, and there are no cheap tricks you can do with q - 2p that makes it possible to ignore the two-unknown problem.
oh wait never mind.
I misread the sign of q, sorry.
manic patrol
not sure where to go from there..im trying to keep f(a)=7 right? how do i find o...
hint: don't find p and q separately.
manic patrol
here's an excerpt of my own writeup of the polynomial remainder theorem (technic...
instead, note that you are dividing by x + 1.
now, compare the expression you're dividing by here (x + 1) to the general term in the polynomial remainder theorem (x - a).
what is a?
karmic sleet
-1?
manic patrol
yes!
and by the remainder theorem, p(a) = r -> p(-1) = 7.
so evaluate your original polynomial at x = -1.
manic patrol
wait why r we replacing x with -1 again?
and because the remainder theorem tells us that evaluating the polynomial at x = a gives us the remainder on division by (x - a).
karmic sleet
p(x) is the polynomial in question.
so p is f?
manic patrol
well yes. I just use p(x) because p for polynomial.
karmic sleet
ahh i see
manic patrol
but you can use f(x).
karmic sleet
so p(x) or f(x) = 7 and because the remainder theorem says that when f(x) is divided by x-a the remainder is f(a)...f(a)=7 which is...the same as f(x)=7 except that x...or well..now a will always be -1 because the general term x-a in which in this case is x+1 (x-(-1))...
so f(-1)=7 and i just plug neg 1 from there and work it out?
manic patrol
do not interchange x with a freely.
p(x) has no definite value because it is still in terms of x. p(a) is when you actually substitute the value of a for x. so saying that p(x) or f(x) = 7 is incorrect.
because the remainder theorem says that when f(x) is divided by x-a the remainder is f(a)...f(a)=7
this...
a willalwaysbe -1 because the general term x-a in which in this case is x+1 (x-(-1))...
...and this... (note the correction)
so f(-1)=7 and i just plug neg 1 from there and work it out?
...and this are correct.
karmic sleet
tryna understand remainder theorem
where is f(a) plugged? and why is x now -1
...
just cause claude said -4
idk how they lost the first -1
manic patrol
so if my eyes are not failing me, that's 2p(-1) - 4 + (-5) + q in the second line.
where's the entire 2p term to begin with after that?
manic patrol
just cause claude said -4
also, please refrain from using AI if you are not already familiar with the topic.
manic patrol
so if my eyes are not failing me, that's 2p(-1) - 4 + (-5) + q in the second lin...
by the way, up to this point, you are correct.
but moving from line 2 to line 3, the 2p term just vanished.
karmic sleet
where's the entire 2p term to begin with after that?
i didnt add it yet, wasnt sure if i was to subtract the 4 from the -1 or if it was supposed to stay with the 2p
manic patrol
2p(-1) is a single term. you should multiply those two.
remember, multiplication before addition.
also, don't forget that this entire expression is equal to 7.
karmic sleet
-2p?
manic patrol
correct.
karmic sleet
manic patrol
and so your final answer is?
manic patrol
is -2p + q not the same as (+)q - 2p?
karmic sleet
how? i thought u couldnt flip subtraction problems
manic patrol
but you are bringing the signs with the terms.
you cannot flip q - 2p to become 2p - q, sure.
but you can reorder terms as long as you bring their sign with them.
manic patrol
if that doesn't stick in your mind, -2p + q = q + (-2p) = q - 2p.
karmic sleet
0-2p+q = 0+q-2p
manic patrol
if that works for you, then sure. it's not wrong, it's just a little awkward personally.
so I presume you're done with the question?
karmic sleet
if that doesn't stick in your mind, -2p + q = q + (-2p) = q - 2p.
WOAHHH OK
yeah yeah for sure i get it now
manic patrol
well done!
karmic sleet
🤗 tysmmm for ur help
manic patrol
unfortunately my eyes are really starting to fail me now, so I will have to take my leave. I'm sorry if you have any further questions.
all the best!
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brisk turret
Help needed in number theory and combinatorics:
I want to prove that a sequence characterized by floor(1.26*m^{\frac{3}{2}}) follows this identity. I know empirically that the sequence does follow this identity :
r(d)<=d-1
Where r(d) counts how many times a distance d shows up as a positive difference between any 2 elements. So like a golomb ruler, but instead of every difference d limited to appear once, they can appear atmost d-1 times
An optimal set that follows the above identity would be for example:
[0,2,5,8,12,16]
Any suggestions on how I can prove it? Even a probabilsitic proof approach would be fine
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Help needed in number theory and combinatorics:
I want to prove that a sequence...
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devout scroll
Use the fact that 1) after a certain point, consecutive difference are strictly increasing, and 2) that if the difference of two numbers are d, and you look at the consecutive differences between those two numbers, their sum is d
shrewd herald
Hello. My current understanding of fraction multiplication is the following:
When multiplying a fraction by a whole number, it'd be like increasing the magnitude of the fraction by the amount the whole number indicates. In multiplying a fraction by another fraction, it's as if the product's magnitude of growth were fractional, so it wouldn't really increase in numerical value, but even regress.
Is my understanding appropiate? Anything I missed?
safe radishBOT
Hello. My current understanding of fraction multiplication is the following:
Whe...
drowsy moss
basically, yes.
the magnitute changes by the size of the number multiplied (fraction or not)
If you multiply by 2/3 the magnitude shrinks, if you multiply by 3/2 the magnitude grows.
shrewd herald
If you multiply by 2/3 the magnitude shrinks, if you multiply by 3/2 the magnitu...
Thank you. On a similar topic, does something similar happen with division by fractions?
drowsy moss
yes, but it's reversed.
division is like multiplying by the reciprocal. i.e. Dividing by 2 is the same as multiplying by 1/2 and dividing by 2/3 is the same as multiplyin by 3/2
shrewd herald
Is that why the algorithm for division between fractions is crossed multiplication?
drowsy moss
one of the reasons, yea
shrewd herald
Are there other relevant reasons?
drowsy moss
With what you're doing now, that's enough of an understanding.
shrewd herald
Alright, thank you! Before you go, I'd like to get your feedback on my reasoning behind division by fractions.
If fractional multiplication is fractional magnitude growth or change, then fractional division is multiplication by the reciprocal, which essentially means magnitude growth by more than one fraction (at least for proper fraction division).
outer pollen
fractional division is multiplication by the reciprocal
I agree with this part, not sure about the part that comes after it. (sorry for jumping in.)
drowsy moss
Not sure what you mean by the last part of that, the first part is fine
shrewd herald
Thank you!
I'll refine it further later. If you don't mind, I'll close the chat
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frigid sedge
hi guys, can someone help me with this?
safe radishBOT
hi guys, can someone help me with this?
opaque fern
hi guys, can someone help me with this?
what function transformations do you know
nimble wyvern
-# context that they asked for what functions are in discussion
frigid sedge
i know the basics, but when graphs are given i tend to get confused
wintry bronze
first change the origin transformation..
then apply scale transformation @frigid sedge
frigid sedge
how do you 'move down' a graph?
f(x)-b
frigid sedge
yes
opaque fern
what is the value of the peak for both
frigid sedge
for f(x) its (0,6) and for g(x) (0,-2)
frigid sedge
-# context that they asked for what functions are in discussion
no haha, i know what functions are obviously. its just that sometimes domain and range questions get a bit tricky for me although theyre the basics
opaque fern
for f(x) its (0,6) and for g(x) (0,-2)
ok lets keep that in mind
now
there is the 'flat corner' to the right of both peaks, can you tell me the coordinates of that as well, for both graphs
frigid sedge
the rightmost point?
opaque fern
this
opaque fern
ok so
for f(x), the peak is at (0, 6) and the corner point is at (3,3)
for g(x), the peak is at (0,-2) and the corner point is at (3,-8)
frigid sedge
yes
opaque fern
for both functions, how much is the vertical drop between the peak and the corner point?
frigid sedge
wait i dont get what ur asking
opaque fern
how much is the difference between the second number in the parantheses between the peak and corner point
frigid sedge
3 and 6?
opaque fern
yeah
so the vertical distance has doubled
review your function transformations
what type of transformation is this
opaque fern
oh stretch factor 2 vertically
yep!
its a vertical stretch by 2
so now
we need to figure out the vertical translation
to do that
opaque fern
for f(x), the peak is at (0, 6) and the corner point is at (3,3)
for g(x), the p...
try to multiply the second value in parantheses by 2 for f(x)'s corner and peak
frigid sedge
(0,12) and (3,6)
opaque fern
yeah
so now
could you please calculate the vertical difference between the peak of f and g
frigid sedge
8?
frigid sedge
ooh so without multiplying the g's peak with 2?
opaque fern
nope!
opaque fern
yeah
frigid sedge
does the peak of g remain as (0,-2) or is it now (0,-4)?
frigid sedge
okay so the veritcal distance becomes 10 then?
nimble wyvern
no
frigid sedge
14?
opaque fern
yeah
nimble wyvern
yes
frigid sedge
wait i have a few questions,
- why 14
- why didnt we mutiply g(x) with 2?
nimble wyvern
because the distance between 12 and -2 is 14
because we are changing f(x) to g(x)
nimble wyvern
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frigid sedge
.close
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pulsar pine
I am trying to find the shortest distance between two points if there is a triangle in the way, like this desmos geometry example: (the black line is the shortest path in the current setup, but it wont necessarily be if you move the triangle or the points around)
i dont even know where to start here aside from just checking every combination of vectors that make the path (start point)->(1-2 points on the triangle)->(end point)
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I am trying to find the shortest distance between two points if there is a trian...
manic bane
By shortest distance do you mean along the lines?
manic bane
By shortest distance do you mean along the lines?
If I understand you right you might be interested in shortest path algorithms, e.g https://en.wikipedia.org/wiki/Dijkstra's_algorithm
smoky nacelle
idk how to implement algorithms in desmos lol
but if you just present the desmos as an example for a graph
then yes
dijkstra's
a*
etc
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outer pollen
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ionic blaze
quick question is there a number theory theory on this
safe radishBOT
quick question is there a number theory theory on this
ionic blaze
(number theory) theory on this or postulate or whatever those fancy things are
cursive remnant
id suggest just doing casework, honestly
if n is divisible by 3, then the expression is 3 times some cube, so it's not prime for any n divisible by 3, n>3
ionic blaze
id suggest just doing casework, honestly
😔
cursive remnant
similarly, if n^3 is 1 mod 9, then the expression becomes n^3-1/9
which you can show quite easily isn't prime for all but easily computable list of n
i'm sure there's some other tricks you can think of to make it less lengthy
ionic blaze
id suggest just doing casework, honestly
(k+3)^3=k^3+9k^2+27k+27 => 3k^2+9k+9+k^woops nvm
oh yeah nvm that's actually really easy to do wow
🥀
wait
not mod
cursive remnant
its not really lengthy, you only have to consdier mod 3, not mod 9
oh yeah that's way better
myb
yeah then its pretty trivial
ionic blaze
3k, 3k+1, 3k+2
I'm being stupid rn can u expound
brave wolf
I'm being stupid rn can u expound
well, n has to be either 3k, 3k+1 or 3k+2
brave wolf
N? naturals?
ionic blaze
ain't naturals not including 0
brave wolf
depends on context (or rather convention)
if you wanna be clear, you can just write N_0
ionic blaze
we should end separating numbers
ionic blaze
well, n has to be either 3k, 3k+1 or 3k+2
then wut
after cubing I don't like looking at the quotient
oh wait
oh thanks
nvm I'm stupid
brave wolf
,w expand (3k+1)^3/9
flat frigateBOT
brave wolf
should simplify nicely
ionic blaze
yeah so we only have to consider k(3k^2+3k+1) or when it's 2 like k(3k^2+6k+4)
wo there'sreally only two choices
man the things people have to do in timed stuff 🥀
truly a 30s question of all time
.close
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brave wolf
truly a 30s question of all time
30s? Damn this has to take at least 2 mins
ionic blaze
30s? Damn this has to take at least 2 mins
u figured it out in 30s 😭
brave wolf
i didnt do the algebra lol, thats the hardest part (in sense of time)
ionic blaze
.if I was quite frank I'm not sure if it was 15s or 30s
they say "easy round" but it kinda changes from 15s to 30 a lot
ionic blaze
i didnt do the algebra lol, thats the hardest part (in sense of time)
.people can be imaginative I guess 😭
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hoary seal
I need help
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I need help
opaque fern
I need help
the third to last row in A is saying 0 = 2
hoary seal
which matrix?
opaque fern
I said A
hoary seal
what about this ?
outer pollen
why did you put -3/2?
opaque fern
you used the 4 frmo row 1
instaed of the 1 from row 2
remember its important to make a pivot
and stick with it
you effectively undid your previous work
outer pollen
wait. you seem to have identified the right pivot but somehow you're taking 3 and 2 from... where?
outer pollen
if that 3 and 2 is from the i and j, take note that i and j are the row numbers.
opaque fern
i think you plugged in the indices instead of the values lol
opaque fern
if that 3 and 2 is from the i and j, take note that i and j are the **row number...
yeah this lol
hoary seal
you used the 4 frmo row 1
how?
hoary seal
wait. you seem to have identified the right pivot but somehow you're taking 3 an...
i got the values but i mis subbed it?
opaque fern
i got the values but i mis subbed it?
what is the number you want to turn to 0
can you tell us what that is
hoary seal
6
opaque fern
what is the number you are using to turn the 6 into a 0
opaque fern
ye
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hoary seal
ye
also do u know how to find the critical pont but the non differentiable parts
the spike
opaque fern
can u just open a new help channel btw
less clutter
as this one was pertaining to your old question
hoary seal
yeah after this because I already typed the stuff
astral glacier
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glass edge
State the coordinates of D and E
safe radishBOT
State the coordinates of D and E
upbeat swan
!original
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
glass edge
this is the original problem
upbeat swan
did the problem have any text
glass edge
yeah
upbeat swan
...
upbeat swan
ok im assuming D is directly above C?
glass edge
yes
upbeat swan
im pretty sure
so its parallel to the ground
glass edge
so its parallel to the ground
i dont know their slopes so i cant tell for sure, but i would assume so
glass edge
no
upbeat swan
interesting
glass edge
from the diagram, you can see that D is clearly above A
upbeat swan
its called perspectivew
glass edge
that was my thinking
upbeat swan
👍
glass edge
upbeat swan
there we go
glass edge
how did that help tho now
upbeat swan
ok so im assuming that there is a prism which lies flat on the ground
would you agree
glass edge
yeah
glass edge
yea
glass edge
no
upbeat swan
see that's what people call a contradiction
glass edge
D has a height of 5
upbeat swan
yeah and where did you get the 5
glass edge
what
upbeat swan
is this your first 3D problem you're doing?
glass edge
kinda
upbeat swan
ok makes sense
glass edge
so ur telling me that unlike a xy plane
we can't measure the x,y, or z value of a point
upbeat swan
ok imagine watching the prism from the right side
glass edge
using the x,y,and z axis
glass edge
ok
glass edge
okay
upbeat swan
and you're looking at the pyramid
you see the line
BE
which lies flat on the ground
glass edge
uh huh
upbeat swan
and you look up
to the top of the prysm
and see the line at the top where the prism ends
AD
glass edge
oh, i get they have the same height
glass edge
yea
glass edge
thats hard to visualize, damn
upbeat swan
it becomes ver yver yeasy with time
you just need to practice
and imagine yourself
in the plane
glass edge
so E would be (something, 4, 0)
upbeat swan
looking at stuff
glass edge
oh
glass edge
(-7,4,0)
glass edge
confusing
upbeat swan
haha
glass edge
rectangle
upbeat swan
yes
glass edge
rhombus
upbeat swan
good
glass edge
45 right
glass edge
Z and Y make 90 degrees obv cuz theyre perpendicular
glass edge
X and Y are also 90 edgrees?
upbeat swan
the only difference is that you added a third axis
that is perpendicalar to both x and y
glass edge
first, i visualized it like the X axis is a line going through the 2d Z and Y axes
upbeat swan
and goes up
glass edge
it exactly splits it in half
and thats why it was 45 degrees
im still thinking about it in a 2d way ;/
upbeat swan
the ground plane can be visualized exactly like a regular 2D plane
glass edge
yeah
glass edge
90
upbeat swan
OBE
upbeat swan
AOC
upbeat swan
DCB
upbeat swan
DCB
glass edge
90
glass edge
can we do b
glass edge
my teacher told me not to use formulas for calculating surface areas and stuff
upbeat swan
then what should you use
glass edge
idk
i think for the volume its fine, because we did a problem including cylinders and he used 4/3 pir^2
^3
glass edge
i have no idea
upbeat swan
its A_triangle * height
upbeat swan
well we are taking the base to be AOB
glass edge
A_triangle means area of triangle right
upbeat swan
yes
glass edge
i think im not visualizing it in a 3d way
i see the height of triangle and prism as 3
the base of triangle as 4
but i know its not going to be that easy
upbeat swan
just imagine
we take the prism
and put it on its triangle base
so that it stays upright
so it will stay on its base
<@&268886789983436800>
upbeat swan
like imagine
glass edge
this?
whole hill
imagine a giant
FEE-FI-FO-FUM???
upbeat swan
FEE-FI-FO-FUM???
wdym
glass edge
ok
upbeat swan
done?
glass edge
yes
upbeat swan
and now the giant sits up, puts his hands on the DE line
glass edge
its sitting outside the prism
upbeat swan
and pulls it towards him
glass edge
so by the height they mean the distance AD
upbeat swan
well yes
glass edge
multiplied by the height
sqrt(49+9)
oh no
no
nvm
sqrt[(-7-0)^2+(0)^2+(0-3)^2]
sqrt(49+9)
wait what
i was right??
glass edge
rectangle
glass edge
-7
upbeat swan
length cant be negative
glass edge
|-7|=7
glass edge
AD must be 7
upbeat swan
yes
upbeat swan
sqrt[(-7-0)^2+(0)^2+(0-3)^2]
turbid ore
triangular based*
upbeat swan
,w sqrt((-7-0)^2 + (3-0)^2)
flat frigateBOT
glass edge
yeah see its 7.6
not even 7.5
so theres no way they messed up and rounded 7.6 to 7
i think our D coordinates are wrong
glass edge
oh..
upbeat swan
,w sqrt ( (-7-0)^2 + (3-3)^2 )
flat frigateBOT
turbid ore
,w sqrt ( (-7-0)^2 + (3-3)^2 )
umm
upbeat swan
so now the volume is unironically 6x7
yeah
glass edge
why
upbeat swan
wdym why😭
turbid ore
glass edge
why did it have to be 7
upbeat swan
https://tenor.com/view/taylor-series-expansion-trigonometry-sin-67-67-meme-gif-1...
lol
upbeat swan
why did it have to be 7
idk
glass edge
:/
upbeat swan
they predicted the 67 joke
upbeat swan
so what the asnwer
glass edge
what the ai
glass edge
so what the asnwer
5
upbeat swan
good
glass edge
surface area ;-;
turbid ore
can ask anyhting bout 2d
upbeat swan
surface area ;-;
what do you think we shoulld do
upbeat swan
like when the question is only is asked in x axis and y axis
yeah what about it
upbeat swan
and multiply it by 2
ok
glass edge
since there are 2 similar triangles
turbid ore
yeah what about it
i only learnd that
upbeat swan
ok
upbeat swan
i only learnd that
if you have a specific question you go refer to #❓how-to-get-help
turbid ore
we should assume the ABED = AOCD
where's O
glass edge
then use the coordinates to find the heights and lengths of the rectangles, find the area and sum it all up
upbeat swan
yes
glass edge
yes
the thing is tho
how do we write it
cuz my teachers not gonna accept some
working
turbid ore
ohhhh
glass edge
*calculation
turbid ore
now i can see this a total dif way
upbeat swan
just find all the areas of the rectangles
upbeat swan
and add them with 2*area rectangle
glass edge
and add them with 2*area rectangle
BE would be 4 right
glass edge
this question is soo easy
yeah, srry im not as smart as you
glass edge
rectangle
upbeat swan
turbid ore
yeah, srry im not as smart as you
surface area is 96
upbeat swan
and whats the length of oc
upbeat swan
yes
upbeat swan
surface area is 96
turbid ore
https://tenor.com/view/bad-bunny-covering-eyes-covering-face-crying-grammys-gif-...
it is
glass edge
surface area is 96
bro
upbeat swan
surface area is 96
!nosols
safe radishBOT
surface area is 96
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
upbeat swan
please
turbid ore
um
glass edge
this isnt who's going to be a millionaire where you just say the answer, and get it correct. you have to show working.
turbid ore
this isnt who's going to be a millionaire where you just say the answer, and get...
hmm
glass edge
hmm
plus i cant trust u u just used ai to solve this didnt you? chat is really unreliable
upbeat swan
plus i cant trust u u just used ai to solve this didnt you? chat is really unrel...
just focus on the question
turbid ore
plus i cant trust u u just used ai to solve this didnt you? chat is really unrel...
i will send a pic of solution
glass edge
just focus on the question
okay
turbid ore
wait a min
glass edge
AOCD = 21
upbeat swan
yes
glass edge
OBEC = 28
upbeat swan
yes
glass edge
total surface area is 96
upbeat swan
yes
glass edge
units^3
upbeat swan
no
upbeat swan
thats for volume
upbeat swan
um
glass edge
as you can see, im pretty egregious
upbeat swan
just imagine yourself being in the plane
glass edge
;-;
glass edge
so like standing at the y axis
upbeat swan
from behind, from the left etc
upbeat swan
whatever helps you picture the shape
turbid ore
upbeat swan
just imagine
being on a field
with a giant prism in front of you
and how it would look like
walking around
upbeat swan
you're welcome
glass edge
.close
heavy vector
help
heavy vector
please someone tell me at the last step how -x^2 became +x^2
exotic anvil
add x^2 to both sides and subtract 40 x from both sides
outer pollen
alternatively, subtract 400 from both sides, then multiply the equation by -1.
exotic anvil
because usually with polynomials one likes the term of highest degree to have a positive coefficient
its neater
-x^2+40x-400=0 would give you the same answer if you solved it for x
exotic anvil
its neater
Also a lot of factorisation methods are cleaner if your polynomial has a leading coefficient of 1
safe radishBOT
azure harbor
Also a lot of factorisation methods are cleaner if your polynomial has a leading...
lance lance helper arc?
vro mustve had a life changing experience
safe radishBOT
Available help channel!
pearl silo
someone help me for this integral question?
safe radishBOT
someone help me for this integral question?
wild copper
The base of this exponential part looks annoying. I wonder if there is a way to simplify it into one single variable:
$(x^4+1)^5$
flat frigateBOT
Xwtek
summer lark
How do I graph this
safe radishBOT
How do I graph this
summer lark
Find the volume of the solid generated by revolving about the line x = 2 the region bounded by y = x ^ 2, x = 2 and y = 0
viral wren
Where do you want to graph it?
brave wolf
are you trying to graph the solid or just the region?
For finding the volume, it suffices to graph the region
brave wolf
you will find out after you sketch the region
summer lark
Whre will it rotate?
brave wolf
itll rotate around x = 2
but the disks will be like this
sorry for the terrible drawing lol
but the discs will basically lay flat (parallel with x-axis)
summer lark
Ohh okeyy okeyy
brave wolf
you're forgetting the square
brave wolf
yeah, it will be essentially just integral of y
but i think you might be forgetting some constants
and you havent stated the bounds yet
summer lark
The bounds is 4 and 0 right
brave wolf
yep
summer lark
The final answer will be 8piu³
brave wolf
wdym u?
brave wolf
what the hell did they do
this doesnt look correct at all
oh wait
yeah mb, integrating (sqrt(y))^2 is wrong
but their pic is also wrong it seems
sqrt(y) is this distnace
summer lark
It should be (2-√y)² right?
brave wolf
yeah
summer lark
Okeyy okeyy
brave wolf
brave wolf
But can I use the vertical
youd have to use shells