#help-23
1 messages · Page 446 of 1
$x^2+x-6$
geoxcaliber
geoxcaliber
Im just saying for a quick mistake check.
geoxcaliber
so I did x^2 and 3^2 = 9 in the top then -2x^3 in the left
ohh am so stupid
$-2x^5 - 18x^3$
geoxcaliber
Ok I get it better now, thanks a lot. My main confusing point was the fact that x = (x - 0)
so how would I check my expansion is correct in this one?
put 1 into each x?
.
I mean thats not guaranteed to check if its correct
its just checking if its wrong.
this looks incorrect.
if ur doing this
@tawdry salmon Has your question been resolved?
bruh
so does that mean doing x^2 and + 9 is wrong?
Shuri2060
$$(a+b)^2 \neq a^2 + b^2$$
Shuri2060
geoxcaliber
lmao
just look up a video how to multiply out brackets
cus this aint working for you clearly
how is -2 times 3 -9
I think I read the 2 as 3
but it's supposed to be 9 right
(x+3) = 3x
(3x)^2 = 9x^2
??????????????????
im gonna get an algebra book and just start algebra from over lmao
is it wrong
you can't add x and 3?
3x is 3 times x
x+3 is x plus 3
what is the question again? the discussion is super long lol
$-2x^3(x+3)^2$
geoxcaliber
geoxcaliber
so if that doesn't work I turned to PEMDAS, which has parenthesis first so I attempted adding the two
so if neither that or this doesn't work
$$(a+b)^2 = a + b^2$$
geoxcaliber
this equation is wrong
$$(x+3) (x+3)$$
geoxcaliber
blackmamba[they/them]
I don't remember factoring too much but I think the best thing to do right here is to open the brackets
either through calculating (x+3)^2 via the equation I posted
or calculating it via $-2x^3(x+3)(x+3)$
blackmamba[they/them]
I see
well all imma say is I hate algebra :/
that one has nothing to do with this right
Oh I see, nevermind. I had notes on this "square of a binomial" which calculates like you said
blackmamba[they/them]
then open the brackets by multiuplying each element with $-2x^3$
blackmamba[they/them]
probably yes but don't think you're gonna get to that
you'll get a cube but the factor won't look like that
oh ok
is it because a factor is supposed to look like x - 5 and that looks like 3 -/+ 5? (a + b)
it's called zero, x-intercept, solution (of a function)
an intercept is when the lines reach the x or y axis
that;'s when the entire equation equals 0
(for x-intercept)
not the root, that's where the function is undefined
your equation here is (x^3 + 5x^2 -3x + 6) / (x-2)
in other words
to find r... you need to find an x such that f(x) = 0
or (x^3 + 5x^2 -3x + 6) / (x-2) = 0
2 is NOT a root here
2 is undefined
@tawdry salmon Has your question been resolved?
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im solving for tan2x
where sinx is 4/radical 19
is the answer positive or negative
when i plug that expression in the calculator, it says negative
but this is in quadrant 1
so is the answer positive?
this is the formula i used
this is what it says in the calculator
@lean otter Has your question been resolved?
@lean otter Has your question been resolved?
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can someone explain why i am getting the critical point wrong?
it is meant to be -3/2 but i got 0 and -5/3
cant read the q
find the point on the line y=3x+5 that is closest to the origin
ok
by the way
critical point
has a different meaning
so avoid using that
i was confused
no, avoid critical
or just zeroes of the first derivative?
wait what
ok ignore me
i just assumed from your picture we were doing a linear function lmao
didnt actually read
thats okay 🙂
i dont get where all that math comes from
i think it can be done a lot simpler than that?
oh i see,
ur finding the circle which is tangent to it
ahh im not sure, this is from organic chemistry tutor. i am practicing optimisation problems
he used this as an example
it is a common optimisation problem it hink
well alright
i feel like basic trig should get u answer
but i can check your way as well
just gonna try it this way first to check
hyp = 5sqrt10/3
sqrt10 is ratio
1/6-5/3
yh so i get x = -3/2
Then calculus way 🤔
im so confused haha
i am thinking he has made a mistake
thats so weird no one pointed it out
here is the mistake
in the comment section
wait nvm its me who made a mistake
give me a second
oh yeah
that makes sense
thank you :3
way quicker with geometry lol
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you can just use the channel
i just closed it so it doesnt have my name on it anymore
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<@&268886789983436800> (posting in all channels)
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What does it mean by a>1?
That a is greater than 1
Yeah but why does it mention it in the question
It has no use or am I wrong?
<@&286206848099549185>
It’s so that the denominator will never be negative
But why does that matter?
because if it was you'd need to change the direction of the inequality
Oh
So let’s say a<-1
How would we do this equation to solve for x
probably the same way
but when dividing by 3a-2
you flip the inequality
side it would be negative
I believe so
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what exactly is your goal here
I think they wanna factor it
p/q
uhm
why r u saying uhm
use ur words
yes or no question
how do u know when to use p/q
cuz theres also a grouping fcoting method
lmfao calm down chief i'm trying to see if i can factor this by grouping
yes i'm aware of what factoring is lmao
k
i'm not sure you can
when other methods fail
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hi
this is kind of like a one-dimensional bezier curve
you can think of it like having some percent of x added to some percent ofy
that percent will always be between 0 and 100
bezier curve??
isn’t this supposed to be elementary algebra
i’ve been told it is
sorry didn't mean to scare you; some people are familiar, you use them a lot in like paint applications
you can ignore it tho
are you asked to prove this, or are you looking for intuition?
i was always bad at analysis and inequalities lol
hmm maybe rearrange center t (x - y) + y
just thinking out loud
how does that help
i’m investigating concave functions and their equivalent definitions
i suppose that’s not analysis
idk you gotta play with it, again i'm just thinking out loud
<@&286206848099549185> ?
suppose t ∈ (0, 1)
for any x, y ∈ R, if x < y, why is x < tx + (1 - t)y < y true?
Can you see what that middle expression represents?
@meager chasm
yes
congrats on your role
so the rhs can sort of come from this
x < y
x - y < 0
t (x - y) < 0
t (x - y) + y < y
also kinda…?
yea
anyways, I don't think its too hard to show if you tackle one inequality at a time
let’s start with x then?
x < tx + (1 - t)y
x - tx < (1 - t)y
(1 - t)x < (1 - t)y
then same for other side
this is me showing it backwards
you show forwards ofc
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I just don't get q 27 ;-;
,rotate
How do I do it
;-;
i'd prob just factorize it; don't really see another way
like 216 = 6^3 = 2^3 * 3^3
then use exponent rules
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@copper wraith Has your question been resolved?
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Let T be the smallest positive integer which, when divided by 11, 13, 15 leaves remainders in the sets {7, 8, 9}, {1, 2, 3}, {4, 5, 6} respectively.
how a number gives 3 remainder when divided by one number
I think they meant that the remainders are somewhere in sets
And not that all of the elements in each set is a remainder
oh 3 different ones
3 remainders*
hm
maybe
i ll check the solution later
i was trying it on my own first
this is what they meant
whoever is wondering
thanks Shuri2060
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for sinsiduoal functions, when i find the k value and x value on a graph and write the equation, do i still need to factor
Can u be a bit more specific
Like show the exact question
What do u mean by K value
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Ok
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Stuck again on a similar problem as last time 😩
Again I can do the zero vector axiom, but when it comes to showing X + Y is closed on addition or scalar multiplication, I'm stuck
So first line, you will write? @zinc bronze
$Let a,b \in X and c,d \in Y$
hello2248
ehh u can do that
yes that is fine
Let $\boldsymbol{v_1},\boldsymbol{v_2}\in X+Y$.
Then let $\boldsymbol{x_1}, \boldsymbol{x_2}\in X, \boldsymbol{y_1}, \boldsymbol{y_2}\in Y$ such that $\boldsymbol{v_1} = \boldsymbol{x_1} +\boldsymbol{ y_1}$, $\boldsymbol{v_2} = \boldsymbol{x_2} + \boldsymbol{y_2}$.
Shuri2060
Perhaps I would prefer this lettering
Then it is clearer than a, b, c, d?
it doesnt matter in the end, though
Yah makes sense
.
First we are doing addition
Usually to prove a property, you just use the same property (if you have something combined from vector spaces)
$x_1 + x_2 + y_1 + y_2 \in X + Y$ because $x_1 + x_2 \in X$ and $y_1 + y_2 \in Y$
hello2248
So $v_1 + v_2 \in X+Y$
yes, thats the way
hello2248
yes good
Ok, scalar multiplication
Do you know how to start the proof?
By the way, it's been a long time for me. We just need to prove closure for both and 0 is in it? I forgot haha
Yep, just those 3
Let $v \in X + Y$ such that $v = x + y$ where $x \in X$ and $y \in Y$ and $λ \in (howToDoInLatex?)$
$λx \in X$ and $λy \in Y$
thus $λx + λy \in X + Y$ hence $λv \in X + Y$
X + Y is closed on scalar multiplication
hello2248
idk how to use latex apparently
Shuri2060
Sure, your proof is fine
Aha alrighty thanks again!
Usually, since the concepts are so simple
I write out every step
v = x + y
kx, ky in V
you had those
but then i write
kx + ky = k(x + y) = kv in V
Ok sure yeah, makes sense to be detailed
So here you are technically using distributative property of vector spaces for that factorisation
Mhm thanks for the help and advice!
👌
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$e^(iy)*sin(x)/(cos(x)-1)=O$
does this stay true if i swap around the fraction?
Use curly brackets instead of parentheses for exponents
Sparky
$e^{iy}\cdot\frac{\sin(x)}{\cos(x)-1}=O$
Luca
thx 😄
Hold up, was that an O, like the letter or zero?
Cause latex says it's the letter
$e^9×9=
You mean $\frac{\cos(x)-1}{\sin(x)}$?
Luca
$e^{-iy}\cdot\frac{\cos(x)-1}{\sin(x)}=O$
Sparky
is this also true?
what you wanna say is $e^{iy}\cdot\frac{\sin(x)}{\cos(x)-1}=0=e^{-iy}\cdot\frac{\cos(x)-1}{\sin(x)}$
Luca
yeah exactly
you mean if the same x'es satisfy this equation?
what?
i am confused by the question
$e^{iy}\cdot\frac{\sin(x)}{\cos(x)-1}=0\not =e^{-iy}\cdot\frac{\cos(x)-1}{\sin(x)}$
Luca
i have a linear system of equations and one equation is what i posted first. And i want to transform it so that i just turn around my fraction. Am i allowed to do this?
because to turn the equation around $\frac{\cos(x)-1}{\sin(x)} = \frac{\sin(x)}{\cos(x)-1}$ would have to hold
Luca
so no, you can't turn around the fraction
or do you mean this
$e^{iy}\cdot\frac{\sin(x)}{\cos(x)-1}=0\qquad\bigg|()^{-1}\\ \frac{1}{e^{iy}}\cdot\frac{\cos(x)-1}{\sin(x)}=0$
Luca
yes thats what i want to do
that you can do
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Hi! I don’t get q 11
@lean otter how familiar are you with exponent laws?
Idk mb 50%?
kind of weird that you'd give a percentage like that.
but ok
can you say which exponent laws you are familiar with enough to remember them off the top of your head?
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I want to find the zeros of $f(x)=x^4+4$. Wolfram Alpha tells me its $\pm(1+i)$ and $\pm(1-i)$. But when i use the quadratic formula i get $\pm\sqrt{2i}$ and $\pm i \sqrt{2i}$
Kurama
what am i doing wrong
can i ask a dumb question
how are you using the quadratic formula
just substitution?
yes, just substituting x^2
without the root both answers make sense
you have to substitute it back. now you have the solution for x^2, and to get it for x^4 you have to take the root again
but i might be doing something worng
idk if you start from like 2i and then just solve x^2=2i
youll get out the two sensible solutions
same with -2i
these correspond well with the original solution set you got
like 2i=(i+i+1-1)=(1+i+i-1)=(1+i)(1+i)=(1+i)^2
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I know I'm supposed to explain what I've tried and how far I've gotten, but I have basically no clue how to even approach these. A push in the right direction at minimum or a good explanation would be great.
@fleet saddle Has your question been resolved?
Is that a known rule or just intuitively finding the inverse?
Also for the middle one do I just assume f(x)=x-5?
Never mind, that doesn't work.
@fleet saddle Has your question been resolved?
@fleet saddle Has your question been resolved?
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hi
look at this question
it is an right riemann sum approximation for a definite integral from 1 to 4
the function we are integrating is rf(r)
let's say we know r is increasing
and f(r) is also increasing
is that enough reason to say that their product (rf(r)) is also increasing?
not necessarily
say f(r) = r
r f(r) = r^2
r, f(r) both increasing
r^2 not increasing in (-inf, 0)
is (rf(r))' > 0 ?
oh yeah I guess
wait but
well
yeah
ok what about this
(rf(r))' = f(r) + f(r)'r
since f(r) is increasing, f(r)' is positive
hence, f(r)'r is also increasing
do you know exactly what f(r) is or do you only know that f(r) is increasing
ah okay
so its derivative is positive
can you limit the range of r?
is f(r) > 0 hopefully when r in [1, 4]
hence it's also positive and increasing
yes
wait butt
since they're both positive
over the interval
r*f(r) is always positive
and
r*f(r) is increasing
ah nvm
yeah the other way is much better
yeah trhanks
brother
np
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I want to find a cubic function with a y-intercept at 12,000, a minimum at (5, 6000), and a maximum at (10, 10000). I've tried ax^3 + bx^2 + cx + d and its derivative, but I can't get all of the equations into one system.
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Ok, this is might be a very silly question but this isn't working for me. This is how the question goes, "If the unit price for almonds is $0.13 per oz, how much does a 3 pound tub cost?". Isn't the answer suppose to be $0.39? Because that what I got and the answer to the problem is $6.24. Is there a step that I am missing because I'm just using cross multiplication. Thanks.
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How do you get the domain?
Domain is where the function can be defined.
you can start from the fact that a fraction is not defined if the denominator is zero
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i am trying to calculate this from x=0 to x= 10 with 5 rectangles only
the solution is above im trying to figure this out
what i do know so far
but im a little stumped as to where to go from here
do i have to plug x into this?
you just find the area of each rectangle
essentially yes
but it looks scarier than it is
and add them up
those function values are the heights of each rectangle
right this makes sense let me try
command+shift+4 exists
what does this do?
screen capture lol
takes a screenshot....
drag a region for the screenshot
@next gulch Has your question been resolved?
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$\int x^3e^x^2dx$
look man im new to this
jan Niku
ur good
yeah but why the dd?
it shouldnt be coded that way
its not important
wow \dd, fancy
you can juste use dx
do i need to type the \ before the dx?
jan Niku
from my book? or what do u mean?
try substituting $t = x^2$
xdk1235
i did
reading the integral as $\int x^3 e^{x^2} dx = \int \left(x^2 e^{x^2} \cdot x \right) dx$ might help
xdk1235
jan Niku
thats where im stuck, do i go ibp now?
yes
but honestly i think ibp for that is kinda silly (this is how textbooks tell you to do)
$(x e^x)' = x e^x + e^x$ so you can kinda guess the answer from this
xdk1235
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thanks, didnt know how to close b4
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$NN(x) = \sigma ( w^{(3)} \sigma (w^{(2)} \sigma ( w^{(1)} x + b^{(1)} ) + b^{(2)}) + b^{(3)} )$
$\pdv{NN}{x} = ?$
is this WA thing right or did I screw that up
THEBIGTHREE
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Hello.
How can I find the number of perfect squares between two number?
find the lowest and highest perfect square possible
Okay and then?
find the number of numbers between them?
uh
so what?
The values I am getting are 2559999 and 6250001
...so?
Then how to solve?
- find the highest possible a^2 in the interval
- find the lowest possible b^2 in the interval
- find the number of numbers between a and b inclusive
Getting 3690002
do you even know how the method works
it's literally the easiest thing in the world
Thank you very much.
Hello can I ask for help please?
.close
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Alright so about these I just don't know how to start and go from there so if we can go through them at least somewhat completely so I can grab the fundamentals that would be great!
@zinc hearth Has your question been resolved?
<@&286206848099549185>
@zinc hearth Has your question been resolved?
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.
arc length = central angle x radius
apply this u get ur answer
dude i already told u
arc length = central angle x radius
apply this u get ur answer
arc length = central angle x radius
that they must give
or assume it as r
55
take it as r
apply the definition / relation between the central angle and the measure of the respective arc
(note that you aren't being asked for arc length)
@lean otter Has your question been resolved?
@lean otter arc length formula is (a/360) ( 2 pi r )
apply the definition / relation between the central angle and the measure of the respective arc
(note that you aren't being asked for arc length)
where does it say that
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A recursion equation is determined by:
[pic]
a) Show that the equation can be written in the form y_n + 1 = a · y_n
b) write down all the solutions to the equation
c) determine the solution to the equation that satisfies that y0 = 6
@fervent igloo Has your question been resolved?
are you able to isolate $y_{n+1}$ from the equatoin $9y_{n+1} - 3y_n = 0$?
Ann
like if im allowed to?
"able" and "allowed" are two different things
well I can yes
so do it
Isolate y in:
9y - 3x = 0
then divide with 9 on both sides?
Now that you have that, you can see a clearer pattern. What function gets multiplied by 1/3 every increase in n?
True lol. I mean, polynomial? Trig? Exponential? Logarithmic?
Linear would be adding something every n
Exponential was good, where something gets multiplied every n
Namely, (1/3)ⁿ works
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How would we find the range
Can anyone help pls
@lean otter Has your question been resolved?
f(x) is decreasing for all x
so maximum value will be at x = 5
and minimum will be the asymptote at x = infinity
range will be b/w them
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I need help for an equation : (-10)-(11,3*x)+(2,67*x^2)=y and i need X in function of Y
Could anyone help with this please ?
use the quadratic formula
move y to the x side and then use the quadratic formula
assuming that (-10 - y) = c
yeah these are decimal points lol
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.reopen
✅
except how am i supposed to find the delta
how am i supposed to know it's positive
@zinc crown :/
also Y never goes under 0
i mean for the quadratic formula
,w graph 2.67x^2 - 11.3x -10 = y
Yottachad
yeah ik that
well y isn't defined for x values < ~ -23
so you don't have to worry about the square root because it would simply be not in the domain of x(y)
yeah
gonna try that
see how the function isn't defined for some y values (that is, it doesn't drop below a certain point)?
so we could simply say that our x of y function doesn't have those y values in its domain
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How do I find the resultant force on the right hand side
<@&286206848099549185>
Which question?
Well both but if you explain one of them I’ll know how to di the other
What's the question asking for?
Magnitude and direction of the resultant force
That force that is straight down, find the x and y components of that force
With respect to the box
Then sum up the x forces and the y forces, find the magnitude, then angle
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I’m trying to find the equation used to solve for this sequence but it’s been years since I solved for something like this and even something as simple as this eludes me.
Here’s what I know: the sequence decreases by a set value (at first this value seems to be 10%) then +40 is added and the number decreases by a set value again.
What I’ve tried: I solved for the percent each set goes down by then when I got to the end of the set I calculated the amount it decreased by 707 and divided it by the original number thinking it’s supposed to tell me something I’m not sure what but that did not work. It’s possible that +40 being added to the number chain is being ignored when it decreases by a set value but wouldn’t that have a bigger impact on the larger number and the effect would decrease as the numbers got smaller idk even this simple stuff makes the gears in my head screech to a grinding halt
@rancid solstice Has your question been resolved?
<@&286206848099549185>
@rancid solstice Has your question been resolved?
@rancid solstice Has your question been resolved?
@rancid solstice I don't know what you're asking. Can you rephrase your question with only the minimal details
@plucky elk point A is 2583 and point B is 0 how did I get from A to B
The sequence is written on that paper but it goes
2583
2325
+40 2365
2106
+40 2146
1860
+40 1900
1502
+40 1542
835
+40 875
0
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2583
2325
+40 2365
2106
+40 2146
1860
+40 1900
1502
+40 1542
835
+40 875
0
Of this sequence how do I find what it is decreasing by
idk what those numbers mean, you're just adding 40
So the start is 2583 then it decreases to 2325
Then 40 is added and it decreases to 2106
ok it seems to be decreasing by different amounts, so you'd need more context to know what's happening
What context do I need?
The meaning of the numbers. If this is a hw question, post the whole thing
@rancid solstice give us the exact question
It’s not an exact question nor is it any sort of homework. I could post a video that might give more context but I’m not sure it will help with the math
Just type the context where the numbers come from
No one's gonna watch a video lol
It’s 15 seconds long
Alright let me put it like this you have 2583 health after one second it drops to 2325 then you gain 40 back leaving you with 2365 then another second passes and your health decreases to 2106 and gain 40 back
That is all the context I can give in words because that is all the information I have
Yes
I remember there is pre calc math or algebra II math that’s supposed to allow you to work out equations by graphing them and running the numbers thru a specific method but I can’t remember how
@lean otter is this not what the channels are supposed to be used for
I’m sorry I’m not interested in this
Lol
@lean otter can you tell me the name of math that would be used to solve for this so I can look it up
sus
Sus you
Oh
It is basically this
Nvm it’s not an AP either
It’s some weird shit
I thought it was a sequence with an AP and +40 stitched together
But nope
No I’m not sure it would be an arithmetic process I want to say the equation y=abX is useful for modeling the relationship and somehow you can do some number wizardry to magic the numbers for the equation up
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(10^(10^76)*((10^(10^100))^(10^185))
How can I express this as a single power tower?
@little mountain Has your question been resolved?
@little mountain can you write your thing out on paper? the parentheses look a little cluttered
actually your parentheses are unbalanced 
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Can someone solve this puzzle. I am doing this from past 2 days. Anyone knows the answer?
U can only move top cube it means u are not allowed to move two cubes simultaneously or cubes below the top cube. Just top one on the stack you can move. find number of moves
wdym by moving?
@undone fiber Has your question been resolved?
It's similar to tower of Hanoi problem
Moving= taking the top cube and placing it on any of the stacks
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<@&286206848099549185> I need help doing this problem
Use the Quadratic formula
@ruby cloak Has your question been resolved?
@ruby cloak u still need help?
so do u know what the quadratic formula is?
i can teach you but i haven't used it in like... 2+ years so i might be a bit rusty
It’s fine
and in ur quadratic a is the number before x^2, b is the number before x, and c is the number on it's own
this is the easiest method
it isn't possible to do another method with ur quadratic i don't think
Can you write my equation into that formula
at least not with ease
well u need a calculator to do it
but first tell me what a b and c are
like i said, a is before x^2, b is before x and c is the number on it's own
just a sec, i need 2 check something
K
ok i'm back
there is another method mb
like i said i'm rusty
ok so this is gonna be a bit hard to explain but i'll try my best





