help-17

[languid ridge]

Okayy

Can you give me a question?

[split wind]

another one?

do you want harder or similar?

[languid ridge]

Harderrr

very hardd

[split wind]

ok

[languid ridge]

Hehehehe

[split wind]

lol

I'll make it more steps

[languid ridge]

Imma just use my instincts in solving

[split wind]

If x varies inversely with y+1, and y varies inversely with z+1. Given x=1 when y=1, and y=1 when z=1, find x when z=0

it's just doubling the situations

[split wind]

and for ease of checking by yourself, I'll type the answer here: ||x=2/3||
feel free to click to reveal it, hope everything's fine with youe studies!

i gtg, seeya!

[languid ridge]

Im sorry for taking long, my internet go off

[languid ridge]

Okayy thx for the helppp

[languid ridge]

Your better than my teacher lol

.close

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[silk wind]

A body suspended at the point Q = (0, −2, −1) [m] weighs
with force F = (0, 0, −900)T
[N] on the three bear lines QP1,2,3, there
the support points have coordinates (ON coordinate system in [m]):
P1 = (1, −3, 2), P2 = (0, −1, 2) and P3 = (−1, −2, 2).
In the three ropes, tension forces f1,2,3 arise, directed along respectively
line. Determine these forces and state their magnitude in [N]. Finally,
which of the ropes is most loaded?

[silk wind]

does anybody know how to solve this?

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@silk wind Has your question been resolved?

[silk wind]

<@&286206848099549185>

[jolly lava]

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[jolly lava]

I think you can solve by using the fact that Net force on weight with eact x,y and z axis are all 0

3 variables(forces) and 3 equations, so should probably able to get the size of three tensions

[silk wind]

okay so can i do an equation and use gauss formula?

[jolly lava]

what is gauss formula?

[silk wind]

its just a way to solve a matrix

[jolly lava]

gauss elimination?

[silk wind]

oh yes sorry i meant that

[jolly lava]

you can, I think

[silk wind]

okay but is the first line in the matrix 1 0 -1 or 1 -3 2?

[jolly lava]

wdym you have to set for x,y,z axis for each tension

[silk wind]

cant i just make a matrix instantly?

[jolly lava]

x component of each tension sums up tk 0 and giss on

[jolly lava]

i dont think so? not sure

[silk wind]

yes is that not 1 0 -1 = 0

and so on for the reamaning

[jolly lava]

but what about y component?

[silk wind]

yes -3 -1 -2 = 0

and z is 2 2 2 = 0

[jolly lava]

Not sure if it will work

btw you should consider gravitu for z

[silk wind]

okay what would you have done?

[jolly lava]

this

[silk wind]

okay but i dont really know what that means

[jolly lava]

there should be each x,y and z component for each tension right?

as they are 3d forces

[silk wind]

okay

so do i do three equations?

[jolly lava]

That's what I'd do

[silk wind]

okay so 1 + 0 -1 = 0?

or should they have x, y and z?

[jolly lava]

1,0,-1 things are for coordinates

not for actual forces isnt it?

[silk wind]

oh okay

should i use q the or f?

[jolly lava]

what is q&f?

[silk wind]

q= (0, -2, -1) and F = (0,0, -900)

[jolly lava]

you should set size of tensions to some kind of variable

[silk wind]

Okay x?

[jolly lava]

what would be the x component for that force?

[silk wind]

well i dont really know

1 0 and -1?

[jolly lava]

for ex P1, the force is aligned on P1Q string

you might need to do some trig

[silk wind]

okay i think i will do this one another day could you help me with anotherone instead

Given the two vectors from R^4
: u1 = (1, 3, 2, 1)^T and u2 = (2, 7, 7, 1)^T
. Find, if possible, two linearly independent vectors v1,2 ∈ R^4, such that v1 is perpendicular to both u1 and u2 and likewise v2 ⊥ u1,2.

[jolly lava]

simple way might be setiting $v=(a,b,c,d)^T$ and solve equation for $v\cdot u1=0$ and $v\cdot u2=0$

[twin meteor]

Dri111

[silk wind]

oh okay

[jolly lava]

or now thinking using null(A) is orthogonal to row(A) would be one way

[silk wind]

Yes okay

[vocal sleet]

@silk wind Has your question been resolved?

[silk wind]

so did you mean put (a,b,c,d)*(1,3,2,1)?

and then do (1a, 3b, 2c, 1d)?

[silk wind]

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[kind ruin]

Can anyone help me with this matrix proof?

[kind ruin]

I'm not really sure how I start

[gaunt sparrow]

Compute the matrix product and then use the product to sum identities for sin/coa

[kind ruin]

I'm sorry, could you explain a bit more?

[gaunt sparrow]

Are you able to compute the product of the matrices?

[kind ruin]

Yep should be able to

Is A(beta) actually just replacing alpha with betas

?

[gaunt sparrow]

Yes

[kind ruin]

ok ill send a picture when im done with the product

@gaunt sparrow sorry for being so slow had to do something rq before this

[gaunt sparrow]

Ok, now you can use this

[kind ruin]

Yep, thought I recognized it lol 😉

Alright lemme check I'll send another pic when im done

@gaunt sparrow for the one in row 1 column 2, is it just -sin(a+b)?

oh yeah nvm

makes sense

ok i got the correct solution, thanks! @gaunt sparrow

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[lament arch]

what happened from step one to step two?

Where did the minus one go?

[sage dew]

they just multiplied both numerator and denominator by x+1

for the "1"

they did this so that you can combine that term and the first term because originally they didn't have a common denominator

[lament arch]

I see

And why is it ok to multiply by 1/x

[sage dew]

that comes from the original problem

instead of writing it as {some fraction divided by x} they wrote it as *1/x

[lament arch]

damn ok

They use a lot of techniques here

Is there a lot of other ways one can solve this

[sage dew]

$\frac{\frac{1-x-1}{x+1}}{x}=\frac{1-x-1}{x+1}\cdot \frac{1}{x}$

[twin meteor]

Triaxyz

[lament arch]

Would you have thought to solve it this way

[sage dew]

this is like the very first thing I came up with so

[lament arch]

so you would've multipled 1 with x + 1/x+1 to get common denominator

[sage dew]

you just have to develop proficiency in algebraic manipulation; especially*** for limits

[sage dew]

yes

[lament arch]

U really need a good eye to know what to do

[sage dew]

and apart from just numerically solving it, I believe that's the simplest way to solve it

[lament arch]

thanks

do they divide by x to cancel?

the left fractin

but then you'd have 1/x at the denominator

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[ebon current]

Can we use L'hopital rule on undefined forms? like infinity/0

[hidden kelp]

No, but you can sometimes play around with your expression to get an indeterminate form

[urban edge]

you can only use it on inf/inf and 0/0, you can usually change the other indeterminate forms into one of those

[ebon current]

Thank you.

close

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[vast shale]

Infinity/zero is going to be plus or minus infinity, if it is anything at all. You just need to work out whether it is the same limit from both directions. L'Hopital doesn't come into it even

[heavy yoke]

infinity/0 and 0/infinity are not indeterminate, yeah

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[sudden hare]

yoo

[sudden hare]

I need help

[twin pumice]

just ask your question

[sudden hare]

I need help with those

I started functions 2 days ago

Today we did review

And I forgot everything I learned

Since it's been over a year now

[twin pumice]

what help do you need, what do you not understand

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[young hollow]

Hello I'm trying to figure out how to do an equation

[young hollow]

I tried multiple times and I keep getting -1 and 0

But 0 isn't a solution only -1 is

[hushed pewter]

!show

[vocal sleet]

Show your work, and if possible, explain where you are stuck.

[young hollow]

Sorry for my messy handwriting

I keep getting 0 and -1 but if you put 0 at the start it's not correct

[sudden hare]

The question

Idk how to do it

[young hollow]

Uhh your thing was closed

[young hollow]

<@&286206848099549185>

[raven current]

the degree is the highest power value in variables
terms is how many variables there are.

[sudden hare]

Oh ok

Ty

[vocal sleet]

@young hollow Has your question been resolved?

[copper axle]

careful $\Big((x+1)^\frac{1}{3} + (3x+1)^\frac{1}{3}\Big)^3\neq (x+1)+(3x+1)$

[twin meteor]

nico

[young hollow]

Why's everyone using my channel

[copper axle]

?

what do you mean?

[young hollow]

Everyone's using my channel for random shit and I still didn't get any help

[copper axle]

that's me helping you

[young hollow]

What

Oh

Yeah I know that

I never wrote that that's is the case

I wrote (x+y)^3=x^3+y^3+3xy(x+y)

Welp looks like I'm fucked

[copper axle]

i'm here right now
$((x+1)^\frac{1}{3})^3 + ((3x+1)^\frac{1}{3}) ^3 + 3 ((x+1)^\frac{1}{3})^2*((3x+1)^\frac{1}{3}) + 3*((x+1)^\frac{1}{3})((3x+1)^\frac{1}{3})^2\
(x+1+3x+1)+3(x+1)^\frac{2}{3}(3x+1)^\frac{1}{3} + 3(x+1)^\frac{1}{3}(3x+1)^\frac{2}{3}\
(4x+2)+3((x+1)^2)^\frac{1}{3}(3x+1)^\frac{1}{3}+ 3((x+1)^2)^\frac{1}{3}((3x+1)^2)^\frac{1}{3}\
(4x+2)+3((x+1)^2 * (3x+1)) +3*((x+1) * (3x+1)^2)\$

[twin meteor]

nico

[copper axle]

update $(4x+2)+3*((x^2+2x+1)(3x+1))+3((x+1)(9x^2+6x+1))\
(4x+2)+3(3x^3+7x2+5x+1)+3*(9x^3+15x^2+7x+1)\
(4x+2)+(9x^3+21x^2+15x+3) + (27x^3+45x^2+21x+3)\
36x^3+66x^2+40x+8\$

[twin meteor]

nico

[copper axle]

$36x^3+66x^2+40x+8=x-1\
36x^3+66x^2+39x+9=0\
36x^3+66x^2+39x=-9\$

[twin meteor]

nico

[copper axle]

alright, so in conclusion by solving 36 x^3 + 66 x^2 + 39 x = -9 we get only x = -1 without the x=0

Marcod, are you still here ?

@young hollow ?

[young hollow]

Yes let me check what you sent

Omg thank you so much this is a huge help

[copper axle]

you're welcome

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[gray veldt]

need a tip on how to solve this

[gray veldt]

sorry for writing so crookedly

lol

isn't quite right I think

oh maybe it is right

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[winter ibex]

heres the questions im not sure on how to do. I missed some class and cant find the teachers video lecture on this topic.

[wraith python]

Just post screen caps.

[flat whale]

!ss

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@winter ibex Has your question been resolved?

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@winter ibex Has your question been resolved?

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@winter ibex Has your question been resolved?

[winter ibex]

<@&286206848099549185>

[quasi rover]

This limit definition is just the actual way to differentiate

So I assume it’s just asking you to differentiate it

This should probably be taught in your first calculus lesson

[vast shale]

Could also use schro

But thats harder

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[timid vessel]

can anyone help me with the chain rule of diferentiation?

[timid vessel]

I have trouble with recognising it

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[prisma kernel]

what help do you need

[timid vessel]

leave it, I got it @prisma kernel

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[gloomy ginkgo]

Hello, I’m currently working on a problem involving mathematical induction, specifically question 3. I’ve managed to prove the base case, which is either n=1 or n=0, depending on the problem. I’ve also assumed that the statement is true for an arbitrary integer n=k.

However, I’m having trouble with the next step, which is proving that the statement is true for n=k+1. I think this involves substituting a part of the equation from the second step into the third step, but I’m not entirely sure. Could you clarify this for me? I apologize if my explanation isn’t clear.

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[gloomy ginkgo]

<@&286206848099549185>

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[lethal aurora]

I just started a unit of l'hopitals rule and can't get my head around this problem, after taking the derivative 3 times I feel like there's nothing else to do. Any guidance would help.

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[rose shard]

I feel like I have done this proof correctly because I do arrive at f_n+3-1

But first, I show that the base case holds and then after I assume that formula for n holds and I then prove that it holds for and n+1 as well

[lethal aurora]

<@&286206848099549185>

[worthy citrus]

Yeah looks good

[rose shard]

Awesome, thaaank you!💪❤️

[flat whale]

no u look good

😉

[rose shard]

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[worthy citrus]

Buy me dinner first

[flat whale]

Oreo cookies best I can do

[vast shale]

🫵🤨📸

mathematical rizz

[tropic juniper]

You don't need l'hopital's rule I don't even know what that is 😂

hint: write the whole fraction under the same square root

@lethal aurora

[lethal aurora]

you've got to be joshing me rn, thanks nonetheless

[tropic juniper]

lol what do you mean?

[lethal aurora]

i've been watching videos on l'hopitlas rule for the past 2 hours trying to figure this out 😢

[tropic juniper]

Ohh that sucks

[lethal aurora]

my own fault, that was kinda goofy of me

[tropic juniper]

I guess you'll need it for trickier limits though

[lethal aurora]

yeah hopefully, thanks anyways tho

[tropic juniper]

No problem!

Wow did you take the derivative 3 times?

gawd dayum

Can you actually do something with the 3rd derivative?

[lethal aurora]

nope it was a waste of time ngl

[tropic juniper]

Sad but did you solve it now at least?

[lethal aurora]

yeah i got it, thanks

[tropic juniper]

Ok good!

[lethal aurora]

unfortunately i have an exam tmrw so I will likely be on here regularly for the next 24 hours 👍

[tropic juniper]

Lol

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[tropic juniper]

Wow l'hopital's rule is cool

[tropic juniper]

Broski I didn't claim the channel that wasn't a question

[lethal aurora]

lmao

[true grail]

just do .close

[lethal aurora]

you right

.close

oh wait not my q

[grizzled halo]

.close 🗿

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[red bone]

someone has the idea how to solve this?

[red bone]

We were asked to find at least one infinite set that satisfies this linear equations

is my way correct

[pale perch]

create an augmented matrix

[misty spear]

what is exactly "your way"

[red bone]

Took some solution for Ax=0, then found out some private solution for above equation which is (1,3,0) and added it to the solutions i found

[red bone]

ax1 + bx2 + (3a-b)x3=0
so i tried getting a general solution, by playing with the 3rd variablbe, and got (-3t,t,t) for all t in R

again we were asked to find at least one infinite set solutions

not all of them

[red bone]

it's not efficient for this exercis

is my way correct? how'd you solve this

bump

[tropic juniper]

this guy is awesome @lethal aurora https://www.youtube.com/watch?v=Gh48aOvWcxw

[lethal aurora]

Yeah I watched that one and the advanced version, love the organic chemistry tutor ❤️

[tropic juniper]

He's great

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[fair vault]

Suppose vector BC = AD. If I want to find the opposite vector of AD, that would be -BC correct?

[fair vault]

Or am I tripping and the book is right when it says -CB? Isn't -CB just BC?

[hushed pewter]

!original

[vocal sleet]

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.

[hushed pewter]

BA=-AB for any vector

[fair vault]

I made a correction. BC = AD. The opposite vector of AD = -BC?

[hushed pewter]

Yes

[raven current]

yes

[raven current]

and yes

[lethal rock]

Obviously

[fair vault]

The book is stupid wtf

[raven current]

whats the book saying

[hushed pewter]

Assuming I understand the small amount of context you are giving me

[fair vault]

Don't obviously me bru, book is saying it's -CB

[fair vault]

@raven current

[raven current]

the opposite must include a minus

so it cant be bc

thats not how vectors work

[hushed pewter]

Could you show us what the book is saying?

[raven current]

wrong ping

[hushed pewter]

Oops

[fair vault]

From this image, BC = AD, they are equal vectors

Then, I must find a pair of opposite vectors

Which is -BC = AD

[lethal rock]

-bc will be cb and yes cb and ad are opposite

[fair vault]

.close

[vocal sleet]

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@vast shale Has your question been resolved?

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

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[vocal sleet]

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[worthy anchor]

I need help with this question, I got the answer to part A (I think it's 37.5%? Correct me if I'm wrong)
I need help with part B

[worthy anchor]

The 25th percentile is 14.25%

I just need help finding which value that corresponds to

Btw the numbers in least to greatest order is 9, 12, 15, 27, 33, 45, 63, 72

...... I'm stupid lol the one corresponding is 15

Anyways did I do part a right? 💀

[vocal sleet]

@worthy anchor Has your question been resolved?

[vocal sleet]

@worthy anchor Has your question been resolved?

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[inland flower]

does this seem right so far

[fallen wave]

im assuming f(x) = 2x^2

[inland flower]

yes

[fallen wave]

the 2 shouldnt be in the parentheses at the start

it should be 2(x+h)^2

[inland flower]

oh

[fallen wave]

imagine ur replacing the x in 2x^2 with (x+h)

you dont start magically squaring the 2

[cunning saddle]

(-2x)^2 = 4x^2

[inland flower]

huh

[cunning saddle]

my bad u rigt

[inland flower]

@fallen wave idk if pinging is ok sorry if it isnt but is this looking right now

oh wait

no

i messed up

factoring hold up

mb😬

[fallen wave]

Nah

the answer should be 4x

[inland flower]

i think it was supposed to be 2h(2x+h)/h

i just put h

[fallen wave]

yeah ur right

[inland flower]

.close

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[onyx spade]

im not siure what this meawns

[onyx spade]

and how im suppose to do this

[dusky willow]

do you know what even and odd functions are?

[onyx spade]

yes

[dusky willow]

well

kinda visualizing the graph of these functions can help in this situation

if lim f(x) x->inf = -inf

when f(x) is an even function

where do you think lim f(x) x-> -inf would go?

[onyx spade]

pos infinity?

[dusky willow]

no

here

wait

this is a decent visualization for the first problem

its an even function

as the x values go towards infinity, the y values go towards negative infinity

similarly, as the x values go towards infinity, the y values also go towards negative infinity

@onyx spade do you understand this?

[onyx spade]

yes

[dusky willow]

try #63

lmk what you get

[onyx spade]

neg inifinity?

[dusky willow]

uh no

notice how it states

f is an odd function

use this to visualize

[vocal sleet]

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[vocal sleet]

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[vast shale]

how do i solve this without a calculator?

ik how to find sin but idk how to find sin using the trig identity

how do i do that?

without a calculator

this is how far i got

idk what to do next

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

idk how do i solve this without a calc?

[lone linden]

a bit of an abuse of notation here, also you can't just "divide out" the square root

[lone linden]

note that ||sec = 1/cos||, and ||the denominator of a fraction cannot be 0 if you want it to be defined||

[vast shale]

thank you

do u know the other 2 questions also

[lone linden]

I only see one other question

but do yk abt reference angles

[vast shale]

yeah

this

[lone linden]

oh I answered that already

[vast shale]

and this

without calc tho

[lone linden]

do yk how to find exact trig values w/ reference angles

[vast shale]

yeah i think so

but im scared if i do that the teacher will put off points

since the question says do it with the trig function

do u know how to solve cos7pi/6 without calc?

[lone linden]

so does she want you to use expansion formulae?

[vast shale]

i have no idea

i didnt go to class and this is the practice exam and i have the exam tomorrow

its trigonometry class before calculus

[lone linden]

do you have any examples of this procedure you're referring to

[vast shale]

which

[lone linden]

...

[vast shale]

this is in our text book

i just found it

[lone linden]

did you mean that for this

because they aren't rlly related

[vast shale]

no this is also a question

it says solve that without calc

[lone linden]

yk what

one at a time

fixing up your algebra

what did you get

[vast shale]

i will try now

[vast shale]

idk what i did wrong

i was suppose to 1 minus not 1 +

[lone linden]

yeah the squares of negative numbers are still positive

in this case, $$(-12/13)(-12/13)=\frac{144}{169}$$ b/c a negative number times a negative number is a positive number

[twin meteor]

Civil Service Pigeon

[vast shale]

oh

wow thank u so much

since cos is negative and tan is positive

its quad 3

making this -5/13 as the answer for sin

thank u for helping me on this

[lone linden]

k I gotta dip

but for this one, it's just using your reference angles to find trig values

look it up if you don't know it

this one I gave a cursory overview of already

note that ||sec = 1/cos||, and ||the denominator of a fraction cannot be 0 if you want it to be defined||

[vast shale]

cos = x/r

is that what u mean

oh no okay thank u

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

.close

[vocal sleet]

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[vocal sleet]

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[sinful lion]

Does the direction of the standard deviation affect the probability of occurrence of the event? Below the mean; above the mean

[flat whale]

Wot

standard deviation is a number

Numbers don't have directions

[sinful lion]

The normal bell curve in the empirical rule; I am determining the sex by the humeral head through the measurement of standard deviations, so if my mean is below the expected mean of a male or female

does the direction of the deviation matter in the probability of the determination

does the direction of the sd relate the probability of the event

[somber flame]

direction is not the right word but here but i might know what you mean

[sinful lion]

please explain

[somber flame]

i don’t really know anymore after what you just said lol but something about a normal distribution being symmetric around the mean

[vocal sleet]

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[proper river]

i don't understand what this question means

[proper river]

do they just add another equation on the graph?

the answer is zero solutions

[vocal sleet]

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[stone birch]

Hi ya'll, mostly just trying to check my answers because I'm new to set notation and not 100% positive that I've done this right but I have:

Suppose A = {0,2,4,6,8], B = {1,3,5,7} and C = {2,4,8}

and I have to find

A∪B - This is just everything in both sets I think?
A∩B - Empty set cause they have no cross over
A - B - They don't have any crossover so this is just the set of A
B∩C - Empty set again

But I am not sure if I'm right :)

[split wind]

Checking

[split wind]

all correct

[stone birch]

Awesome, thank you!

.close

[vocal sleet]

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[waxen hawk]

As the diagram illustrates, A and B are the centers of circles. Given the bigger circle intersects with the smaller at point B; and their radius are 2 and 1 respectively.

points C,D are line AB's intersection with these two circles.

If E is one of the intersection between these two circles then:

Would the length of DE be greater than 3/2

I need a human to check on my attempt.

for I got a different answer as opposed to that of the book.

[waxen hawk]

is the usage of "as opposed to" correct?

[river kettle]

I mean it’s grammatically not wrong but other words sound better in that context

Like “compared to that of the book”

[waxen hawk]

is it correct to say "something is opposed to another thing" to express that these two things mentioned are different.

For instance, "my answer is opposed to that of the book"

[waxen hawk]

does the expression sound understandable and common?

[waxen hawk]

Also, can someone check this.

just the "3" part.

[vocal sleet]

@waxen hawk Has your question been resolved?

[vocal sleet]

@waxen hawk Has your question been resolved?

[sudden compass]

SOH-CAH-TOA + cosine law + sine law

[waxen hawk]

I still have no clue about what you’re talking about

[sudden compass]

....

[sudden compass]

By definition of sine and cosine in a right angle triangle, sin ECB = Opposite/Hypotenuse meaning sin ECB = 1/4

and sin EBC = Opposite/Hypotenuse = sqrt(15)/4

=> EBD = 180 - cos^(-1)(1/4)

By triangle angle sum property in EBD, angle BED = (sin^(-1)(sqrt(15)/4))/2

meaning CED = 90 + (sin^(-1)(sqrt(15)/4))/2

then use sine law

@waxen hawk

[waxen hawk]

Trig expert is on the way!

[full bobcat]

if you know CD and CE, DE shouldnt be hard to find

[waxen hawk]

Too explicit, your pfp, people cannot bare their upper body in Mickey’s kingdom

[full bobcat]

my apologies

[sudden compass]

Oh wait I didnt realise that

well its simply cosine law then

[full bobcat]

you have one side CD = 5

CE = sqrt(15)

and c = arccos(sqrt(15)/4))

so

DE ^ 2 = 15+25 - 2 * sqrt(15) * 5 * sqrt(15/4)

[sudden compass]

btw if u can, could u help in #help-26 as well? He doesn't seem to understand what I say

[full bobcat]

where did i go wrong

40 - 15*5 is negative

[sudden compass]

lemme see

[sudden compass]

it isnt negative bruh

its sqrt(2.5)

approx 1.58

[sudden compass]

so yes

[full bobcat]

,w 40 - 2 * sqrt(15) * 5 * sqrt(15/4)

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by diddletoucher

[full bobcat]

@sudden compass

[sudden compass]

.........

[full bobcat]

oooh nvm

,w 40 - 2 * sqrt(15) * 5 * sqrt(15)/4

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by diddletoucher

[full bobcat]

ye

[sudden compass]

yes

[full bobcat]

DE^2 = 5/2

(3/2)^2 = 9/4 = 4.5/2

so DE is greater than 3/2

[vocal sleet]

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[delicate totem]

to prove question

https://tenor.com/view/shocked-surprised-gasp-what-cat-shock-gif-635629308990545194

[vocal sleet]

@delicate totem Has your question been resolved?

[sudden compass]

use expension cos(x+y) = cosxcosy - sinxsiny

then factorization trick, (1-a)(1+b) = 1-a+b-ab

wait also

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[delicate totem]

?

[vocal sleet]

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[wet tendon]

How to prove that AEC and ABC are similar triagnles? Except for that 80 angle I have no idea what to do

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[vast shale]

What's the other set

[outer warren]

can you show your work

[vast shale]

i was achuilly being helped with a mathlab tutor in school

hello

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[hushed pewter]

Say derivative is undefined at x=a. Is f(x) continuous at x=a?

[weak thunder]

yes, for example sqrt(x) is defined at x=0, but its derivative is not

what do you mean?

[hushed pewter]

It's not sufficient that f(a) is defined. It must be that f(x) is continuous at x=a

[weak thunder]

I know that's what I said
sqrt(x) is defined at 0 but the derivative of sqrt(x) is not

wait am I mixing definitions? is a function being continuous at a just it being defined at a?

are these interchangeable? I usually don't do math in english

[hushed pewter]

No. They are not the same. Consider $f(x)=0$ when $x\ne 0$ and $f(0)=1$. Then $f$ is not continuous at $x=0$.

[twin meteor]

SWR

[weak thunder]

true ok

oh I read the definition for continuity a while back I remember

also close this thread if your question was answered (idk if it was) @vast shale

ok I read it it was answered

.close

doesn't work you have to do it

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[obsidian ore]

how do i do this? sorry i'm new to sigma notation

[dark kiln]

maybe you're supposed to divide it

[austere trench]

hi, is this a free place to ask for help or do i need to pay?

[obsidian ore]

free place, open a channel

[austere trench]

....any clue how to solve this? dont really wanna know the solution ,just a clue, feels so simple but i havent done geometry in like 4-5 years -_-

[hushed pewter]

!occupied

[vocal sleet]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[obsidian ore]

i havent learnt that yet 😭

long division?

[dark kiln]

i haven;t learned that either

it's not divisible

[hushed pewter]

!xy

[vocal sleet]

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.

[dark kiln]

it divides like this

[obsidian ore]

literally just that

[hushed pewter]

then what is this equal sign?

What is the problem asking you to do?

[obsidian ore]

i put it in wolframalpha so that it's easier to read

[obsidian ore]

find the answer in terms of n

[hushed pewter]

put what in wolfram alpha?

[hushed pewter]

Where does it say that?

[obsidian ore]

i just typed this and screenshotted the problem part

[hushed pewter]

And where did this expression come from?

[obsidian ore]

The question?

is literally

this

[hushed pewter]

!xy

[vocal sleet]

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.

[hushed pewter]

Oh it has a simplified form?

dang

I thought it was a harmonic series

those usually don't simplify

So what, you just want to know how it got to that?

[obsidian ore]

yeah

@hushed pewter

i have no idea what is method of differences

[hushed pewter]

Oh jesus method of difference

[hushed pewter]

This is exactly why I kept asking for this

[sly sierra]

is that some fancy way of saying "telescoping sum"?

[obsidian ore]

idk 😭 sorry

can someone explain what that is

[hushed pewter]

that's okay

Sorry I got mad

[obsidian ore]

Its okay

[hushed pewter]

But please. This context helps in the future

[obsidian ore]

Im sorry, since it was from an AL past paper i had to find it

[hushed pewter]

you may think what you are showing is the whole problem, but it's often not

That's okay. Just please keep it in mind in the future is all I ask

[obsidian ore]

alright

so how do i do this

[obsidian ore]

do we turn it into this form first..?

if i do that i can cancel out the 5/(r+1) i think

[hushed pewter]

Basically, your sum can be reduced to $6\cdot\left[\sum_{r=1}^n 1\right]-5\cdot\left[\sum_{r=1}^n \frac{1}{r^2+r}\right]$

[twin meteor]

SWR

[hushed pewter]

The first sum, I'm sure you can figure out

The second one, is where you need to use method of differences

[obsidian ore]

1/r^2+r? why?

[hushed pewter]

Because that's what was on the denominator

You split $\frac{6r^2+6r-5}{r^2+r}$ into $\frac{6(r^2+r)-5}{r^2+r}$ into $\frac{6(r^2+r)}{r^2+r}-\frac{5}{r^2+r}$

[twin meteor]

SWR

[obsidian ore]

ye

hold on lemme try

so 1/r^2+r i gotta use partial fractions?

wait i cant

[hushed pewter]

You could but it wouldn't help. You'd just end up with harmonic series, which doesn't have a simple summation

It's why I first though something was wrong

Nah you need method of differences

[obsidian ore]

how do i do that here?

i have a brief knowledge of how it works

[hushed pewter]

Basically, let $a_r=\frac{1}{r^2+r}$, and examine what $a_{r+1}-a_r$ is, and see if you can recognize the pattern.

[twin meteor]

SWR

[obsidian ore]

oh we are trying to find an arithmetic series

?

[hushed pewter]

I do not believe so.

That would be something like $b_r=r$

[twin meteor]

SWR

[hushed pewter]

You want to simply find $a_{r+1}-a_r$

[twin meteor]

SWR

[hushed pewter]

Anyway, I'll be back in a little while

But I'll ping <@&286206848099549185> in case someone else can help while I am gone

[obsidian ore]

oh

ill try

[sly sierra]

why can't use you use partial fractions? what went wrong?

[obsidian ore]

how would it look like

[sly sierra]

you're starting with $1/(r^2 + r)$?

[twin meteor]

Bungo

[obsidian ore]

ye

[sly sierra]

should be of the form $a/r + b/(1+r)$, do you know how to find $a$ and $b$?

[twin meteor]

Bungo

[obsidian ore]

yeah i think

but

question wants method of differneces

differences

[sly sierra]

this will give you that method

you need to get it into a "difference" form

aka telescoping sum

[obsidian ore]

oh

i will try that later

[sly sierra]

did you find a and b?

[obsidian ore]

hold on

lemme try

a = 1 b = -1

@sly sierra

[sly sierra]

yes

so let me typeset what you have:

$$\sum_{r = 1}^n \left(\frac{1}{r} - \frac{1}{r+1}\right)$$

[twin meteor]

Bungo

[obsidian ore]

oh lemme try

ye

[sly sierra]

do you see how that helps?

[obsidian ore]

-1/2 and 1/2 cancel out

[sly sierra]

yea

[obsidian ore]

but idk whats the significance of this

[sly sierra]

and then -1/3 and 1/3

and then -1/4 and 1/4

in general everything except the first 1/r and the last 1/(r+1) cancels

if r starts at 1 and ends at n, what are you left with?

[obsidian ore]

1+(-1/n+1)?

[sly sierra]

yes!

[obsidian ore]

YAY

[sly sierra]

$$1 - \frac{1}{n+1}$$
aka
$$\frac{n}{n+1}$$

[twin meteor]

Bungo

[obsidian ore]

YEP

yay

thanks so much @sly sierra and @hushed pewter

[sly sierra]

yw, cheers

[obsidian ore]

.close

[vocal sleet]

Channel closed

Closed by @obsidian ore

Use .reopen if this was a mistake.

[obsidian ore]

its 2am rn lol thanks guys

[hushed pewter]

Oh derp partial fractions was the way. I was too focused on looking at them individually

[obsidian ore]

i didnt even see that we could factorize 6r^2+6r

lol

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[vast shale]

can someone teach me how to do literal equations

[hushed pewter]

Can you show what you mean?

[tidal dock]

define/show an example of a literal equation

[vast shale]

ok wait

A literal equation is an equation with more than one variable, and every variable has an important characteristic.

[dark kiln]

mind blown

[vast shale]

like mx + b = y (m)

[dull bear]

You mean linear equations?

[vast shale]

😭 im asking cause im suppose to learn that in 8 grade but never did

[tidal dock]

so a formula or a linear equation?

[vast shale]

wait what

😭

[tidal dock]

maybe show an example of a problem?

that would be the easiest to understand

[vast shale]

i did

[dull bear]

Where did you get this statement from? Do you have a screenshot of what it says, and anything else?

[vast shale]

this

[tidal dock]

it's not a problem, i mean like a question from your textbook/test/homework/whatever

[vast shale]

you know what funny about this is that i dont have a math teacher TT and trying to teach myself

[tidal dock]

huh

[vast shale]

😭

[tidal dock]

okay i have never ever heard of them being called that way but i gotchu on these

[hushed pewter]

ahhh

[vast shale]

thank you can you teach me how to do them TT

and what there use for..

[tidal dock]

well

that depends on what you mean by "doing them"

it is usually written in a problem you are doing

[vast shale]

teach me how to do equations like that

[tidal dock]

wdym "do"

[vast shale]

😭 solve them?

[tidal dock]

okay

well there are like a bajillion different examples of them and they have different approaches but the common strategy is that you need to 'isolate' the variable you want to solve for

[vast shale]

isolate the variable?

[tidal dock]

yea

[vast shale]

how do you isolate a variable

[tidal dock]

like suppose you are solving for some variable 'x' in an equation, isolating means transforming that equation into something that looks like
$x=...$

[twin meteor]

artemetra

[vast shale]

like finding what x is?

[tidal dock]

yes

[vast shale]

oh ok

[tidal dock]

but i do have to say that i am not a teacher and i don't have any notes on this or anything. again, a concrete, specific example of a problem you are struggling with is the easiest way to get help on this server

[vast shale]

12x - 4y = 20 (y)

[tidal dock]

awesome

so

[tidal dock]

this picture has a very similar example

[tidal dock]

but i'll go through this anyway

[vast shale]

alright

[tidal dock]

we have $12x-4y=20$

[twin meteor]

artemetra

[tidal dock]

firstly, you can simplify this by dividing both sides by 4

[vast shale]

do we change the - to a +?

😭

[tidal dock]

why?

or like

wdym

write it out

[vast shale]

i heard that you need to change the symbol to the opposite

[wicked tundra]

whats the matter

[tidal dock]

no need to

you are dividing by a positive number

positive/positive = positive

[vast shale]

ohhh ok

[tidal dock]

so

[vast shale]

12 divide by 4 is 3 and 20

divide by 4 is 5

[tidal dock]

mhm

4 divided by 4 is ?

[vast shale]

0

[tidal dock]

no, it's 1

[vast shale]

😭

math isnt mathinggg

[tidal dock]

it's okay

in any case

we get $3x-y=5$

[twin meteor]

artemetra

[tidal dock]

looks a bit simpler

[vast shale]

since we got two variables how do we find what each one is

[tidal dock]

we are only solving for y, right?

[tidal dock]

you wrote (y)

[vast shale]

😭
i just remember

[tidal dock]

if we are solving just for y, we don't have to know what x is

[vast shale]

ohh

[tidal dock]

now you can subtract 3x from both sides. in some places this process is also called "moving 3x to the other side", if that sounds more familiar to you

[vast shale]

5 - 3 = 2
3-3= 0

[tidal dock]

no no

[vast shale]

WAIt

[tidal dock]

we subtract 3x, not 3

[vast shale]

what-

but we dont know what x is TT

[tidal dock]

that doesn't matter

it's just something

a placeholder

[vast shale]

so how are you even suppose to

[tidal dock]

we want to have y=something

right?

[vast shale]

ye

[tidal dock]

on the left hand side we want to have y, but we have a stinky little 3x term

if it can't be on the left side, it needs to be on the right one

[vast shale]

so we switch the positions of 3x?

[tidal dock]

yes but carefully

in order to move it to the other side we can subtract 3x (not 3) from both sides

[vast shale]

😵‍💫

[tidal dock]

$3x-y-3x=5-3x$

[twin meteor]

artemetra

[tidal dock]

we just put a "-3x" to the end of both sides

[vast shale]

when did math go from substrating numbers to subtracting letters

😢

[tidal dock]

well in the original problem you already had "12x-4y" so idk why you are surprised lol

[vast shale]

uh-

😭

[tidal dock]

^

[vast shale]

math is the end of me

[tidal dock]

okay i think i'll call someone else here

i am not the best at explaining specifically the basics of math in an accessible way

[vast shale]

whats the point of puting 3x in both sides

[tidal dock]

so on the left side we get 3x-3x, which is the same as 0

[vast shale]

ohh ok

[tidal dock]

$\cancel{3x}-y\cancel{-3x}=5-3x$

[twin meteor]

artemetra

[tidal dock]

so

we get $-y = 5-3x$

[twin meteor]

artemetra

[tidal dock]

almost there!

[vast shale]

why is 3x still there-

[tidal dock]

because we subtracted it from both sides. on the right side, there was not 3x before and now there is one

[vast shale]

ohh

[tidal dock]

while on the left side they canceled with each other

[tidal dock]

now from here we can negate both sides

so essentially slap a minus in front of them

[vast shale]

I WAS JUST GOING TO ASK why the y turn negative

😭

[tidal dock]

it was always "negative"

[tidal dock]

there's a '-' in front of y here too

[vast shale]

that was a substration sign

[tidal dock]

okay

we get $0-y = 5-3x$

[twin meteor]

artemetra

[tidal dock]

same thing

[vast shale]

oh ok

[tidal dock]

^

[vast shale]

all of them?

[tidal dock]

eh

in front of the whole side

so basically

$-(-y) = -(5-3x)$

[twin meteor]

artemetra

[vast shale]

oh

[tidal dock]

what does the left side simplify to?

[vast shale]

2x?

[tidal dock]

the left side

[vast shale]

oh

[tidal dock]

the -(-y) thing

[vast shale]

-y?

[tidal dock]

that's what we started with

okay, what is -(-1) ?

[vast shale]

its 1

[tidal dock]

yep

so -(-y) is y

$y=-(5-3x)$

[twin meteor]

artemetra

[tidal dock]

we are essentially done but the right side can be simplified a bit

[vast shale]

we substract? 5- 3x

[tidal dock]

no

again, it's 3x, not 3

[vast shale]

5 - 3x = 2x

[tidal dock]

still no

expand the bracket

[vast shale]

what do you mean expand the bracket..

y=3x−5?

[tidal dock]

yep

that's your answer

[vast shale]

thanks you

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[civic hound]

Ehm, how do i start?

I know that the inverse function is f^-1(x)

ehm

[dull bear]

If you can show it's injective, then you're good, and strictly increasing/decreasing functions are injective...

[civic hound]

Well, i don't know what kind of function this is

atm

I don't think i can plot this

[civic hound]

How do i know it is striclty increasing or decreasing?

[dull bear]

Good question

[tidal dock]

another hint: f(x) is even

[civic hound]

Ohh god i truly need to restudy all definitions

even meant?

[tidal dock]

so f(x) definitely cannot be injective

[dull bear]

f(-x) = f(x)
[odd functions are those such that f(-x) = -f(x)]

[civic hound]

OK THANK YOU

so

lemme think

[dull bear]

[have you dealt with derivatives before?]

[civic hound]

Yes

Should i study the first derivative?

[dull bear]

That would be a good idea

[civic hound]

niceeee

Well, this is always positive, so its always increasing