help-39

[snow skiff]

this isn't doing anything

[jolly parrot]

active mental mutilation liker

[turbid moss]

what if f were continuous

[snow skiff]

where

[turbid moss]

everywhere

[snow skiff]

doesn't imply it's everywhere differentiable

are you doing calc 3 or analysis btw

[turbid moss]

analysis

[snow skiff]

alright

can you pull up the exercise

which has this

[turbid moss]

this was a question prof asked us at office hours

just some thinking is what he wanted out of us

[snow skiff]

hmm

[turbid moss]

but now im a bit stumped

[snow skiff]

are you sure he wrote this

and not f(x)

[turbid moss]

yeah

[snow skiff]

exactly this?

[turbid moss]

of course it is also possible that nothing can be concluded from this

[snow skiff]

because if he wrote exactly this

[turbid moss]

but all i need is an explanation

[snow skiff]

then by definition

f'(x_0) exists

because the usage of this already immediately implies that f is differentiable at x_0

and the definition of derivative there is

$f'(c) = \lim_{x \to c}\frac{f(x) - f(c)}{x - c}$

[jolly parrot]

active mental mutilation liker

[snow skiff]

maybe ask him to clarify if he meant lim (x to x_0) f(x) instead

because that's more interesting

[turbid moss]

ok ill see about it tomorrow

[snow skiff]

otherwise yes it is defined

[turbid moss]

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[celest roost]

can anyone help me with this?

[west sapphire]

some of the possible answers are obviously false, which ones?

[celest roost]

only the first one is I believe is true

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[smoky saffron]

This is my approach to answering the question is this how most people would do it?

[hollow cobalt]

I believe so

[smoky saffron]

ok thx just needed assurance

[hollow cobalt]

The approach doesn't really matter as long as it's correct

[smoky saffron]

Oh okay

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[graceful island]

how would i find 'a' here ? the first bit (asymptotes) was easy but the only thing i could think of for this part didn't work

[distant skiff]

check ur multiplication

[graceful island]

i--

💀

[distant skiff]

!help

[pearl pond]

Please read #❓how-to-get-help

[verbal furnace]

How Kan I do This ?

[distant skiff]

open your own channel, don't usurp someone else's

[graceful island]

i always make the dumbest mistakes while doing the right steps

tysm tho ksjdksjd

[distant skiff]

🙏

[graceful island]

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[verbal furnace]

.Do this

[pearl pond]

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[unique gyro]

Second image is solution.

[verbal furnace]

<@&286206848099549185>

[unique gyro]

Was wondering if someone could help with this problem. I'm unsure where/how to apply the last two conditions

[glass salmon]

This channel is occupied

[unique gyro]

work is incomplete

[plush bramble]

use trig identities to simplify this when x = x + L

similarly for the derivative $u'_x$

[jolly parrot]

riemann

[unique gyro]

That is the solution I am suppose to arrive at though

[plush bramble]

oh

do you know that this is a linear combination in terms sines and cosines

then use this in your solution

Example 1 explains a very similar problem decently well
https://tutorial.math.lamar.edu/classes/de/solvingheatequation.aspx

[unique gyro]

okay I am looking at it, thank you

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[tall tangle]

what did i do wrong

the question is finding the value of a and b

but clearly -1 and 3 don't make sense

[timid spindle]

how did you get a = -1?

[supple spindle]

pretty sure it’s from the solutions

[midnight haven]

are you sure the a and b on the rhs are the same as a and b on the lhs?

[supple spindle]

Oh

[midnight haven]

boki moment

[supple spindle]

pfff

[midnight haven]

,w factor x^4-6x^3+7x^2+6x+1

[supple spindle]

[midnight haven]

pls refrain for using / to mean or

i thought it was division

[supple spindle]

same

[jolly parrot]

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[midnight haven]

3*2=6, not 3

yeah, you wrote a=3 tho, not a=6

[supple spindle]

or -3

[tall tangle]

ok

.close

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[tight flint]

what is the answer? is it 344.73 acres? I plugged in 15 for t

[fallen lotus]

that should be it

[tight flint]

thanks you.

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[flint wyvern]

am i right with D?

[surreal smelt]

yes D=80 * cos(60)+30 * tan(45)=80 * (1/2) + 30 * 1=70

[lavish oar]

i agree

[flint wyvern]

THANK YOU SM BOTH!!!

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[glass jewel]

not sure if this is the place to ask, but is there a website where i can guage my skills on certain topics (limits) and adapts to what you know?

[midnight haven]

you could try doing the quizzes on khan academy

https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity

[glass jewel]

yes perfect

how could i forget about khan

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[spark skiff]

For pivoting on a tableau of the simplex method, why do we pivot on the row that minimizes b/a and not maximize b/a? Shouldn't it be maximize because then your objective value will be maximized when you zero out the negative term in c?

[pearl pond]

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[spark skiff]

@vast sluice

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[viscid mural]

I’m getting confused with rate of change word problems, I’m stuck on how to line my numbers in the fractions

Everytime I order it wrong, it ends up making my answer different

Anyone have a way to remember which way to set it up

[pearl pond]

@viscid mural Has your question been resolved?

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<@&286206848099549185>

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[inner zenith]

consider four charges placed at the corners of a square with sides of 1.2 m, as shown in the right. What is the magnitude of the electric force on q4 resulting from the electric force from the remaining three charges?

[old marsh]

!status

[pearl pond]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@inner zenith Has your question been resolved?

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[frail rapids]

help pls🙏🏻🙏🏻

i need help on h, j, k, l, 2, 3, 4, 5

[late moon]

Hmm

What is troubling you in h?

[frail rapids]

idk how to minus

a whole

from a fraction

cuz im like rlly dumb

can u pls tell me the answers?

oh okay

[real sleet]

never undermine your abilities

You can learn

[frail rapids]

ohh rlly

ohh okay

tyy

so

whats for

j

[late moon]

Multiply the big number by the denominator and add it to the numerator

[frail rapids]

ik but

[late moon]

Then make them all have a common denominator

[frail rapids]

irs hard

ik

i have thw answer

but idk how to simplify

[late moon]

Hmm

Simplifying as in?

[frail rapids]

like

73828/278282 to 1/2

im in the washroom rn

and my hw

is in the lviing room

i think im sick

[late moon]

[frail rapids]

yeahhh

im pooping rn

but that not relevant

so

[late moon]

That's a ridiculous situation. You won't encounter that type of fraction in school

[frail rapids]

ik

thats js an example

abt?

[late moon]

Guess the factors

[frail rapids]

wdym

[late moon]

Like

500/1775 looks divisible by 5

[frail rapids]

ohhh ye

[late moon]

100/355

Then divisible by 5 again

[frail rapids]

yeahh

[late moon]

20/71

That type of stuff

[frail rapids]

yeahh

ik

whats for k then

ohhh

so 15?

OH

so 30

3x4x5?

60

ohhh

wait im still on the toilet

my mom

walked in on me

and said to not throw my clothes on the ground

oh whats for 2

oh

thats all?

okk

damn so how

do u teduce

868/84

[late moon]

Divide by 4

[frail rapids]

ohhhh

so

217/21

[late moon]

Yeah

[frail rapids]

oh how

ohh

what abt 87

i mean

84

wait oops

i mean

217/21

i simplifeid rhat

ohh

okayy

thanksss

i js did k

how do we do 3

[pearl pond]

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[viscid mural]

Fourth time the charm

[viscid mural]

I need help with how to set this problem up

I know it’s y1-y2 but I end up mixing it up anyway

[grizzled dust]

i dunno if this is helpful but i'll try to give you a more intuitive example: say you were traveling in your car and at one point in time you notice you pass mile marker 400 then some time later you pass mile marker 420, how many miles did you travel and how did you go about calculating that?

@viscid mural ?

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[midnight haven]

hi, can i have help on the b i dont understand it

[brisk hull]

Have you solved a?

if yes you can find the equation of that line using the slope point form (slope of a vt graph is the acceleration) and then substitute t=55 to get the speed

or if you know equations of kinematics you can use them directly

[midnight haven]

i have solved the a one

[midnight haven]

thanks so much

.close

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[vivid crescent]

Absolutely Convergent Series in Normed Vector Space is Convergent iff Space is Banach

I'm trying to understand this proof but i dont get how this sequance "uk" become absolutely convergent without knowing the limit exist in the space or not .we only know absolute sum of "uk" is bounded.

[vivid crescent]

Here

[plush bramble]

which lines specifically

just copy paste the link here

[vivid crescent]

https://proofwiki.org/wiki/Absolutely_Convergent_Series_is_Convergent_iff_Normed_Vector_Space_is_Banach

[vivid crescent]

Here

Its just an upper bound for sum of |uk|'s

It doesnt mean limit exist in the space

[plush bramble]

which line EXACTLY

[vivid crescent]

It conclude this is absolutely convergent

And use his assumption after that

[plush bramble]

do you know the definition of absolutely convergent?

[vivid crescent]

Doesn't limit being exist necessary?

[plush bramble]

that has nothing to do with my question

click the link to check the definition
https://proofwiki.org/wiki/Definition:Absolutely_Convergent_Series

[vivid crescent]

.close

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[hazy horizon]

are these right?

[warm current]

✅

[pearl pond]

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[distant plinth]

tips on these two?

[distant plinth]

for 6, I'm not sure if FED is similar to ABC or if FE is parallel to BC

[glass salmon]

Show us your diagram

[distant plinth]

k

[pearl pond]

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<@&286206848099549185>

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[tender mortar]

hello I need help with an exponential function.

[unborn swallow]

ask your question

[tender mortar]

I'm supposed to figure out how long it's going to take for 85 000 to get to 500 000 with a 20% yearly increase. So I put it like 500 000=85 000 x 1.20^t. Which is correct, but I dont know how to put it into geogebra

to figure out when it's reached 500 000

[unborn swallow]

you're using geogebra to graph it? why not desmos?

[tender mortar]

we're using geogebra on the test

[unborn swallow]

and, regardless, this can be calculated by calculator using logarithms

[tender mortar]

okay

[unborn swallow]

you want to plug it in and see its intersection with y=500000

since at that intersection, it's reached a magnitude of 500k

[tender mortar]

I think so

[unborn swallow]

ta da

[tender mortar]

oh okay thanks, I put it in the wrong way

[unborn swallow]

it was my pleasure

[tender mortar]

I just put the whole thing in as one

[buoyant panther]

you can put

[unborn swallow]

I mean that works too

[buoyant panther]

1.2^t * 85000 - 500000

then see when it's 0

[unborn swallow]

find the x intercept of 85000(t^1.2)-500000

stealing my words ):

it's just more intuitive to find where it meets y=500000 rather than doing it more efficiently

[tender mortar]

this seems like the easiest way

thanks for the help guys👍🏻

[unborn swallow]

oh wait damn didn't even see it was you who posted that lol

thought it was Hjalmar

[tender mortar]

.close

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[warm current]

!status

[pearl pond]

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'm told it's wrong
4. I got an answer and would like my work checked
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6. None of the above

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[midnight haven]

I keep getting fractions for the solution when the book is giving solution: [0,-1,1] + t[9,-10,-7]

[midnight haven]

The book uses gauss elimination and from what I understand would use a non-leading variable as the free var. So why are they giving x as the free variable?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[vocal lark]

https://tutorial.math.lamar.edu/Solutions/CalcIII/EqnsOfPlanes/Prob8.aspx

it isn't obvious to me that x is the "free variable" in their working since you have only provided the parameterized answer

just fix one of the variables and solve for the other two so you have a point on the line of intersection.
Then take the cross product of the normal vectors of both planes to get a vector which is parallel to the line of intersection. Then you can write the actual equation of the line using the fixed point and the parallel vector

@midnight haven

I gotta go but I think you can totally do this. Follow along with the example first if you need to

[ivory swallow]

,w rref ((3,2,1, -1), (2,-1,4,5))

[jolly parrot]

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Requested by Mr. Gamer#6658

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[elfin stirrup]

$x = \frac{x^2}{x} \text{ but } f(x)=x \neq g(x)=\frac{x^2}{x}$

[jolly parrot]

tobi.

[elfin stirrup]

is this correct?

[broken ivy]

yes

[elfin stirrup]

or is x^2/x only equal to x if x =! 0

[broken ivy]

this too

[elfin stirrup]

is this the reason why its not the same

[broken ivy]

yes, f(x)=g(x) if x!=0

[elfin stirrup]

okay

.close

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[midnight haven]

Help

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[timber zinc]

can someone give me a small hint on how to solve this for equality?
so far i was able to get (x,y) = (1,2) but im not sure if that is the only pair of numbers which makes this equation true

[timber zinc]

(hint for the second part of the problem)

I just need a link or something I could look into to be able to solve it

[rotund talon]

hint: AM GM

[timber zinc]

oh

ok ty

I made the equation to:
y/2 + 2/y + x + 1/x = 4

and to get y/2 + 2/y = x + 1/x
y has to be 2*x

rihgt?

[rotund talon]

apply AM GM to each of the terms in brackets individually and multiply

[timber zinc]

ok

[rotund talon]

dont know you got to this,
but if you individually apply the condition for equality in each of the two cases i mentioned,
you get xy = 2 ; y = 2x which you can solve

[timber zinc]

oh ok ty

[pearl pond]

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[tidal terrace]

i got the lcm and idk how to do hcf

[tidal terrace]

pl

turns out i was wrong

and idk how to do either

c i got as 103 680

and d i got as 15120

[pearl pond]

@tidal terrace Has your question been resolved?

[tidal terrace]

no

[pearl pond]

@tidal terrace Has your question been resolved?

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[strong furnace]

Hello i have a probably problem

[strong furnace]

Theo and Andreas toss a coin. Outcomes are 1 or 0. They toss it until getting 001 or 100. First case scenario Andreas wins, otherwise Theo wins. Do they both have the same chance of winning ?

How can i rigorously prove Theo has more chances of winning ?

[pearl pond]

@strong furnace Has your question been resolved?

[strong furnace]

<@&286206848099549185>

[vestal tapir]

i thought andreas has advantage

darn

[strong furnace]

🙁

[warm current]

fwiw I simulated this, theo def has advantage

[strong furnace]

But how you rigorously write it i have no idea

[warm current]

Yeah. Still trying to figure that out..

[strong furnace]

Definitely makes sense but yeah

[warm current]

simulations suggest theo wins 75% of the time

so that's worth considering

[strong furnace]

Damn that’s a massive difference

[warm current]

If theo wins with 110 instead of 100, then its 50/50

Because the patterns are identical

simulations confirm this

[vestal tapir]

also i thought it's hard to prove

[warm current]

The longer the string, the more advantage theo gets

[vestal tapir]

but it's not

[warm current]

1000000 vs 000001 is a huge advantage for theo

[strong furnace]

?

[vestal tapir]

if the first two flips are 00 andreas will definitely win

[strong furnace]

Also makes sense yeah

[vestal tapir]

otherwise theo will definitely win

[warm current]

ah that's right

frog mvp

[strong furnace]

Don’t get it 😂

[warm current]

why it's true or what you get from it being true?

[strong furnace]

How does that help ?

2nd option haha

[warm current]

Okay so, let's consider just the first two flips like frog said

andres can only win if the first two flips are 00

Any other outcome means theo will win

[vestal tapir]

because they both need 00 to win

[warm current]

So ask yourself: what is the probability of 00?

[strong furnace]

Oh shit

Damn that’s so smart

[warm current]

[strong furnace]

Thx guys love yall @warm current @vestal tapir ❤️

.close

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[stuck arch]

Im starting to work with Taylor polynomials again, is it a problem if my R is negative?

[stuck arch]

where R is the Rest term / Lagrange form

[pearl pond]

@stuck arch Has your question been resolved?

[plush bramble]

no

[stuck arch]

thanks

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[sullen leaf]

Is this odd or even?

[sullen leaf]

Having trouble telling the difference

Anyone? <@&286206848099549185>

[limber glacier]

is what odd or even

[limber glacier]

!15m

[pearl pond]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[sullen leaf]

The graph, and sorry

It’s asking if red and blue are even or odd

[limber glacier]

do u know what odd and even mean

[sullen leaf]

If it’s symmetrical about the y axis it’s even, if it’s odd it’s symmetrical about origin?

[limber glacier]

okay..

so can u rotate the blue one around the y axis

[sullen leaf]

Wdym?

[limber glacier]

like is the blue one symmetric about the y axis

or not

can u like flip it around the y axis, and end up with the same thing

[sullen leaf]

Yes?

[limber glacier]

yea

so theres ur answer

now look at the red one

[sullen leaf]

The red one isn’t symmetrical..

[limber glacier]

so it is not even

is it odd?

[sullen leaf]

Yes

Right?

I suppose..?

[midnight haven]

@sullen leaf do you know the valúes

[limber glacier]

so its odd, if u can rotate it 180 degrees around the origin and end up with the same thing

can u do that with red

more precisely, a function f is even if f(x) = f(-x), and it is odd, if f(-x) = -f(x)

[midnight haven]

^

[limber glacier]

so u can also check for whether this happens

[pearl pond]

@sullen leaf Has your question been resolved?

[pearl pond]

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[graceful gale]

Hi, I need help with this one. I really appreciate any kind of help

[pearl pond]

@graceful gale Has your question been resolved?

[west sapphire]

hint: minimizing |a+tb| is equivalent to minimizing |a+tb|^2. Can you express the latter using a dot product?

[pearl pond]

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[manic umbra]

How to simplify, tan70 + cot20 - 2tan70

[vague rock]

hi

use this

sin(90-x)=cos(x)
and
cos(90-x)=sin(x)

[manic umbra]

Could you perhaps explain it more in detail?

[midnight haven]

cot(90-x)=tan(x)

try to see how you can apply that in the second term

[pearl pond]

@manic umbra Has your question been resolved?

[manic umbra]

Thank u

.close

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[hard crystal]

!status

[pearl pond]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[hard crystal]

Please help me

Any hint will be enough

[cursive fulcrum]

ACB and FCE are similar too

[hard crystal]

This one i noticed

How is it similar?

[fallen lotus]

Nevermind i thought they were
My bad

[hard crystal]

Any ideas?

[pearl pond]

@hard crystal Has your question been resolved?

[pearl pond]

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[summer hound]

maybe relate bases with areas?

.reopen

[hard crystal]

.reopen

[pearl pond]

✅

[hard crystal]

I figured that ar(ABD)=ar(ADE)=ar(AEC)

After this i don't know what to do

[summer hound]

yes and you should apply it more

ok notice

[ADE]=[AEC]
[DFE]=[EFC]
2[EFC]=[AEF]
2[DFC]=[FDA]

you can derive all of these from the bases

then just decompose them into smaller areas and solve the linear eqn

you prob can get the sol

[hard crystal]

I got the [AHF]=24 ? IS IT CORRECT?

[summer hound]

could you show your working?

[hard crystal]

Ok then you have to wait i have to write more clearly

I was writing in rough

I was doing wrong

[summer hound]

Let [ADH]=c+24, [DHE]=a, [AHF]=b, [HFE]=c, [FEC]=d
so we have
c+24+a=b+c+d
=> 24+a=b+d

a=c+d

b+c+24=2(a+c+d)
=>b+24=2a+c+2d

2d=c+b

Combining these we get=>
24+c=b
a+c=12
a+b=3d

=> d=12,

you can maybe go from here

so a+b=36

[hard crystal]

Ok thanks

[summer hound]

just manipulate it and you can prob get something

[hard crystal]

Thanks for your help

.close

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[sharp patio]

In a lottery, the thousand numbers from 000 to 999 are used. We draw a number: 205, and number 205 wins the jackpot. THE
five numbers 025, 052, 250, 502 and 520 win a second prize. Finally, all other numbers having at least two digits in common with
number 205 get a consolation prize. How many numbers will have a consolation prize?
I don't understand how I am supposed to find the numbers without writing all numbers from 0 to 999.

[autumn fossil]

Do numbers with 3 digits in common win the prize too?

[sharp patio]

Yes

[autumn fossil]

Number 205 is made from digits 0, 2, 5. Let's pick a pair of digits. E.g. 0 and 2. How many numbers can be made from 0, 2 and some other digit?

[sharp patio]

Hmmmm

Probably all the numbers from 20 to 29 and all the hundreds who have 02 at the end.

+012, 022, 032, 042, 062, 072, 082, 092

[autumn fossil]

002, 012, 022 ... 092
002, 102, 202 ... 902

020, 021, 022 ... 029
020, 120, 220 ... 920

200, 201, 202 ... 209
200, 210, 220 ... 290

This is list of all the numbers

[sharp patio]

Yeah

[vestal tapir]

it's ambiguous, if 222 has 3 digits in common or 1

[autumn fossil]

I guess that since the 5 numbers 025, 052, 250.... didn't include also 555, 222 etc, 222 wouldnt count as having 3 digits in common

[autumn fossil]

Anyways, are you able to count all the numbers here and exclude duplicates?

[sharp patio]

I will do it at the end

[vestal tapir]

do you have the answer?

[sharp patio]

It was a problem online, the answer is like 144

[autumn fossil]

Once you count them, you have to find how many pairs of numbers can you choose from 0, 2 and 5

and then again exclude duplicates

[vestal tapir]

i can't get 144

it's 126

[sharp patio]

Are you sure at 100%?

[sharp patio]

Okay I will try it

[vestal tapir]

the question is ambiguous

[sharp patio]

Yeah

I took an old formulary of a small math competition

[autumn fossil]

I got 150 xD

[sharp patio]

That's close

[autumn fossil]

If I exclude 502, and those 5 numbers, I get 144

@vestal tapir how did you get 126?

So my solution is correct

[sharp patio]

Nice!

I'm still doing the problem

[autumn fossil]

Btw, 222 doesnt count

and it must include exactly 2 same digits

[sharp patio]

You're good

[autumn fossil]

I am not. I was too lazy to think so I coded it

[vestal tapir]

yeah i made a mistake

[autumn fossil]

lemme try mathemmatical solution now...

[sharp patio]

What? How can you code it?

I haven't learned probabilities so I do it one by one

[autumn fossil]

Enumerate all numbers from 0 to 999

very inefficient code btw

[sharp patio]

This looks even harder

[autumn fossil]

What I did was go from 000, 001, 002, and check if each of those satisfies condition

thats all

and counted them up

using computer

[sharp patio]

Nice

[autumn fossil]

Alright, I got the mathematical solution

[sharp patio]

You did it yourself?

[autumn fossil]

yep, this time I didnt use computer

[sharp patio]

You're fast af

[autumn fossil]

This is really useful

just find how many duplicates are there

[vestal tapir]

i don't get how 144 makes sense
3 different digits: 3*7*6 = 126
two and one, like 220: 3*2*3 = 18

no okay that's actually all that counts

[autumn fossil]

126+18=144

[vestal tapir]

so 144

i thought "but there's more cases"

guess there isn't

[autumn fossil]

Damn thats actually really smart solution

[sharp patio]

I need to find the duplicates

[autumn fossil]

I dont get it tho

[sharp patio]

Me too It is supposed to be a logic and math contest

[vestal tapir]

if 3 digits are different you pick which digit is missing (0,2 or 5) then pick which digit replaces it (10 minus 3) and pick the order

[autumn fossil]

This solution is much smarter

[vestal tapir]

if it's 2+1, you pick which digit is missing: 3
which digit is doubled: 2
where in the number is the single: 3

[sharp patio]

I've got too much

[pearl pond]

@sharp patio Has your question been resolved?

[sharp patio]

The duplicates are annoying to find

[glass salmon]

Just split into cases

Either 3 distinct digits or 2 distinct digits in the number

[sharp patio]

I think I got it

[glass salmon]

Oh yeah I read what the others wrote and they did the same

[sharp patio]

.close

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[pearl pond]

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[viscid pivot]

need a little guidance as to how to go with solving lg(10x^2)*lgx=1

[old marsh]

is ‘lg’ log

[viscid pivot]

log with base of 10

[limber comet]

ok

u mean

log with base 10 of value 2 *log x =1

[viscid pivot]

umm

no

log/10/(10x^2)

and log/10/(x)

[limber comet]

umm

[light helm]

$\log_{10}(10x^2)\cdot \log_{10}(x) = 1$

[viscid pivot]

yesh

[limber comet]

ohh

[jolly parrot]

ℝamonov

[limber comet]

now i get it

its easy

[viscid pivot]

oh yeah

I just saw it

10^0=1

[limber comet]

do u know the propertis of log

?

[viscid pivot]

I guess

[limber comet]

u can apply

her

here

the

property of logmn = log m+logn

and log m^n = nlogm

[viscid pivot]

are you sure that property can be applied here, as it's log*log, and not logmn

[limber comet]

write log10x^2 as log (base 10)10 + 2logx

no

i am talking about

each log function alone

[viscid pivot]

ohhh

I see it

[limber comet]

do u get it noe

now

[buoyant panther]

$$\log_{a}b+\log_{a}c=\log_{a}(bc)$$
but:
$$\log_{a}b \cdot \log_{a}c \neq \log_{a}(b+c)$$

[jolly parrot]

Modus

[viscid pivot]

helped out taking lg10 out of lg10x^2

thank you

.close

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[untold oracle]

An exam had this vector space and asked to find the bases and dimensions of W for all $ \alpha \in \mathbb{R} $.

$$ W_\alpha = { (x, y, z) \in \mathbb{R}^3 | 2 \alpha x - 10y = 0, (\alpha - 1)z = 0 } $$

The solutions say that there are only two cases: $ \alpha = 1 $ and $ \alpha \neq 1 $. While solving it I found that $ \alpha = 0 $ is also an interesting case where the x term goes away and so the first coordinate is free. $ W_0 = { x \in \mathbb{R} | (x, 0, 0) } $

Is this not the case?

[jolly parrot]

Hawk

[midnight haven]

yeah i agree it should be alpha = 0, alpha = 1, rest

[pearl pond]

@untold oracle Has your question been resolved?

[pearl pond]

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[elfin stirrup]

I want to proof that every a monotone increasing sequence is converging, when its bounded above.

So I know I could proof it by contradiction, but can I also do it with the bolzano weistrass theorem?

My Idea is that every monotone increasing sequence is also bounded below, therefore I can apply the bolzano weistrass theorem, that at least 1 convergent partial sequence exists, now that this exists, we see that every partial sequence is also monotone and increasing, therefore every partial sequence is converging against its supremum, and therefore the original sequence converging against its supremum

My Question is, is that explained well enough, in particular is this explanation:

every partial sequence is also monotone and increasing, so therefore every partial sequence is converging against its supremum

good enough

[elfin stirrup]

because I don't feel like that this is a proof

more like an assumption even tho its true

[near echo]

i don’t believe this works

[autumn narwhal]

You only showed it's bounded from below, you can't use that

[near echo]

by bolzano weiertrass, there is a converging subsequence, but that doesn’t mean every subsequence is convergent, unless i missed something in your explanation

[near echo]

boundedness above was given

[autumn narwhal]

oh I see

you could show it converges to

$\sup\set{a_n \where n \in \N}$

[jolly parrot]

RedstonePlayz09

[near echo]

well yeah that’s clear, they’re just asking if this can be done through bolzano weiertrass

[autumn narwhal]

ok hm

I think you can show it by taking a subsequence that converges, and then taking the sequence that completes it.

and showing that it also converges to the same value.

[pearl pond]

@elfin stirrup Has your question been resolved?

[elfin stirrup]

Yeah I asked if this reasoning would work

I also don't find it as clean as a proof by contradiction

[autumn narwhal]

What would your proof by contradiction be?

[elfin stirrup]

Sry if u can't reas that languages

Language

[autumn narwhal]

yup I cant but I'll try to understand

what's n_0 here?

also is this the contradiction proof?

[elfin stirrup]

It says a-eps is not an upper boind

[elfin stirrup]

Ye

It should be correct because it's just a copy out of my textbook

I was just wondering if I could proof it with Bolzano Weinstrass

[autumn narwhal]

I said what my approach would be, you can try to work out the details if you want

Either you can always bound the completing subsequence with the original subsequence, or from a certain point the original subsequence is just the original

in both cases you get your result

[pearl pond]

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[flint sleet]

I'm stuck on part b of this question

[flint sleet]

i've gotten the wrong answer

i've factorised the left side

to (z-i)(z^2+z+1)

[tired sage]

Hi

[flint sleet]

hi

[tired sage]

Can somebody please help

[merry carbon]

How did you do this?

[flint sleet]

i just used the sum of 2 cubes formula and got (z+i^(1/3))(z^2-zi^(2/3)+i^(4/3))

[merry carbon]

Hmmm why is is i^(2/3) and i^(4/3) that you did?

Also note that i = -i^3

[flint sleet]

yeah so it became this: (z-i)(z^2+z+1)

wait

it's wrong

is (z-i)(z^2+iz-1) right

alright so z = i, z=(+-sqrt(3)-i)/2

thanks for the help chartbit

.close

[pearl pond]

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[tired sage]

Graph the domain: {h | 0 ≤ h ≤ 3} on a coordinate plane

[pearl pond]

Please don't occupy multiple help channels.

[merry carbon]

#help-12

.close

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[tough void]

https://i.imgur.com/aGOVcIe.png
https://i.imgur.com/yROUYz7.png

I think I got the right answer but I'm getting kinda confused about M(y)

My answer is ∃x∀y(A(x) ∧ (M(y) → ¬T(x,y)))

It seems to make sense, because I am saying there exists a part time student(A(x)), and if all Y are math classes, then it implies that this part time student is not taking them. Is this the correct answer? Feels like I'm off but I'm not sure.

[tough void]

M(y) seems like a weird proposition to me

It seems like the only way I can state this is by assuming that the set of all classes are all math classes

Also for this:
https://i.imgur.com/OAEWJ7Z.png

I got ∀x∃y((A(x) ∧ F(x) ∧ U(y)) → T(x,y))

I think this is right because I lay out some conditions: I am saying that in the set of all students, if three conditions are met, then it implies something

I am saying that that in the set of all students, if part-time, freshman, and y is an upper level course, then then it implies that the student must be taking that y upper level course

[pearl pond]

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[mortal sparrow]

Hi I'm asked to find a hermite interpolant to x**3 at x0 = -1 and x1 =1. I'm told I don't need to find various coefficients but can instead be lazy

[mortal sparrow]

Not sure how to approach this can someone help please

[pearl pond]

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[midnight haven]

can someone help explain this to me in two-column proofing format using conv of angle bisecting theorem?

[midnight haven]

i have this so far but im so confused idk what the two givens have to do with each other

[midnight haven]

<@&286206848099549185>

.close

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[violet pumice]

I think I've made a mistake somewhere, but I can't really pinpoint the place, if someone has any insight I'd be thankful

[violet pumice]

the question is a differential eq, I don't know the method I used for solving in English ☹️

[pearl pond]

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[median fable]

K is an integer greater than or equal to 8. Is my work correct? This is part of a larger induction.

[median fable]

The very first step to get to 3(k^4) is by assumption

[plush bramble]

Show the whole problem you're solving

[median fable]

So I showed it for n =8. And then I assume it's true for some k>=8. Then my induction step was as pictured.

[snow sail]

do you have to do it by induction?

theres only 7 cases

granted its probably a good exercise

[median fable]

Yeah, it's from a chapter all about induction. But I am curious about your way too.

[snow sail]

i mean youd just calculate directly

i guess build a table

of 3^n and n^4

for n = 1 2 3 4 5 6 7

[median fable]

But you have to prove it's true for every n greater than or equal to 8. Not less than 8?

[snow sail]

oh yea sorry

im sleepy

well induction is fine

[median fable]

You're good XD. Made me question reality for a minute.

Yeah, I just wanna know if the work in my picture is okay. I'm sleepy too, but I got a quiz coming up and I want to know if my steps are fine.

[snow sail]

oof im not sure im the one to be proofreading

lemme look

i think you could do it faster

[median fable]

You mean like not show every step?

[snow sail]

yea i take it back

i am not the person to be helping with this, im more tired than i thought

sorry

[median fable]

No worries man!

[snow sail]

if someone else comes, theyre just asking for a quick check on this logic

[cunning condor]

could you type this or something

no offense but can't read it

[snow sail]

you could probably get away with just doing the induction on your own

,rotate 90

[snow sail]

does this help

[cunning condor]

hmm ok

[snow sail]

im wondering if you can just like

[median fable]

I'm not offended at all. My typing sucks so you might have to wait a minute if you want me to type it.

[cunning condor]

what dies the second line mean? 7 3(k power of 4) = k power of 4 × 3?

sorry I cant write the symbols

what does the 7 mean?

[median fable]

is greater than 3(k^4) = k^4 +k^4 +k^4

[cunning condor]

ah

so ^ is used for power of

I see

[median fable]

yeah

[cunning condor]

Im sorry what grade is this? I might've done this for nothing as Im very young

[median fable]

Well technically this is from a college course. But the image of my work itself is really just an algebra problem.

My goal was to show that 3^(k+1) > (k+1)^4
So to do that I slowly transformed the starting expression by breaking it down and taking advantage of the fact that k >= 8

[cunning condor]

yeah

might be able to solve it

give me a minute

i did this last year I must do it

so the 2nd line and the first equation in total mean that

3^k+1 > 3(k^4) = k^4+k^4+k^4

[median fable]

yep

[cunning condor]

kk

[pearl pond]

@median fable Has your question been resolved?

[pearl pond]

@median fable Has your question been resolved?

[median fable]

<@&286206848099549185>

[pearl pond]

@median fable Has your question been resolved?

[pearl pond]

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[cunning condor]

hmm

[regal herald]

its not worded well but i assume so

[cunning condor]

wait

so while sorting the 26120 pennies they found another 289?

[regal herald]

yeah thats whats confusing

[cunning condor]

what does 1960 have to do with anything?

[regal herald]

exactly

[cunning condor]

tf lol

american pennies dont differ their value based on minted year though

do they?

unless its like another design from that much time

[regal herald]

i dont think it was meant to be read into this much

[cunning condor]

assuming the problem wants us to add the newly found pennies

[regal herald]

,calc 26120+289

[jolly parrot]

Result:

26409

[cunning condor]

mrs ciao has 26409 pennies

yes

[regal herald]

[cunning condor]

is 26409 not the answer?

problem solved then (???)

yup

what

youre not supposed to know the answer to a question before you solve it

wtf

yes assuming youre in 2nd or 3rd grade maybe even 1st

you're in a very low grade I see

anyways

problem solved

remember to .close

just .close

you solved it

[pearl pond]

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[fringe rune]

hi

[fringe rune]

been stuck for ages hekp will be appreciated

[pearl pond]

@fringe rune Has your question been resolved?

[spice peak]

does the question gives you A and B ?

[warm current]

You don't need them

[limber glacier]

A is a point on the x axis

what can u say abt its coordinates

[pearl pond]

@fringe rune Has your question been resolved?

[fringe rune]

uh tried subbing in x=0 and solve to get one variable

always 0=0

[fringe rune]

nope

[spice peak]

You can let A(m,0) and B(0,n) to solve

[pearl pond]

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[pearl pond]

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[elfin stirrup]

Hey i have an old exam multiple choice question

[wet osprey]

Use a new channel

[elfin stirrup]

Oh ops mb

[pearl pond]

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[crude crown]

Simplify 6(a - 2) - (2x - 1) = 2

Pls help I’m dying

[cursive fulcrum]

!status

[pearl pond]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[toxic lichen]

dying?

gunpoint or cancer?

@crude crown

[crude crown]

Nah maths point

[toxic lichen]

are you about to die of disease or is somebody intending to murder you

or were you not serious when you claimed to be "dying"

in any case... i must ask: are you sure you copied the problem correctly?

as-is, that's an equation in two variables.

maybe that was intentional.

[crude crown]

Are u gonna help me?

Or some random dude

[toxic lichen]

i do want to help you, but i also want to know for sure there's no copying errors in the problem

otherwise we're gonna have a bad time

[crude crown]

Nope no errors

6(a - 2) - (2x - 1) = 2

[toxic lichen]

should we understand that you have no idea where to begin?

[crude crown]

Pretty much

[toxic lichen]

copying errors on not, a good first step would probably be to expand the parentheses on the LHS.

@crude crown did you do this ^

[crude crown]

So basically like

[toxic lichen]

"yes, i did it" "no, i didn't do it" or "i got stuck"

[crude crown]

I did it

But I feel like@it’s wrong

[toxic lichen]

then show us

[crude crown]

6a - 12 - 2x + 1 = 2

[toxic lichen]

so far so good.

did you do anything else?

[crude crown]

Yea add like terms

So

-12 + 1

Equals to 11

6a - 11 - 2x = 2

[toxic lichen]

-12 + 1 is -11, not 11.

[crude crown]

Oh I forgot the sign

[toxic lichen]

may be more of an even-number-of-mistakes thing in this case, since you did rewrite -12 + 1 as -11 despite not having said it,

but ok, so now you have 6a - 2x - 11 = 2

did you do anything else after that

[crude crown]

6a - 2x is not possible

Not like terms

So

Idk what next

why did u put -11 after 2x

[toxic lichen]

why did u put -11 after 2x
aesthetics.

[crude crown]

so it doesnt natter?

[toxic lichen]

of course it doesn't matter.

it's just that i don't like having a constant term placed between two variable terms, generally.

[crude crown]

oh

[toxic lichen]

whatever way you wish to shuffle the terms around, now i would add 11 to both sides.

[crude crown]

when u say both sides do mean 6a + 11
2x + 11?

and why not -11

why positive

[toxic lichen]

when u say both sides do mean 6a + 11
2x + 11?
no

i mean going from
6a - 2x - 11 = 2
to
6a - 2x - 11 + 11 = 2 + 11
and simplifying by additive cancellation to
6a - 2x = 13

[crude crown]

why isnt it
6a -2x -11 +11 = 0

i ask alot cause i want to learn so bear with e pols

[toxic lichen]

why'd you rip out the right-hand side and replace it with zero...?

[crude crown]

cause how did the 11 come to right side

[toxic lichen]

i mean going from
6a - 2x - 11 = 2
to
6a - 2x - 11 + 11 = 2 + 11

i added 11 to both sides.

[crude crown]

OHHH

so then we have 6a - 2x = 13

what about 6a and 2x

[toxic lichen]

well now there is nothing we can do, or so it appears.

at this point, we might be done, but i'd like to see the instructions for the problem as they were originally written.

[crude crown]

what

u want to see my working?

[toxic lichen]

no