help-38

[stiff girder]

k so

[split chasm]

the value of x is what you're trying to find
which you'll get upon applying the distance formula

[stiff girder]

Distance formula = sqrt((x1-x2)^2+(y1-y2)^2)

correct?

[split chasm]

and solving

[delicate bobcat]

$\DistanceBetweenTwoPoints$

[solid kiln]

Modus

[stiff girder]

ah-

[stiff girder]

ok so yes its this right?

[stiff girder]

Thank you!

I enter the value of y as 0

[delicate bobcat]

x1 - x2 and y1 - y2 also would be ok

since we have square

[stiff girder]

since

[split chasm]

the y coord of the point you're trying to find will be 0, yes

[stiff girder]

but what would be the values for x? would they just be 7 and 3?

or wait

would it be x and 7

and then we would do the same thing for x and 3?

[split chasm]

distance between A(3,4) and P(x,0)

distance between B(7,8) and P(x,0)

[stiff girder]

ohhhh okay okay

so the result of x would be the point at which they would be equal

im confused as to how that works out.. but I think the question has been answered

Thank you so much Ramonov!

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[balmy wolf]

if its not realy a mathproblem its okay if not be answered but i give it a shot.
Its from regulation technology

I have given U0/U1 = 70*(s-200)/((s-5000)(s-7)) how does the Block diagramm looks like?

I have no idea how to start because i dont see any "normal" form that i can see in my tables

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[wise dagger]

hmmm.... i have no experience on regularion technology
what is U0, U1, s, Block Diagramm and "normal" form that you are looking for?

[balmy wolf]

yeah ok, than you have to jump completly into this topic because of me..
you can close the question.

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[sterile dew]

For an RSA modulus N=1,040,399 = pq = 1019*1021, what is the e-th root for e=23 of the ciphertext c=35,346?

Can someone please explain this?
I have calculated d to be 496,607 and the group order is 1,038,360

However i am not sure how to calculate the e-th root in my notes it says "Raising the argument c with d mod N yeilds the eth-root." However this does not give me the correct asnwer

The correct answer is supposed to be 361,406

[sterile dew]

any help would be appreciated to explain how to get that answer

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[sterile dew]

Anyone have any advice?

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@sterile dew Has your question been resolved?

[marble wharf]

https://i.imgur.com/yTUqXXU.png

what exactly is the problem?

did you typo somewhere?

[sterile dew]

@marble wharf oh weird sagemathcell gave me a different answer

any idea how to do this on a normal calculator?

[marble wharf]

well depends on what you count as a normal calculator

I wouldn't expect most calculators to be able to do this

[sterile dew]

like a scientific calculator, eg casio fx-85

[marble wharf]

no clue if that has it implemented. look it up in the manual I guess

or otherwise you can do it manually I guess. with the binary representation of the exponent

but that is painful

[sterile dew]

this has a different answer which is why i was confused

[marble wharf]

why are you doing ^^

sage has ^

https://i.imgur.com/dUoDjba.png

[sterile dew]

ah damn lol

thanks

[marble wharf]

not sure what ^^ does

but clearly the wrong thing

[sterile dew]

yeah lol

to do this 'manually' I could break down the powers somehow to simplify it?

[marble wharf]

as an example, to calculate 37^50 mod 290 or something, you can first calculate 37^25 mod 290 and then square the result

and to calculate 37^25 mod 290 you first calculate 37^24 mod 290 and then multiply by 37

and then for 37^24 mod 290 you can square 23^12 mod 290

etc

so in general you only need roughly log_2(exponent) steps

which is not too bad

and how in general a^b mod n is implemented

[sterile dew]

right, but what about for a much larger example?

[marble wharf]

pain

[sterile dew]

I see

[marble wharf]

but well in principle the same thing

[sterile dew]

alright thanks

[sterile dew]

@marble wharf sorry to tag

We are doing modular arithmetic modulo the prime number p=1009.

What is the multiplicative inverse of 97 (mod 1009)?

Do you think you could explain how to do with fermat little theorum?

I tried with eea but got 5

the answer is supposed to be 957

[marble wharf]

I mean then you fucked up eea

by flt you know that 97^1008=1 mod 1009

so 97*97^1007 = 1 mod 1009

so 97^1007 is the inverse

[sterile dew]

hmm but i don't think i did
using an eea calculator i got
https://www.extendedeuclideanalgorithm.com/calculator.php?mode=1&a=1009&b=97#num

thes same answer

[marble wharf]

https://i.imgur.com/171vbmn.png

you are misinterpreting the result

the important number is t=-52

=957 mod 1009

you have to pay attention in which order you put a and b

[sterile dew]

sorry how does -52 give that?

[marble wharf]

-52=957 mod 1009

[sterile dew]

I see, normally when I do eea I get the answer straight from that

any idea why had to do an extra mod this time?

which is why I had assumed hte answer was 5

[marble wharf]

you used the wrong order

1009 first, 97 second

that means the first coefficient belongs to the 1009 and the second to the 97

and well, getting negative numbers from EEA happens quite regularly

[sterile dew]

I see, so whenever you get an negative number have to do that extra step?

[marble wharf]

well you don't have to

it's also perfectly fine to say that -52 is the inverse of 97

it's a bit like saying that $\frac{-1}{-2}$ is the inverse of $2$. not false, just maybe not the most standard form

[solid kiln]

Denascite

[sterile dew]

I see, makes much more sense now thank you

[sterile dew]

last thing, you think you could explain this step?

[marble wharf]

97^1008=1 mod 1009, yes?

[sterile dew]

Yes

[marble wharf]

and by basic exponent properties, 97^1008 = 97 * 97^1007

yes?

[sterile dew]

yeah, but how did you know to do that

[marble wharf]

just the classic trick to calculate the inverse using flt

[sterile dew]

reducing the power by one?

[marble wharf]

well noticing that if a^k=1, then a*a^(k-1)=1. which is now the product of a and another element

[sterile dew]

I see, its always by one?

[marble wharf]

well yes otherwise it would not be the product of a with another element

if a*something = 1, then something is the inverse of a

[sterile dew]

right

thanks again

Sorry to be a pest @marble wharf
Can you spot my mistake? Getting -2 instead of -52

[marble wharf]

why are you not plugging the 39 in?

and that's ignoring the very shit notation of writing gcd(1009, 97) = 10 remainder 39

[sterile dew]

lol
ah yeah I see that gives me the -52

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[late merlin]

How do I find this limit?

[minor shadow]

have you learnt l'hopitals rule?

[late merlin]

I haven't

[minor shadow]

thats odd this seems like it was made to solve it with l'hopital

[whole coral]

Well you could multiply by 3/3 I guess?

[late merlin]

Oh - l'hopital rule I think is next unit, this is probs a challenge problem, is there another way to solive it?

[whole coral]

Then sub for a standard limit

[late merlin]

Why 3/3?

[haughty oasis]

t = 3x+6

[whole coral]

Get $3\frac{\sin(3x + 6)}{3(x + 2)} = 3\frac{\sin(3x + 6)}{3x + 6}$

[solid kiln]

chartbit

[late merlin]

OH I SEE tysm!!!

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[late merlin]

I graphed this using Desmos and apparently the limit is 1/6
I thought it would be negative infinity, since the "denominator" is like x to the power of 0, but the numerator has x to the power of 1? So that would make the limit infinity, and since the question is asking for as x approaches negative infinity then the limit would be negative infinity? Which part did I do wrong?

[fresh pecan]

multiply by $\frac{3x - \sqrt{9x^2-x}}{3x - \sqrt{9x^2-x}}$

[solid kiln]

Gijs

[late merlin]

Oh, I did not . think of that, ty for the help!

[whole coral]

Might also help to note that $\sqrt{x^{2}} = |x|$ as well

[solid kiln]

chartbit

[late merlin]

Ah right, ty!

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[thorn wasp]

How can I prove that these representations are not isomorphic?

[thorn wasp]

I tried proving that they have different character but the characters actually turn out to be the same

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[thorn wasp]

On another note, how can I express the permutation (1 2) as a product of even permutations from A_4? Is it possible? If so, how?

<@&286206848099549185>

[quartz yoke]

well i cant help with the first one but

[quartz yoke]

lets have a look at this

(12) is already in A_4

can you see why

[thorn wasp]

No?

I thought this is an odd permutation so cannot be in A_4

[quartz yoke]

wait crap lmao

yes it is odd

I really should be going to sleep

let me think for a bit

yes ok

S_2 is isomorphic to A_4

or rather

a subgroup of A_4

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[lunar lance]

.help

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[lunar lance]

.reopen

[austere echo]

can somebody help me with this question, what form of integration would be the best approach

[austere echo]

the limits are pi/8 and 0

[dusty hound]

undeniably u-sub

[austere echo]

ty

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@wraith hinge Has your question been resolved?

[pastel prairie]

Is there a specific step you're unsure about?

So first it's just adding AD and AB which gives you AC right

does that part make sense ^

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[cunning fox]

/close

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[azure moon]

I found v(t) by integrating a(t). I solved for C by plugging the starting value v(0)=2, but my answer doesnt match any of the choices

[wraith hinge]

you need to find p(t)

so repeat the same steps

[azure moon]

oh makes sense

thanks

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[wraith hinge]

Help

[zinc ginkgo]

now ask your question

oh you asked in the other channel

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[split dew]

Does the top equal the bottom?

[split dew]

The n would be 20 of course

[digital bison]

doubt it.

how did you get that they were equal?

[split dew]

K^2 is what I wrote over 6

[digital bison]

right.
the 20 is inside the power, but is still only 20 in your final
and (k-1)^2 isn't the same as k^2 - 1, so you can't bring the sum inside of the square.

[split dew]

Ahhh so I just need to square those?

The 20 and the -1?

[digital bison]

you for sure need to square the 20, which you can then bring outside of the sum

but then what you have is the sum of (k-1)^2

[split dew]

Do I not just square the one and then do the special sum of k?

[digital bison]

no. (k-1)^2 is not the same as k^2 - 1

[split dew]

So how would it be done

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[digital bison]

note that $\sum_{k=1}^{20}(k-1)^2 = \sum_{k=0}^{19}k^2 = \sum_{k=1}^{19}k^2$

[solid kiln]

Zybikron

[split dew]

The 1 doesn’t change anything then? Oh wow

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[zinc ginkgo]

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[rare lance]

Have I done this right?

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[rare lance]

<@&286206848099549185>

[rare lance]

.close

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[agile prism]

\how do i do this

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[solid kiln]

Stephen

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[sturdy hare]

So I have the following issue

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[sturdy hare]

Going from our original equation to the first step where we multiply both sides by the integrrating factor.

How is it that e^-4x*(-4)y = (e^-4x*y)dy/dx

where does the -4 go in the original equation?

[eager juniper]

what ? write in latex plz x) I don't understand

or put a \ before a *

[sturdy hare]

Sorry, I don't understand how to use latex - I am trying to figure it out now.

[eager juniper]

ok wait

[sturdy hare]

I just want to know how the left side of the equation comes to be at step 1

[eager juniper]

$(e^{-4x} y)' = y'e^{-4x} - 4 e^{-4x} y$ you agree ?

[solid kiln]

Silfer

[sturdy hare]

is this the reverse product rule?

[eager juniper]

no

just $$(uv)' = u'v + v'u$$

[solid kiln]

Silfer

[sturdy hare]

oh, I thought that was the product rule

but that is what I was thinking in my head -

okay, thank you, I will close.

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[wary wraith]

So I'm doing Kahn Academy average value of a function over a closed interval and I'm really confused on how they simplified this to ln(2). Any help appreciated...

$$ln(8)-ln(4)$$

[solid kiln]

Stephen

[stoic iron]

$\ln(a)-\ln(b) = \ln(\frac ab)$

[solid kiln]

ΣAC

[wary wraith]

Are there any articles I can do to understand this rather than memorize it? I was going to calculate each of them and would get this problem wrong on a test

[stoic iron]

"logarithm laws/rules"

google is your friend

[wary wraith]

Okay thanks!

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[quaint kettle]

Is this one correct?

[haughty oasis]

looks good

[quaint kettle]

ty

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[grand parcel]

Did I get this right

[grand parcel]

one with the colored points is my work

textbook one is answer

yellow is the final one

this is the question I had to graph $y=\sqrt{-2x+6}+1$

[solid kiln]

Zyme><SOL

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[grand parcel]

<@&286206848099549185>

.close

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[grand parcel]

.reopen

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✅

[grand parcel]

.close

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[wary sparrow]

In the diagram, each small square is 1 cm by I cm. Determine the area of the shaded region.

[wary sparrow]

How would I go about solving this?

[reef nimbus]

area of tringle is bh/2

[wary sparrow]

So

the angle is like

tilted thoug

@reef nimbus Can you help me

[worldly wing]

that doesn't matter

[reef nimbus]

b = 2 and h = 3

[wary sparrow]

The area of square ABCD is 64. The midpoints of its sides are joined to form the square EFGH. The midpoints of its sides are J, K, L, and M. Determine the area of the shaded region.

[reef nimbus]

if you are unsure, you can draw it into the two right triangles

[wary sparrow]

Nevermind i got it

thanks

[wary sparrow]

How about this?

[reef nimbus]

Do you know the formul for the area of a trapezoid

[wary sparrow]

no

[reef nimbus]

Do you want to just use the formulas for area of triangles and rectangles

how do you wnt to split up the area

[wary sparrow]

which one is easier/simpler?

[main sigil]

You can think about this example like this: You can cut the triangle to small pieces, and move them to right

[wary sparrow]

i would say split up the area

[wary sparrow]

ahh ok

[reef nimbus]

It would probably be easier to find the aera of a trapezoid and then multiply it by 2

[wary sparrow]

how do i find it

[reef nimbus]

So you do (1/2)(bottom side + top side)(height)

So do you know what the length of the line segment EG is

[wary sparrow]

isnt is 8

[reef nimbus]

Yes

And do you know the length of JK

[wary sparrow]

4?

[reef nimbus]

Yes

And do you know the height

[wary sparrow]

also 4

[reef nimbus]

The height of one trapezoid

Like the blue line

That height should be 2

Because it is half of AE which is 4

[main sigil]

Here is a hint for finding volume of trapezoid using height and base lengths

[reef nimbus]

So the area of one trapezoid is (1/2)(8 + 4)(2), which is 12

So the area of both trapezoids, or the whole figure, is 24

[wary sparrow]

its 24 right

.close

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[peak cave]

Could someone guide me through the process of simplifying this?

[cunning cliff]

difference of squares, laws of indices

[peak cave]

ill give that a try thank you

[cyan zinc]

Use equivalent fractions

[peak cave]

idk what im doing tbh ...

Can i write it like this ?

@cyan zinc ??? @cunning cliff ???

[cunning cliff]

pl don't ping

[peak cave]

Ok sorry

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[sand hull]

what does this mean

pls help

[night zodiac]

Need more context

[cunning fox]

show the full photo

[night zodiac]

There are ratios involved

[rugged latch]

the answer is always aunt jemimas

[sand hull]

this makes no sense

how

ok

[cunning fox]

wth

[sand hull]

i hope its B

[night zodiac]

What was question 1?

[cunning fox]

what are the options supposed to mean?

[night zodiac]

I mean part a

[sand hull]

HOLY SHIT

WHATTTTTTT

[night zodiac]

Lucky guess

[cunning fox]

WTH"

[night zodiac]

It was based on part a

[cunning fox]

clap clap

[night zodiac]

What was part a?

Because it is based on that

[sand hull]

ohhh

[cunning fox]

bruh

[sand hull]

i didnt see part a lmao

[cunning fox]

how tf you on 2b if you didnt see 2a

[sand hull]

i skip around

[cunning fox]

BRUH

[night zodiac]

Part b was based on that chart

[sand hull]

yea ik now

[night zodiac]

If you actually did part a, you would have realized that the percent of sugar in syrup B would be the highest

[sand hull]

yea ik

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[clever folio]

can someone help me to solve them?

[vagrant marsh]

!status

[trim jolt]

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

[clever folio]

I did this for b but i'm not sure if its same for x as well

i dont know how can i find the area and region

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[clever folio]

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[lavish kite]

Hi is there a simpler way to do this one pls?(with riemann sum too)

[lavish kite]

I’m supposed to find 16, but I found 120 for the limit; I guess I made a small mistake due to the length of the calculations

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[lavish kite]

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[hazy light]

Find the number of zeros at the end of 99!

[hazy light]

The highest power of p in n! is,
$$\left[\frac{n}{p}\right]+\left[\frac{n}{p^2}\right]+\dots+\left[\frac{n}{p^r}\right]$$

[hazy light]

where p^{r} ≤ n ≤ p^{r+1}.

How do I use this fact to get the answer?

[trim lichen]

10=2*5

the number of zeros at the end of a number is the exponent on 2 or on 5 in its prime factorization, whichever is less.

[hazy light]

I forgot to mention [•] denotes the greatest integer function, anyways.

[hazy light]

Can you elaborate on this?

I don't understand

[drowsy knoll]

we are looking for factors of 10 in the factorial right

[trim lichen]

the number of zeros at the end of 2^m * 5^n * (number coprime to 10) is min(m, n)

because 10^min(m,n) is the highest power of 10 by which said number is divisible

[hazy light]

Understood.

[hazy light]

Just out of curiosity, does this thing have any special name?

How can one prove this?

[trim lichen]

it happens to have a name: legendre's formula

and it can be proved by means of a counting argument

[hazy light]

I'll study more on it.

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[amber badger]

I'm writing it out

one sec, please

for the first example:

f(x) = sin x (i don't know why x isn't written for sin x here ?)

g(x) = $x^2$

[solid kiln]

Willow

[amber badger]

i take the derivative of f(x) and multiply it by g(x) and then multiply that result by the derivative of g(x)

yes?

[formal depot]

you take the derivative of f(x) with g(x) (underived) still inside, then multipy that by g'(x)

[amber badger]

$\frac{dy}{dx} \sin x^2 = 2x \sin x$

[solid kiln]

Willow

[amber badger]

this is the normal method without the Chain Rule

[formal depot]

do remember that this is sin(x^2) not (sinx)^2

so we take the derivative of sin(x) which is cos(x), replace x^2 for x, then multiply that by derivative of g(x) (x^2) which is 2x

[amber badger]

yes, I thought it should be written $\sin x x^2$

[solid kiln]

Willow

[amber badger]

or maybe $x^2 \sin x$

[solid kiln]

Willow

[formal depot]

no, I think it written right in the whiteboard example, just some parentheses would avoid confusion

[amber badger]

but is $\sin x x^2$ incorrect?

[solid kiln]

Willow

[formal depot]

that would just be sinx^3, and that is incorrect

[amber python]

[amber badger]

$\sin x (x^2)$

[formal depot]

^^^

[solid kiln]

Willow

[amber badger]

$(x^2) \sin x$

[solid kiln]

Willow

[formal depot]

$\2x cos(x^2)$

bruh 2x in front

bot buggin

[solid kiln]

lamp
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[formal depot]

yea it just causes confusion

put the products infront

or use parentheses

[amber badger]

I don't think this is clear

let's return to the rule

for $\sin x^2$, the form f(g(x)) doesn't seem applicable

[solid kiln]

Willow

[amber badger]

why?

because there isn't anything for $x^2$ go inside of

[solid kiln]

Willow

[formal depot]

x^2 goes inside sin

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[stable totem]

what do i do for ii)

what should i try

[trim jolt]

@stable totem Has your question been resolved?

[amber python]

try to bound the integral from above

[stable totem]

i sovled it

[zinc ginkgo]

.close if you're done

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[amber badger]

What's u here in something like $\sin^2x$?

[solid kiln]

Willow

[amber badger]

also, what would be f and g ?

[wraith hinge]

cz sin^2 x is = (sin x)^2

one func is the trig func
and other is the exponential func

[amber badger]

so, what's u there?

[wraith hinge]

sin x?

btw

to understand this better; try proving this.

[amber badger]

what would be f and g ?

[wraith hinge]

y = x^2 ;; u = sin x

f(U) = U^2

g(x) = sin x

.

[amber badger]

this is really difficult to understand!

[wraith hinge]

well

how abt trying to differentiate sin^2(x)

can u do it?

[amber badger]

dy/dx sin^2x = 2sin

[wraith hinge]

huh

no

check this out

[amber badger]

here is my note from class

these three seem simple

[wraith hinge]

that is sin (x^2)

I am telling sin^2 (x)

[amber badger]

just break them all up into f, f', g, and g'

and then, match them up

[wraith hinge]

go thru this step by step check if it makes sense

cz this way is more logical

[amber badger]

my problem is I don't see how to break up sin^2 x

[wraith hinge]

(sin x)^2
one func is the trig func
and other is the exponential func

[wraith hinge]

does this make sense tho...

[amber badger]

it doesn't make sense until I can figure out what f and g are

i think $\sin^2(x)$ may just be f = $\sin x$ and g = $\sin x$

[solid kiln]

Willow

[wraith hinge]

no

that wud be product rule then

and not chain rule

[amber badger]

then, i don't understand

i hate this!!!

[wraith hinge]

u need to realize that fx is a composite function

which is what gives F'(x)=f'(g(x))(g'(x))

[amber badger]

can you please break down $\sin^2(x)$ like my teacher did in the pic above?

[solid kiln]

Willow

[wraith hinge]

look

thing is in sin (x^2)

it is visible

very clearly u can see the 2 functions ingrained in each other

[amber badger]

so, clearly marking f, f', g, g'

[wraith hinge]

that there is a sin (u) and where u = x^2

agree??

[wraith hinge]

okay

[amber badger]

yes, I can see this and I said such here:

#help-38 message

[wraith hinge]

no thats the same function

[wraith hinge]

not 2 different and nor ingained functions

[amber badger]

so, clearly marking f, f', g, g'

I'll wait for this, then.

hopefully, that will clarify this more

but I really think this is true:

#help-38 message

because this explanation matches the answer, which is 2 sin x cos x

[wraith hinge]

g(x) = sin(x)
sin(x)2 = g(x)2

So if the function f(x) = x2 and the function g(x) = sin(x), then the function (sin(x))2 can be written as a composite function.

f(x) = x2

f(g(x)) = g(x)2 (but g(x) = sin(x))

f(g(x)) = (sin(x))2

Let’s define this composite function as F(x):

F(x) = f(g(x)) = (sin(x))2

We can find the derivative of sin^2x (F'(x)) by making use of the chain rule.

Chain Rule :: If F(x) = f(g(x))
Then the derivative of F(x) is F'(x) = f’(g(x)).g’(x)

F'(x) = f'(g(x)).g'(x) = f'(g(x))(cos(x))
= (2sin(x)).(cos(x))
= 2sin(x)cos(x)

---

all the 2's are powers except for last 2 lines

[amber badger]

this doesn't make sense to me and seems complicated

why not simply write f, f', g, g'?

[wraith hinge]

well u asked for it :/

[wraith hinge]

thats literally wat i did......

[amber badger]

I only asked for f, f', g, g' as listed in the pic I posted

not all that

[wraith hinge]

ok

[wraith hinge]

f = x^2 ; f' = 2x ; g = sin x ; g' = cos x

.....

..

[amber badger]

wait, I'm matching the answers

ok!

got it!

$2x \sin x \cos x$

[solid kiln]

Willow

[amber badger]

see! this matches exactly the form that my teacher used!

when analyzing the pictures I posted, all you need to solve the problem is f', g, and g'

multiply them together and that's the answer

that's why I kept asking for those four values

that's the pattern required (for me) to solve Chain Rule problems

so, the takeaway from this is whenever I encounter Chain Rule problems with a seemingly single variable like $\sin^2x$, I have to remember that the exponent is a variable in these cases

[solid kiln]

Willow

[amber badger]

and I know you mentioned this at least twice, but it wasn't clear in my mind what you meant by that

#help-38 message

but at any rate, now that that's solved, let's look at the General Power Rule

i think the exact same strategy of always figuring out g and g' FIRST applies here also

[wraith hinge]

........yes

[wraith hinge]

.this is still by far the best and easiest way ngl imo

[amber badger]

for #6 above, I have to be able to recognize that the two "functions" here (for lack of a better word) are the sq root symbol which is x^1/2 and x^2+1

it really is f and g

although the theorem only uses g

.close

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[wraith hinge]

.open

[unreal lark]

How would u solve this

[wraith hinge]

think how multiplication works

[unreal lark]

??

[wraith hinge]

(10x + y)(10 x + y)

expand

[unreal lark]

100x^2 + 20xy + y^2

[wraith hinge]

hmm

isnt 76 the only number that wud work here

[unreal lark]

Did u just guess and check that

How did u figure it out

[wraith hinge]

hmm

[zinc oasis]

there are only 4 ones digit number which gives same one digits numbers

0,1,5,6

[wraith hinge]

what ur looking for is : y^2 has same last digit as y

yes

[unreal lark]

What does this mean

My brain isn’t loading

[wraith hinge]

.

[unreal lark]

OHH

OOHH

OOOHH

OOOOHHH

OOOHHH

[wraith hinge]

[zinc oasis]

like put y in y^2 as 0,1,5,6

[wraith hinge]

i love that feelng

[zinc oasis]

when you put y=0

[wraith hinge]

wen u feel like wow u get it lol

[zinc oasis]

20x(0) also becomes 0

while the 100x^2 will not interfere with the 10the digit

[unreal lark]

How do u get 72 tho from that

[wraith hinge]

76*

[wraith hinge]

go on

[unreal lark]

Wait I have a question

[wraith hinge]

wanted her/him to figure it out step by step tho but anyw.

[zinc oasis]

what is this smile

[unreal lark]

How do u know y^2 has same last digit as y

[wraith hinge]

read the q

[zinc oasis]

as it does not have any multiple of 10s

It is the nature of numbers

[unreal lark]

Oh wait yeah

[wraith hinge]

its cute smile

[zinc oasis]

11 is 10(1)+1

[unreal lark]

How do u figure out it’s 72 tho

Oh 76

[wraith hinge]

wait

uh

[zinc oasis]

just take y=6

[wraith hinge]

doesnt 25 also work

[zinc oasis]

yes

[unreal lark]

Yea that’s the answer 😭😭

[wraith hinge]

lol

[unreal lark]

76 and 25

[wraith hinge]

yes

W

[unreal lark]

But idk how to get there

[wraith hinge]

niceee

dude 0,1,5,6 ; 0,1, wont work cz of the tens digit rule of expandsion explained by Mr.Garuda

[zinc oasis]

It is the way Told above

[unreal lark]

???

[zinc oasis]

if you take y=5

y^2 comes 25

20(x)(5)=100x

so it won't interfere with 10th digit thus

25

while in 6 6^2=36

[unreal lark]

Uh huh

Ohhh

Wait

I only get small part

[unreal lark]

What is this mean to mean

Meant

[zinc oasis]

.

just put value of y in second term of the expansion

[unreal lark]

What is 10th digit ?

[zinc oasis]

you don't know ones digit

10th digit

100th digit

it is the position of digit

like in 123

3 is ones digit

2 is tenth digit

[unreal lark]

O Right

[zinc oasis]

1 is hundreth digit

[unreal lark]

How does this show that it I won’t interfere with tenth digit

[zinc oasis]

2(100) is

will it add to tenth digit

[unreal lark]

Oh it doesn’t

[zinc oasis]

can there be any number multiplied with 100 which will add to 10th digit

[unreal lark]

Ohh I get it

[unreal lark]

Wht does that prove?

[zinc oasis]

first try everything I told on paper

I am literally mouth feeding

[unreal lark]

ALR

alr*

[unreal lark]

If y squared equals 25 then what’s x? Like what happens to the 100x^2 + 100x

[zinc oasis]

it is not needed in question

but to make x equal you only have a choice of 2

the thing is no mater which value you chose for x answer will always be 25

so to make it equal chose 2

[unreal lark]

Hm ok so then with the 6 it becomes 36 but how do u end up w 76

[zinc oasis]

just repeat the same process

10(x)(6)=120x

now we know that 2x+3 must have ones digit equal to x to statisy our condition

[unreal lark]

Whr did the 12x+6 come from

[zinc oasis]

6^2 is 36

take 3 carry

12x comes from 120x

[unreal lark]

Wdym by this statement and also y did u change it to 2x+3

[zinc oasis]

yup

just write it

120x+30

100x+20x+30

as I am focusing on 10th digit I will ignore 100x

20x+30

as it is tenth digit I will divide it by 10 so

[unreal lark]

Hold up whr did the 30 come from

[zinc oasis]

36=30+6

atleast think something bro

[unreal lark]

💀

[zinc oasis]

any question

[wraith hinge]

hi

is this still going on the same question or a new question?

[unreal lark]

Same question

[wraith hinge]

just had my breakfast.

[wraith hinge]

wow

I- am speechless but ok

[zinc oasis]

36=30+6

[unreal lark]

Lol

[zinc oasis]

so 30 came from there

[unreal lark]

Why did u break it up tho

[zinc oasis]

what same question

isn't it is clear

becuase we are talking about tenth digit

6 is in ones digit

[unreal lark]

O

[zinc oasis]

does 6 has any effect on ones digit

[wraith hinge]

to satisfy the format of 100x^2 + 20xy + y^2 ;; we can ignore the 100x^2 ;; we need other digits and we alreday know y = 6/

[wraith hinge]

u mean on the tens digit.

[zinc oasis]

yup

[unreal lark]

So we just need to find the 20xy?

[unreal lark]

Uh no

[zinc oasis]

oh yes

[wraith hinge]

...6 is the ones digit 😭

[unreal lark]

I meant like the tens

[wraith hinge]

okay :/

[unreal lark]

.

[wraith hinge]

ye

no effect

true

[unreal lark]

Right ok

[zinc oasis]

just review my explanation until now

[unreal lark]

What does this represent

[zinc oasis]

20xy+30

where y is 6

[unreal lark]

Ok so once I get 2x+3 how to get to 76

[zinc oasis]

you already have 6

you just need 7

[unreal lark]

So the 7

[zinc oasis]

2x+3=x

[unreal lark]

huh x=-3???

[zinc oasis]

just add 10

you could instead you trial

just try to keep number in place of x

and see whose ones digit is equal

[unreal lark]

O ok

Thx for ur help🙏

.close

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[grand walrus]

r=what makes f'(0) differentiable

[grand walrus]

I tried to use the definition but I failed

[dense breach]

find the derivative of x^r * sin(1/x) using any method

then look at the limit as x->0+ and x->0-

[grand walrus]

the I should use uv'+vu'

[dense breach]

yeah

[grand walrus]

u was f(x) and v was g(x) right?

something like this?

[sour quest]

Yes, it is correct.

[sour quest]

.

[grand walrus]

I am not good at lim can you show me how

[sour quest]

Just plug in 0+ and then plug in 0-.
You don't end up with any indeterminate form so that is just going to be normal calculations.

[grand walrus]

how should I approach the sin and cos?

[sour quest]

However, I do not think there is any one set value of r here.
@drowsy knoll was right. The derivative at x=0 will exist if r>1.

[sour quest]

sin and cos are always bounded so, even if we have a very large value inside sin and cos, their output will always be between [-1,1].

[grand walrus]

isn't the lim always going to be 0

since x is 0

it would be like 0+0

[sour quest]

Yeah.

[grand walrus]

so the lim x->0 from both sides =0?

then what comes next?

[sour quest]

Then that implies that the derivative at x=0 exists for all values of r except for r>1, I think. For any r less than or equal one rx^r-1sin(1/x) does not exist finitely.

Oh wait, it should be r>2

@grand walrus

[grand walrus]

why tho

I didn't understand the r>1 part

[sour quest]

We want this limit to exist finitely right.
So if r=2 then we have cos(1/x) which is not defined at 0.

And for any r<2 we have (cos(1/x))/x which is tends to infinity.

[grand walrus]

I understand

[sour quest]

The same happens for sin(x) when r<1.

[grand walrus]

I understand

thank you very much

have a good day

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[alpine folio]

Hi help?

[torpid depot]

[main sigil]

https://dontasktoask.com/

[alpine folio]

10th question) Mike has written A,B,C and D in this segment. The space between A and C is 12cm. And the space between B and D is 18cm. Whats the distance between the intersection of AB and intersection of CD

[alpine folio]

Ok

[alpine folio]

Ok did so

[trim jolt]

@alpine folio Has your question been resolved?

[formal sage]

Well let's call AB = x
BC = y
and CD = z

As the question hasn't given any further info other than
x + y = 12
and y + z = 18

We assume that we can rely on the picture

Based on the picture x < y
And also y < z

x + y = 12
$x < y \to y > 6$ (Because if it's equal to 6, then x = y. And if it's smaller than 6, then x > y)

[solid kiln]

rubicminer

[formal sage]

And now we use the same idea for y + z = 18

Based on picture:
$y < z \to y < 9$

[solid kiln]

rubicminer

[formal sage]

So now we know that:
6 < y < 9

Alr I thought I can make forward progress. But nothing comes to my mind rn

So maybe what I did can help others reach the answer (or maybe they know a better way)

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@alpine folio Has your question been resolved?

[lofty gate]

The distance between midpoint of AB and midpoint of CD is
$\frac{1}{2} AB + BC + \frac{1}{2} CD$

[solid kiln]

natsumi3hara

[lofty gate]

From the question, AC = 12 and BD = 18.
This can be broken down into:
AB + BC = 12 and
BC + CD = 18
Adding these two equations, we get:
AB + 2BC + CD = 30

Comparing this to the first equation, the solution to the distance between midpoints is just half of 30! Quite the tricky question indeed!

[alpine folio]

@lofty gate only way to solve this?

Its quite hard

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[waxen willow]

yo hello
given N rolls of a M sided die, whats the probability of at least X being rolled

[waxen willow]

like the sum

of the rolls

M^N is the total, I know how to calculate at least X for a single die, not sure how it works with multiple tho

[marble wharf]

quite a bit harder

[waxen willow]

aw

I was guessing the probability of not getting X would be easier to calculate because theres less posibilites

but thats math thats prolly not even easier

[marble wharf]

https://mathworld.wolfram.com/Dice.html

you can check here for the probability to hit exactly X

it's a bit of a mess

[waxen willow]

i do know how the get exactly X

in 1 roll tho

does this have X in multiple

lemme read rq

okay yeah thats gonna work i guess, thanks

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[near girder]

can someone help me with the process im having trouble

[near girder]

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[slender torrent]

Hey so I got all three equations of: x+y+z=48 ,0.05x+0.1y+0.25z=5.4, 0.1y=0.05x-0.55, and i combined the first two and eliminated z to get -0.2x-0.15y=17.4 so now I’m confused on what to do now thanks

[slender torrent]

or where did I go wrong

thanks

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@slender torrent Has your question been resolved?

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@slender torrent Has your question been resolved?

[hollow heart]

hmm

I can probably solve this using cheating linear algaebra

I'll do that and see if I can remember how to do substitution to make sure it's right

[hollow heart]

I got a different answer when I combined those two formulas:

The purple formula I got by multiplying 0.05x + 0.10y + 0.25z = 5.40 by 4

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[slender torrent]

.reopen

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✅

[slender torrent]

ok so how come we multiplied by 4?

[hollow heart]

When you're doing elimination to solve for z, you want both sides to cancel out.

Since 0.25 * 4 = 1, that means 1-1 = 0. BUT I have to apply the *4 on all of the other parts of the equation:

And then I can cancel out the z's

https://media.discordapp.net/attachments/908078008609431674/1067555258303250482/image.png

[slender torrent]

ah I get it now

Z is one 0.25 *4 1 makes sense

So is the third equation right I did?

then I can use the third to cancel my Y’s or no

[hollow heart]

I think -0.2x-0.15y=17.4 is wrong, sorry

[slender torrent]

oh no I meant the 0.1y=0.05x-0.55

[hollow heart]

No that's right

[slender torrent]

ah ok so I can use that to elimante the ys

And find x

[hollow heart]

Yup!

[slender torrent]

Thank u so much man

[hollow heart]

Sure, no problem!

Oh, real quick

[slender torrent]

Yea

[hollow heart]

Do you have a TI-84 calculator or better?

[slender torrent]

uh no

I use desmos

[hollow heart]

Ah, okay

I swear there's an emulator out there...

[slender torrent]

Is it that important to get the ti

I’m sure there is an emulator

That I can. Download if it’s needed

[hollow heart]

When I do these kinds of problems, I like to "cheat" using the RREF function. It's a linear algebra function that solves systems of equations for you basically

I don't remember the equivalent for desmos

[slender torrent]

yea this is the homework and the teach wanted work shown

[hollow heart]

I mean... you can do RREF by hand 😓
But it's nice because it's super easy to make mistakes and seeing it on the calculator can show you what the answers are so you can get it right faster

[slender torrent]

ah ok I will find an emulator

[slender torrent]

oh like a matrix

[hollow heart]

Yup

[slender torrent]

thanks I will find an emulator or get a calculator lol thank u for all ur help and tips

[hollow heart]

RREF is a linear algebra tool

Good luck!

[slender torrent]

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[tepid prism]

any tips for my first real analysis exam in 2 weeks?

[stoic iron]

practice

[drowsy knoll]

analyise 🧐

[zinc ginkgo]

don't use help for studying tips. go to #discussion

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[rare fox]

Is this correct so far?

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@rare fox Has your question been resolved?

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[wraith hinge]

How do I go about solving this

[slender shard]

A number whose cube root that results in a whole number will be of the type a^3n.

An example would be 2^3 and 3^3 which are 8 and 27 respectively.

Look at the factors of 144 and see if there are any cubed numbers among its factors.

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@wraith hinge Has your question been resolved?

[wraith hinge]

Oh alright

Thanks!

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[twilit whale]

can someone write integral cosx/(sqrt2x^3-5) into the answer thing i wanna know what the result is

[twilit whale]

idk the command

[night zodiac]

Google it

[night zodiac]

It uses wolfram alpha

[twilit whale]

it just says this

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[night zodiac]

You asked for the result, there's the result

[twilit whale]

first it said it ran out of compution time, then gave me some crazy answer with "i" and random ass letters

then it came up with this

and some websites said it cant be done

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[amber badger]

Why is two's complement not used when dealing with unsigned numbers?

[amber badger]

because two's complement is only used for negative numbers

yes?

[night zodiac]

Yes

[amber badger]

i feel this answer is too simple

am i incorrect here?

[night zodiac]

https://stackoverflow.com/questions/1125304/why-prefer-twos-complement-over-sign-and-magnitude-for-signed-numbers

[amber badger]

now that is detail

ty

[night zodiac]

The power of google

[amber badger]

yes, i wasn't using the correct search terms, i guess