help-33

[still temple]

2X is divisible by 6 meaning it will leave remainder 0

2X= 2*3Q +0

Divide both sides by 2

Hence the number is also divisible by 3

And as we know 6 is an even number that means the dividend is even and we know every even number is divisible by 2

[weary sage]

right. that makes sense algebraically but I guess I'm confused at how to get that into a proof-like format

[marsh citrus]

@weary sage Has your question been resolved?

[weary sage]

.close

[marsh citrus]

Channel closed

Closed by @weary sage

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[harsh pumice]

I need helping solving this significant figures problem. I keep getting the number wrong

[proper zodiac]

!status

[marsh citrus]

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

[harsh pumice]

3

[proper zodiac]

Do you have any work you can show

[harsh pumice]

no

i did it on my phone

and I'm typing on my computer

but the answer I got that's telling me it is wrong is 182.50

[proper zodiac]

You should be rounding it to an appropriate number of significant figures

Using the information in the question

[harsh pumice]

i dont know

I'll just use a sig fig calculator nvm

.close

[marsh citrus]

Channel closed

Closed by @harsh pumice

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[cold sequoia]

True or False question, write justification

"f(x) = x³+3 and g(x) = x³-4 are derivatives of the same function"

[cold sequoia]

Like I know it's false but idk how to say otherwise

Like how would I justify that without sounding like an idiot. Is it as simple as stating their antiderivatives or what

[crystal lintel]

yea that would work

two polynomials evaluate to the same thing at every value iff they have the same coefficients on all their terms

so the two families of antiderivatives will be disjoint

so what i mean is any polynomial function of the form $x\mapsto x^4/4 + 3x + c_1$ is not the same as any of the form $x\mapsto x^4/4 - 4x + c_2$

[elfin berry]

💜𝓁𝒶𝓎𝓁𝒶💜

[marsh citrus]

@cold sequoia Has your question been resolved?

[cold sequoia]

Oh alr ty

Gonna kill discord for not giving me notifs

[marsh citrus]

Channel closed

Closed by @cold sequoia

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[floral wraith]

why

[floral wraith]

.close

[marsh citrus]

Channel closed

Closed by @floral wraith

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[latent swift]

Problem:

[latent swift]

My working:

In a rectangle, each angle = 90 degrees, the opposite angles are congruent, and the angles are NOT bisected by the diagonals.

Thus:
Angle ADB + angle CDB = 90
Angle ADC = ADB + CDB = 90
Angle ADC = angle ABC
Angle CBD is congruent to angle CDB

90 = (7k+10) + (8k-55)
90 = 15k - 45
135 = 15k
Thus, k = 9.

Angle CDB = 8k-55
Angle CDB = 8(9) - 55
Therefore, angle CDB = 17 = angle CBD

Why I am confused: I got that angle CBD = 17 degrees, but the correct answer is 73 degrees??? Please explain to me what the correct answer is

[runic temple]

CDB != CBD

[latent swift]

So then how would I solve this problem?

[runic temple]

CBD=EDB

[sharp mortar]

The angles at all the corners are 90 degrees

[runic temple]

ADB*

[latent swift]

CBD = ADB?

is that what u meant

[sharp mortar]

Yea alternate interior angles

[latent swift]

ohh so i should just substitute k in for angle ADB

and that will be my answer?

[sharp mortar]

Yep

[latent swift]

ohh okay thank you so much! that really helped

[sharp mortar]

Np

[latent swift]

.close

[marsh citrus]

Channel closed

Closed by @latent swift

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[chrome jetty]

Hi How do i prove this

[charred jungle]

euler's formula

$e^{i\theta} = \cos(\theta) + i\sin(\theta)$

[elfin berry]

biggboy

[charred jungle]

and remember the parity of the functions sine and cosine

[chrome jetty]

wdym by parity

[charred jungle]

odd function or even function

[chrome jetty]

oh ok yea

but idk hwo to solve with that

[charred jungle]

can you write the numerator in the exponential form

[chrome jetty]

yes

dont u just make it cos(-5theta) + isin(-5theta)

so its like e^(-5itheta)

or something

[charred jungle]

for the denominator, sure

[chrome jetty]

oh lol thats the denom

oh ye

mb

numerator just e^5itheta

[charred jungle]

and plus 1

[chrome jetty]

yea

[charred jungle]

so $\left( \frac{1 + e^{5i\theta}}{1 + e^{-5i\theta}}\right)$

hm

[elfin berry]

biggboy

[chrome jetty]

yes

[charred jungle]

how would you go about "simplifying" this

[chrome jetty]

not too sure

[charred jungle]

hmm

[chrome jetty]

Do you know how?

[charred jungle]

I know the simplified form but can't come up with a way to derive it... 😥

[chrome jetty]

wdym simplified form

[charred jungle]

oh

just got enlightened

so let's take a simply-er form such as $\frac{1+e^x}{1+e^{-x}}$

[elfin berry]

biggboy

[charred jungle]

you can write the denominator as $1 + \frac{1}{e^x}$

[elfin berry]

biggboy

[charred jungle]

and take a common denominator

what would that be

[chrome jetty]

What do you mean common denom

like how do i get rid of the fraction?

[charred jungle]

$a + \frac{b}{c} = \frac{ac}{c} + \frac{b}{c} = \frac{ac+b}{c}$

[elfin berry]

biggboy

[chrome jetty]

oh

so like (e^x +1)/e^x

[charred jungle]

yes

so you are dividing $e^x + 1$ by $\frac{e^x + 1}{e^x}$

[elfin berry]

biggboy

[chrome jetty]

yes.

[charred jungle]

what would that yield to be

[chrome jetty]

dont u bring the e^x to the numerator

[charred jungle]

I guess you can put it that way, yeah

so what do we end up with

[chrome jetty]

e^x(e^x+1)/e^x+1

[charred jungle]

yep

you can simplify it further

[chrome jetty]

ye

so its e^x

[charred jungle]

yep

[chrome jetty]

oh wait damn

that works

then bring it to the power from the bracket

andit prove

shit bro thanks

[charred jungle]

it does

glad to help ya

[chrome jetty]

ye thanks so much

.close

[marsh citrus]

Channel closed

Closed by @chrome jetty

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[static grove]

i dont understand how to set up my intergral form the plot

<@&286206848099549185>

.close

[marsh citrus]

Channel closed

Closed by @static grove

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[bold pendant]

!help

[marsh citrus]

Please don't occupy multiple help channels.

[bold pendant]

A young golfer spent two third his weekly allowance playing mini-golf. He then
earned $7 by cutting the lawn. What is his weekly allowance if he ended the
week with $19?Write and solve an algebraic equation. Show how you would
check your answer.

[graceful garnet]

Let x be the weekly allowance

use appropriate math operations so that the final answer is 19

[bold pendant]

so

formula?

[graceful garnet]

form an equation

based on the information you have

[bold pendant]

i keep getting 18

(2)/(3)x+7=19

2/3x +7 = 19

right?

[graceful garnet]

wrong

your equation is wrong

[bold pendant]

what do i do?

[half rampart]

1/3x + 7 = 19

[graceful garnet]

no that’s Weng

[half rampart]

fuck

I'm dumb

sorry

[graceful garnet]

it’s 2x/3 + 7 = 19

[half rampart]

oh alr

[bold pendant]

im tryna look for value of X

and on calculator

it shows

18

.

[graceful garnet]

don’t type out the whole equation

solve it one by one

[bold pendant]

ok

can u gimme hand pls

im shaky rn

10 mins left

[graceful garnet]

no

[bold pendant]

until deadline

[graceful garnet]

is this a test,

?

[bold pendant]

no

its a work assignment

we hand in

at dedicated times

[graceful garnet]

<@&268886789983436800> can we help people with timed assignments

not exams

[proud ice]

I don't think that's a question you ping mods for

[graceful garnet]

then?

[proud ice]

(But I'm not a mod so what do I know)

You can help someone with a timed assignment. Technically everything is a timed assignment..

[bold pendant]

also

i have a question

is 36 correct

?

1/3x+7=19

[graceful garnet]

no

wrong

[bold pendant]

????

[bright jay]

It's mainly if it's academically dishonest, that's why you can't help with exams and stuff

[graceful garnet]

that’s not the answer

[bold pendant]

HOW

[graceful garnet]

okay

[delicate prairie]

the precise ruling is whether theyre expected to do the assignment alone

[graceful garnet]

Again you formed the equation wrong

[bold pendant]

no

[bold pendant]

BRUH

alright

A young golfer spent two third his weekly allowance playing mini-golf. He then
earned $7 by cutting the lawn. What is his weekly allowance if he ended the
week with $19?Write and solve an algebraic equation. Show how you would
check your answer.

2/3x

[graceful garnet]

you used x/3 just now

[bold pendant]

wrong?

[delicate prairie]

i mean if its 10min left, sorry that sucks but we cant spoonfeed ya

[bold pendant]

2/3x + 7 = 19???

[graceful garnet]

yes

now solve it

[bold pendant]

😮

OMG
ALR

18

ITS 18

W ME

W GUY WHO HELPED

[graceful garnet]

Type .close

[bold pendant]

nonoo

im not done

theres 1 more part to it

show how i would check the answer

how?

[proud ice]

You can put your answer into the word problem and see if it's consistent

[marsh citrus]

@bold pendant Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[analog pier]

If I have a value let's say 2.3 million m^2, how do I convert that to _ million m^3?

[whole hazel]

you can't?

[proud ice]

You can't change area units to volume units

[whole hazel]

thats like asking how do i convert 100 seconds into centimeters

[analog pier]

.close

[marsh citrus]

Channel closed

Closed by @analog pier

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[ionic owl]

I'm aware this needs to be simplified. But is this the correct way to plug f(x) into the difference quotient formula?

[ionic owl]

[f(x) = x^2 - x]
[f'(x) = \frac{((x+h)^2 - (x+h)) - (x^2 - x)}{h}]

[elfin berry]

dopediscorduser

[late geode]

missing the limit as h→0 if you're after the limit

the difference quotient itself is fine

[ionic owl]

Just looking for the difference quotient right now, thanks!

.close

[marsh citrus]

Channel closed

Closed by @ionic owl

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[misty ocean]

Why is the image in the bottom right the correct answer

[misty ocean]

Both of the lines are in the middle of the data
And non of those have a point touching the line
So technically, they are the same

[burnt abyss]

Yeah but point 0 has nothing to do with the data

It makes no sense starting there

[misty ocean]

So the line of best fit must be a decreasing line

It cannot start from 0

[burnt abyss]

Yeah

The line has to have a connection with the points

The line fron your answer has no connection with some points

[misty ocean]

Wait wdym

But neither of the line has connection to any points

[burnt abyss]

Yeah i dont mean that connection

1 sec

[knotty trellis]

Line of best fit is line, which has smallest sum of squared distances to all points

Here are the distances of points to the line

You can see that your line has much greater distances between the points and line

(distance is measured parallel to y-axis)

[misty ocean]

So even they look the same, the one with the smallest distance to the line is the real line of best fit

Am I right ?

[knotty trellis]

Mostly

[misty ocean]

Alr, tysm

.close.

[marsh citrus]

@misty ocean Has your question been resolved?

Channel closed

Closed by @misty ocean

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[scarlet quiver]

Start with differentiating the given function.

[oblique summit]

I DIFFERENtiated it

but when i do dy/dx = 0 i cant

divide by 0

so i just get an error

[scarlet quiver]

I see.

So, correct me if I am wrong

y'=(1-ln(x))/x^2

And we know that x^2 can't be zero. So only 1-ln(x) can be zero.

[oblique summit]

i got 1/x - lnx /x^2

but im not sure how to get what you got.

i differnetiated lnx to 1/x and then multiplied by 1

to get 1/x

[scarlet quiver]

Your derivative is wrong.

[oblique summit]

doesnt ln x differentiate to 1/x ?

[scarlet quiver]

It does. You probably used the quotient rule incorrectly.

[oblique summit]

1/x *x ?

[scarlet quiver]

No. Do you know how to differentiate anything that looks like this:
f(x)/g(x)?

[oblique summit]

yes. f'(x)g(x) - g'(x)f(x)

so the x's cancel

[scarlet quiver]

No, this is the product rule.

[oblique summit]

// g(x)^2

i know the quiotent rule i just learnt it today so im a bit rusty using it

[scarlet quiver]

Yes, this is the quotient rule. You are supposed to use the quotient rule here.

[oblique summit]

i got ahead of my self and also differentiated g(x)

1/x * x so the x's cancel

[scarlet quiver]

I guess, you can take it from here now.

Find the correct y' and then set it equal to zero. That will give you the value of x and that x will be our stationery point. To check it's nature, do the double derivative test.

[oblique summit]

im sturggling to get teh x values @scarlet quiver

in general i can always set the equation to 0 and solve for x but at the minute im not sure how to get the st point

im not sure why

[scarlet quiver]

Ok, so you understand that dy/dx=0 for stationery point.
And dy/dx= (1-lnx)/x^2.
We know that the denominator can't be zero.

So for dy/dx=0, the numerator has to be zero.

[oblique summit]

so 1-lnx = 0

0**

[scarlet quiver]

Yup, so lnx=1.

And we know the value of x for which ln(x) becomes equal to 1.

[oblique summit]

what about the x^2

[scarlet quiver]

It can not make dy/dx=0.

[oblique summit]

so can that be ignored?

[scarlet quiver]

Yes.

[marsh citrus]

@oblique summit Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[light eagle]

here are the ans, but i dont know how to get theeeem

[main idol]

what's the question

[light eagle]

ABCD is a square with sides 10 cm long. Find the
area of each shaded region.

[main idol]

ABCD is made up of multiple quarter/half circles, complements of square minus circles, and two squares. count each of them and add them up

[marsh citrus]

@light eagle Has your question been resolved?

[light eagle]

.close

[marsh citrus]

Channel closed

Closed by @light eagle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[umbral bronze]

help!

[deft apex]

trigo

nometry

[umbral bronze]

yes

[deft apex]

what you tried

[umbral bronze]

wdym

[deft apex]

have you tried to get the answer in any way?

[umbral bronze]

I don't really know where to start

[charred jungle]

well

what's the trigonometric function that relates the hypotenuse with the opposite side length

[umbral bronze]

sine

?

[charred jungle]

yep

so what does that tell us about $\sin(a^\circ)$?

[elfin berry]

biggboy

[umbral bronze]

hm

sin(a) = 750/2000 ?

[charred jungle]

yeah

[umbral bronze]

ouhh okay

[charred jungle]

can you reduce the fraction

[umbral bronze]

mhm

3/8

[charred jungle]

yep

so

we have these trigonometric functions right?

such as sine, cosine, tangent, secant, cosecant...

[umbral bronze]

yes

[charred jungle]

we have inverse functions of this as well

usually written as arcsine, arccosine, arctangent...

[umbral bronze]

right! or looks like sin-1

[charred jungle]

yep

[umbral bronze]

sin-1 (3/8) ?

[charred jungle]

yeah!

[umbral bronze]

yay!

so 20.5!

[charred jungle]

also remember that your angle is an acute angle

yeh

[charred jungle]

because inverse trigonometric functions yield infinitely many values

[umbral bronze]

so is the elevation 20.5? or is there more

[charred jungle]

so you must know your interval

for an acute angle it's just 20.5

[umbral bronze]

what would it be for any other angle

oo wait

what's an interval

[charred jungle]

you can research about invers trigonometric functions for more

[umbral bronze]

okok!

[charred jungle]

an interval is the value range that for example a variable can take

you can research about that aswell

[umbral bronze]

I will

hi! back

how would I do this one

I know it's sine

more specifically sin(40) = EG/10

how would I finish that?

could I just multiply sin(40) by 10?

<@&286206848099549185>

[marsh citrus]

@umbral bronze Has your question been resolved?

[glass silo]

[umbral bronze]

Yay! ok cool

.close

[marsh citrus]

Channel closed

Closed by @umbral bronze

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[jovial crown]

can i get how to solve this? im stuck

[waxen oasis]

recall that cos(2x)=cos^2(x)-sin^2(x)

then you can factor using the difference of squares and manipulate this a bit

[jovial crown]

what do i do once $(cosx + sinx)(cosx-sinx) = cosx-sinx$?

[elfin berry]

ascendant

[smoky plover]

Where are you getting cosx-sinx from

[jovial crown]

difference of square

[smoky plover]

In the RHS

[jovial crown]

$cos^2x - sin^2x$

[elfin berry]

ascendant

[crystal wraith]

RHS has a + in between

[jovial crown]

oh woops

i meant that

[crystal wraith]

$(\cos(x) + \sin(x))(\cos(x) - \sin(x) - 1) = 0$

[elfin berry]

What the hell am I doing here?

[crystal wraith]

Do this.

[jovial crown]

got it, ty

.close

[marsh citrus]

Channel closed

Closed by @jovial crown

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[frigid fulcrum]

Let $V$ be a $\mathbb{R}$ vector space with the basis $\mathcal{B} =(\textbf{v}_1,...,\textbf{v}_n)$ and consider the
$$
f \in L(V,V), \quad \textbf{v}_j \mapsto
\begin{cases}
\textbf{v}j + \textbf{v}{j+1}, & j=1,...,n-1\
\textbf{v}_1 + \textbf{v}n, & j=n
\end{cases}
$$
uniquely defined linear mapping.\
Determine $f$, i.e. calculate $f(\textbf{v})$ for any $\textbf{v} \in V$, and $M{\mathcal{B},\mathcal{B} }(f)$.\
\
How can the function be rewritten, cause I don't understand much from its current notation...

[elfin berry]

Levens

[devout mauve]

maybe it helps to do n=3 explicitly

[frigid fulcrum]

ok let me try

alr im a bit confused

like idk what im supposed to do now

so ig for j=1 id have v_1 + v_2, for j=2 : v_2 + v_3, and for j=3 : v_1 + v_3

first, ig that the j in v_j refers to the columns in v... right?

so then the first column is the original's v first two columns added together

and the second column the 2nd and 3rd column of the original v

and then the last column is the first and last columns added together from the original v

I think I know how to write this in matrix form but idk how to write it as a function

<@&286206848099549185>

[cosmic plume]

hey there

The question says to determine f(v) for all v in V right?

So you don't have to use matrices

I mean you could, but I think it is simpler to just get a vector and apply the formula to it

$$OK\ so\ let's\ consider\ v\ \in\ V\ such\ that\ v= [ \sum_{k=1}^{n} a_k v_k ]$$

[elfin berry]

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

[cosmic plume]

applying f to it gives us the same sum but a_k multiplying (v_k+v_k+1)

you may leave n on its own to not get confused

i meant v_n

then you split the sum and do a change of index on the one with v_k+1

to turn it into v_k

and then fuse the 2 sums together and you get the coordinates of the image of v

[frigid fulcrum]

wait what index would you change it to?

[cosmic plume]

lemme send you a pic

[frigid fulcrum]

alr thank u

[cosmic plume]

We could have avoided that weird dedinition of f had we used indeces in Z/nZ

So it cycles back to 1 when you add 1 to n

Well, to 0 when you add 1 to n-1

But whatever 😜

its matrix would look something like this

@frigid fulcrum was this helpful?

[frigid fulcrum]

ahhh i see what you did there

that makes sense

to pull out that second column where j=n

[cosmic plume]

yeah because it would break my formula for the sum

[frigid fulcrum]

yup yup

[frigid fulcrum]

how do u know this

are the lower ones 1 too?

[cosmic plume]

alternatively you could use the definition of the matrix to determine its coefficients and do a matrix vector multiplication to get the images

[cosmic plume]

no everything that is not shown is 0

[frigid fulcrum]

ok that sounds familiar

[cosmic plume]

the 1st column of a matrix is actually the image of the 1st basis vector by f

We tend to forget the matrices are representative of linear maps in certain bases

that is the matrix associated with f in basis B

so you do the image of v_1 and get its coordinates with respect to all v_j in B and organize then in the matrix

then v_2 and so on and so forth

@frigid fulcrum check this one out

[frigid fulcrum]

ahhhh perfect

thank you so much

i understand now

[cosmic plume]

no probs

[frigid fulcrum]

.close

[marsh citrus]

Channel closed

Closed by @frigid fulcrum

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[chrome laurel]

I’m having trouble with this question

[chrome laurel]

The bottom two pages are my work. I tried applying the formal definition of little o but ended up getting nowhere

[marsh citrus]

@chrome laurel Has your question been resolved?

[chrome laurel]

<@&286206848099549185> ? (sry)

[marsh citrus]

@chrome laurel Has your question been resolved?

[marsh citrus]

@chrome laurel Has your question been resolved?

[chrome laurel]

.close

[marsh citrus]

Channel closed

Closed by @chrome laurel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[latent swift]

Question:

[latent swift]

Why I am Confused: I don't understand how congruency can also show that two lines/segments are parallel. Also, I don't understand how we know that both pairs of the opposite sides are congruent, as we only know that XY and WZ are congruent. Please clarify these points! thank you 🙂

[marsh citrus]

@latent swift Has your question been resolved?

[latent swift]

<@&286206848099549185>

[light frost]

I don't get it either

The fact that XY=WZ isn't enough information

D. looks correct to me

[marsh citrus]

@latent swift Has your question been resolved?

[marsh citrus]

@latent swift Has your question been resolved?

[lucid hinge]

D is right

there are many counter examples to C

[glass silo]

What’s the definition of congruent you’re working with @latent swift?

[novel mist]

It means to say that two lines are same

[dusky topaz]

it isnt enough

D. is correct

[marsh citrus]

@latent swift Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[marsh citrus]

Please don't occupy multiple help channels.

[austere hinge]

🤨

Belongs in a physics server

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[sage gale]

f:R to R is 1-1 and continuous on some interval. show that f inverse is also continuous on that interval

[sage gale]

no it's one to one as in injective

im trying to do it using the thm that a function is continuous if for any sequence y_n that converges to y_0 we have
lim f^(-1)(y_n) = f^(-1) (y_0)

[stoic saddle]

what's "interjective"

[flat raft]

probably injective

[sage gale]

oh yeah

[flat raft]

hmm is it easy enough to show that if A is some open set, then f(A) is some open set? I feel like this would come out of f's continuity

actually no forget that

do closed sets

use the theorem you cited and basically show that the limit points of f(A) are in f(A)

and then apply the characterisation of continuity with closed sets and you're doen

[sage gale]

ok but what is the first thing you said about open sets

are you saying that if f is continuous then f(A) is open for any open set A

ahh i found the theorem that helps with this

.close

[marsh citrus]

Channel closed

Closed by @sage gale

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[azure trench]

Do I need to sketch two graphs to see this

[azure trench]

Since it’s 6 marks lol

[edgy jungle]

Wavy curve

Try it

[azure trench]

Kk thanks

.close

[marsh citrus]

Channel closed

Closed by @azure trench

Use .reopen if this was a mistake.

[edgy jungle]

After taking 3 to lhs

[azure trench]

o

oh wait yh wtff

thx

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[gritty fable]

Could u please help me to solve it?

[gritty fable]

I dont understand how to do it

[marsh peak]

Note that you can rewrite $\log_{0.25}{x}$ as $-2\log_2{x}$

[elfin berry]

A Lonely Bean

[gritty fable]

thanks

[timid wedge]

How?

[gritty fable]

what is next?

[marsh peak]

$$\log_{0.25}{x} = a$$
$$x = (\frac{1}{4})^a$$
$$x = 2^{-2a}$$
$$\log_2{x} = -2a$$
$$a = -\frac{\log_2{x}}{2}$$

My bad, it's being divided by 2

[elfin berry]

A Lonely Bean

[marsh peak]

After that you should get $\log_2^2{x} - 3\log_2{x} + 2 = 0$ which can be rewritten as $(\log_2{x} - 2)(\log_2{x} - 1) = 0$ by factoring

[elfin berry]

A Lonely Bean

[timid wedge]

Is it not $x = a^(\frac{1}{4})$?

[elfin berry]

Adrian

[marsh peak]

No, recall the definition of logarithms

[gritty fable]

okay

[gritty fable]

I wrote it

[marsh peak]

The last equation implies that $\log_2{x} = 2$ or $\log_2{x} = 1$

[elfin berry]

A Lonely Bean

[marsh peak]

So the solutions are x = 4 and x = 2

[gritty fable]

thank you so much

.close

[marsh citrus]

Channel closed

Closed by @gritty fable

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[prisma trellis]

Hey everyone, how do I use the chain rule to derive

F’(x)

I have done less complicated examples

[late geode]

you could start with doing the substitution
u = 3x^2 - 1

[prisma trellis]

Ok

[late geode]

that will make what you'd do a lot clearer

[prisma trellis]

I’ll try

This is what I have done @late geode

[late geode]

consider the chain rule for
$$\dv{y}{x} = $$
with $y,x,u$

[elfin berry]

ℝamonov

[late geode]

it should be one of the first things that comes up when searching chain rule

(should also be quite intuitive as differentials behave like fractions)

[prisma trellis]

Yes I am familiar with these

But I have done less complicated questions

Can you please guide me through this question?

😬

[late geode]

well what's the chain rule for the above?

can you explicitly write it out

[prisma trellis]

Dy/dx=du/dx x dy/du

[late geode]

(i only want to see dy,dx,du and fractions)
(nothing else from your question if i wasn't clear enough in that request)

don't use x for mulitplication

[prisma trellis]

Sorry

[late geode]

$$\dv{y}{x} = \br{\dv{y}{u}}\br{\dv{u}{x}}$$

[elfin berry]

ℝamonov

[prisma trellis]

Yes

[late geode]

though you had questionable notation on the page,
$$\dv{y}{u} = 5e^u$$
$$\dv{u}{x} = 6x$$

[elfin berry]

ℝamonov

[late geode]

dy/dx would simply be their product

[prisma trellis]

So am I on track?

[late geode]

yeh

[prisma trellis]

Niceee

[late geode]

$$\dv{y}{x} = \underbrace{\br{\dv{y}{u}}}{5e^u} \underbrace{\br{\dv{u}{x}}}{6x}$$

[elfin berry]

ℝamonov

[prisma trellis]

Yes

I did it!!

[late geode]

yep

[prisma trellis]

Woah!

[late geode]

don't use x for mulitplication
no excuses on paper

[prisma trellis]

Oh ok 😅

Thanks so much

Have a great day @late geode

[late geode]

u2

[marsh citrus]

@prisma trellis Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[spring remnant]

I need help understanding what a derivative is

[spring remnant]

.close

[marsh citrus]

Channel closed

Closed by @spring remnant

Use .reopen if this was a mistake.

[nova totem]

.reopen

[marsh citrus]

✅

[nova totem]

Do you still need to know or?

[spring remnant]

Yes please :)

[nova totem]

Derivative is the instantaneous rate of change at a selected point/location

It's an "approximation" -- although it's 100% accurate -- of the slope of a function

You recall the equation of a line, y = mx + b

the derivative with respect to x is dy/dx = m ; the change in y/the change in x = m

But for some functions, that rate can change

So what the derivative does is describe the instantaneous rate of change at any given point/location should the rate change throughout the function

[spring remnant]

Its trying to find the slope of a function that is nonlinear?

[nova totem]

Essentially yeah

,tex \dxlimitdef

[elfin berry]

Umbraleviathan

[nova totem]

Where h is the change in x

[spring remnant]

Interesting, does this mean that h is a constant

[nova totem]

h is some constant yeah

But like ... we wanna measure what happens if that change is essentially nothing

Hence the limit as h -> 0

[spring remnant]

And this is how a derivative always is, a limit that approaching the zero with this equation

Ok, I think I understand now- thank you :D

.close

[marsh citrus]

Channel closed

Closed by @spring remnant

Use .reopen if this was a mistake.

[nova totem]

Ehh

Yeah

$\del f(x,y) = \vecb{\partial_x f(x,y), \partial_y f(x,y)}$

[elfin berry]

Umbraleviathan

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[short spindle]

is there a speical rule for expanding this we can use, or do we just multiply normally?

[nova totem]

Normally

I mean

[cunning fiber]

$(a-b)^2 =a^2 -2ab+b^2$ saves time since it's a well-known result, but there's nothing stopping you from rewriting $$(2x-5)^2=(2x-5)(2x-5)$$ and expanding like normal.

[nova totem]

You can use the (a+b)^2 identity

[eternal onyx]

You expand it normally ig

[elfin berry]

Civil Service Pigeon

[short spindle]

alright thank you

.close

[marsh citrus]

Channel closed

Closed by @short spindle

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[median flare]

Hello, could some explain how this type of problem is solved?

[burnt abyss]

Firstly

[median flare]

I can use quadratic formula for x²-4x+4, but then I get (x-2)². What the heck do I do with that?

[burnt abyss]

The bottom cant be negative

(x-2)² will always be positive

[median flare]

Are you talking about +/-?

[glacial hedge]

Yes

It is therefore impossible

[burnt abyss]

Yeah

Meaning only case 2 exists

[median flare]

How did you get to that?

I don't really know how to apply those +/- and -/+ to the problem

[lofty gyro]

actually i think your case splitting is nice!
Generally we will do it this way 🙂

case I
2-3x<0
AND
x²-4x+4>0

so we try and solve these two with an AND relation

[median flare]

I sometimes see for case 1 +/+ and for case 2 -/-. I don't know how we get to those, and even less how we use them to solve the problem 😅

[lofty gyro]

oh

[median flare]

Yes

[lofty gyro]

this is because of >0 or <0

[median flare]

Then we use the formula, and I get a dead end really

[lofty gyro]

like for >0, we have +/+ or -/-

because positive ÷ positive = positive

and negative ÷ negative=positive

[median flare]

Oh, so if something is bigger than 0, we use that splitting type?

[lofty gyro]

like wise, we know why
<0 is +/- or -/+

[median flare]

I see

Okay, how do we use them to apply it to the problem? Or do we just use them to configure the bigger/smaller arrows?

[lofty gyro]

you did great on the arrows

[lofty gyro]

so, i guess we can now start with this

[median flare]

Yes

[lofty gyro]

where you did
-3x<-2
right?

and finally
x>⅔

[median flare]

Yes

[lofty gyro]

next

[median flare]

what about the other thing though?

[lofty gyro]

x²-4x+4>0

usually two methods can be used

[median flare]

We use formulas

[lofty gyro]

one, factorize
two, completing square

[median flare]

So we convert it to (x-2)² naturally

[lofty gyro]

yea

(x-2)²>0

this is a special case

I'll do it the general way so that you'll understand better

[median flare]

Okay

[lofty gyro]

(x-2)(x-2)>0

that means

• times +
  OR

• times -

the same reasoning we did for ÷

[median flare]

So I do another two cases?

[lofty gyro]

then,
(x-2)>0 and (x-2)>0
or
(x-2)<0 and (x-2)<0

since this is a special case so it looks weird

[median flare]

Right

[lofty gyro]

anyways we have
x-2>0 or x-2<0

that is x>2 or x<2

what can you tell from here?

[median flare]

They are crossing

I'd have to draw it to confirm

[lofty gyro]

sure, take your time

[median flare]

Nevermind, they're not crossing

[lofty gyro]

so, what conclusion can you get from this

[median flare]

Well since they're not crossing, it's basically nothing so I write ∅

[lofty gyro]

hmmm

it's an OR relation

so, it's not ∅

do tell if you need more hint

[median flare]

Yeah I'm kinda stuck 😅 Maybe I picked a hard problem so it's not good to start out from to understand

[lofty gyro]

it's okay

since it's an OR relation,
both
x>2
or
x<2 works

all numbers greater than 2 are good

also, all numbers smaller than 2 are good

is it all real numbers are good then?

[median flare]

Ohh

yes, but, I think we write 2

When we need to bring the final conclusion

so we can write sometjing like x€⟨2/3,2⟩

[lofty gyro]

hmmm...

actually

for this
x²-4x+4>0
it will be
x can be all real numbers but 2

[lofty gyro]

so, this is not enough

[median flare]

So, I have to write R instead of 2?

[lofty gyro]

for x²-4x+4>0 , yes

but now

back to the whole case 1

[median flare]

Right

[lofty gyro]

x>⅔ AND x in R{2}

[median flare]

x€⟨2/3⟩U R[2]?

[lofty gyro]

,rotate

[median flare]

Aaah

Ofc

[lofty gyro]

it will be
x in (2/3,2) AND (2,+inf)

[median flare]

Yeee

I understand

Thank you

[lofty gyro]

ok

[median flare]

.close

[marsh citrus]

Channel closed

Closed by @median flare

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[still temple]

so i need a lot of help with some competition math problems from last year to practice for this year as i dont know a lot of the tricks that can be used

[still temple]

id like to start with this one

1. How many six-digit numbers formed with the digits from one to six are multiples of four? A) 200 - B) 192 - C) 180 - D) 160 - E) 144

[main idol]

#competition-math is probably better

[still temple]

closest i think i have been was applying the division rules of four (last two digits must be divisible) and i always somehow end up in 6^4*3^2 but its obviously not the right answer

[still temple]

oh, ok thanks. should i leave this channel occupied just in case someone wants to try?

.close

[marsh citrus]

Channel closed

Closed by @trail ridge

Use .reopen if this was a mistake.

[still temple]

.reopen

[marsh citrus]

✅

[still temple]

they seem to be talking about more advanced competition math problems so i think ill just stick to these channels

1. How many six-digit numbers formed with the digits from one to six are multiples of four? A) 200 - B) 192 - C) 180 - D) 160 - E) 144

[leaden monolith]

Do you know the trick for divisibility by 4?

[still temple]

yeah, last two digits must be divisible by four

and with digits from 1 to 6 the numbers must end in {12, 16, 24, 32, 36, 44, 52, 56, 64}

by working on that a little bit i got that we have 6^4*3^2 possible numbers but thats not right

[leaden monolith]

I’m very confused now

,calc 6^4*9

[elfin berry]

Result:

11664

[leaden monolith]

Must be misinterpreting the question?

[still temple]

it is a competition, if they didnt explicitly say no numbers must repeat im assuming "111112" is valid

[leaden monolith]

Yeah

I just wrote a bit of code to brute force it

It tells me 11664 too

[still temple]

maybe no numbers must repeat

i mean maybe something got wrongly translated as it's originaly a spanish competition

so i think no numbers must repeat which in that case i would get 3*(6*5*4*3*3)

,calc 3*(65433)

[elfin berry]

Result:

3240

[still temple]

maybe if i used permutations... but in that case im gonna need help as it would be a tricky operation

[leaden monolith]

Yeah

You’re right

They can’t repeat

It’s one of the answers if they can’t repeat

[still temple]

ahh so im wrong on this one, because this implies 123412 is an option i think

[leaden monolith]

Yeah

[still temple]

hmm

[leaden monolith]

In here

There’s 8 ending numbers that result in divisible by 4

[still temple]

actually theres 9 right?

[leaden monolith]

Well can’t do 44

That repeats

[still temple]

ah right

[leaden monolith]

So there are 8 ways to get a divisible by 4 ending

What about the first 4 digits

How many ways are there to arrange those?

[still temple]

they could be whatever as long as theres no repetition

[leaden monolith]

So let’s have 6 cards 1-6

We’ve use 2 of them for the ending digits

[still temple]

but ways to arrange 4 numbers having 6 options would be 6*5*4*3

[leaden monolith]

Of which there are 8 combinations

[leaden monolith]

But do you actually have 6 options?

You’ve already chosen 2 to be your ending digits

[still temple]

oh so its just 4!?

*8

[leaden monolith]

That’s for the first 4 digits

Yep

[still temple]

192

im gonna check

and yep it is correct, 192 options

[leaden monolith]

Disgusting code 😦

[still temple]

woah thanks frost!

[leaden monolith]

But hey it works

[still temple]

hahahh but its on mobile so thats some extra credit

[leaden monolith]

Thank you thank you

Haha

[still temple]

well from this problem's reasoning im gonna try some other problems which i think work the same way

.close

[marsh citrus]

Channel closed

Closed by @trail ridge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[untold wolf]

What is the value when n = 0?

[untold wolf]

For this unit step function

[runic temple]

Undefined

[untold wolf]

the next slide has this

where he uses n = 0

its what made me confused haha

[marsh citrus]

@untold wolf Has your question been resolved?

[static quarry]

people normally define u[0] = 1, so u[n] is the integral of delta[n]

the definition probably has a typo

in the second plot, y[0] would be zero if u[0] were really zero

assuming h is the same as the one in the first plot

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[still temple]

can anyone help me find the equation for (7, 5 1/2) and (0,-2)

[still temple]

i found the slope

but i put it as a decimal

it was originally 7.5/7

then i changed it into 75/70

.close

[marsh citrus]

Channel closed

Closed by @halcyon tiger

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[neon lagoon]

I'm having trouble writing this into sigma notation. I'm getting caught up because the numbers are all the same, but the power is changed versus there being an ending number that differs from the first.

[neon lagoon]

I took 2 to the power of 10 and put it on top, but that's wrong. I'm honestly lost.

[weary temple]

Well

[flint jolt]

$\sum_{i=1}^{10}{2^i}$

[elfin berry]

Anagh

[flint jolt]

This is how you write

[weary temple]

Don't just give answers

I assume the want to understand it too

[elder ridge]

Do you know what a geometric series is?

[flint jolt]

Then it will iterate i from 1 to 10

[flint jolt]

Ok sorry

[elder ridge]

Here's a nicer way of deducing the answer:

Are you comfortable with binary numbers?

i.e. 1001 = 9, 10000 = 16, that sorta thing

[neon lagoon]

Not really, no. I'm really new to this, its for my java class.

[elder ridge]

Ok well given you're doing computer science this is the best method to do this

A binary number is just a different way of representing numbers with powers of 2

Like with normal numbers, you have units, tens, hundreds etc. you have units, 2's,4's,8's etc.

the difference is we multiply by two

So for example 11 = 2 + 1 = 3, 1010 = 8 + 2 = 10

Now you might wonder how you add binary numbers?

[neon lagoon]

Yeah, how so?

[elder ridge]

Well it's the same thinf as normal, except once you go over 1, you carry the 1 to the next digit along

like when you go over 9 with normal numbers

so for example 1010 + 101 = 111 (no need to carry anything here)

1011+10 = 1100

1111+1 = 10000

[neon lagoon]

Interesting.

[elder ridge]

do you understand why these relations are true?

[neon lagoon]

Why’s that?

[elder ridge]

As I said before

We add each of the digits together, when we go over 1 we carry the 1 over to the next digit

like how with normal numbers if you add 19+2 you carry the 1 over to get 21

or 9999 + 1 = 10000

Knowing this, could you tell me what 10010 + 1011 is?

[neon lagoon]

I can’t, no, I’m trying to understand though. So with 1111+1= 10000, I get it carry’s over but why does it change from all 1 to 1 followed by 4 zeros?

[elder ridge]

because you keep carrying it over

similarly to 9999 + 1

Remember that binary is the exact same as our normal number system, except that we stop at two instead of ten

Once you understand binary the sum you have will be easy to do

[neon lagoon]

Oh okay, yeah, that makes sense.

[elder ridge]

I think it'll help if you do this example for familiarity

[neon lagoon]

11101 would it be?

or would there be another 0?

[elder ridge]

yes!

you're exactly right don't worry

next idea:

we know 2 is represented by 10, what's say 2^4 =16 represented by?

[neon lagoon]

10000

[elder ridge]

perfect

[neon lagoon]

okay that makes a lot more sense

[elder ridge]

so you see that powers of 2 will be 1 followed by a bunch of zeros

[neon lagoon]

yeah, that wasn’t clicking at first

but I appreciate you helping a lot

[elder ridge]

Well it does now!

nws this is good procrastination

Ok

So lets think of 1 + 2 + 4 + 8 + 16

what'll that be in binary?

[neon lagoon]

11111?

[elder ridge]

yeah that's right

Note that we just summed some powers of two

similar to the question

Could you understand that generally, 2^(0) + 2^(1) + ... + 2^(n-1) + 2^n is n ones in binary?

as each one in each power of two fits in its own digit

[neon lagoon]

Kinda, yeah.

[elder ridge]

remember how we established that 2^n is 1 followed by n zeros

So this sum is like 100000 + 10000 + 1000 + 100 + 10 + 1

but with more zeros ofc

This is just like adding normal numbers e.g. one + ten = eleven

[neon lagoon]

Yeah, that clicked it

[elder ridge]

cool

[neon lagoon]

because 2^4 = 16 which is 1 by 4 zeros

[elder ridge]

precisely

[neon lagoon]

so the power is equal to the zeros that follow?

[elder ridge]

yeah

[neon lagoon]

ohhhhhhh

okay

that helps a lot tbh

[elder ridge]

like with normal numbers except with normal numbers it's the power of 10

Ok

[elder ridge]

So we know that this sum is n ones

So what would be this sum + 1?

in binary

[neon lagoon]

Lost me there, sorry

[elder ridge]

ok so remember we tried 1111 + 1 earlier

and we talked about carrying the 1

[neon lagoon]

right, yeah, and it’s 10000

[elder ridge]

so what happens if you have n ones, instead of 4 like the example above

[neon lagoon]

it’s just not clicking with me, sorry

[elder ridge]

no problem at all

well you see how we had to carry the 1 all the way over with 1111+1?

How about I write this:

111111+1 = 1000000

11111111 + 1 = 100000000

[neon lagoon]

That part makes sense

11111111 + 1 = 100000000

Wouldn’t it then?

Nvm I just saw your second example there with the same digits

[elder ridge]

no worries lol

but yeah the point is it carries all the way over

so you could argue that this happens with any number of ones?

[neon lagoon]

I would think so

[elder ridge]

I guess why wouldn't it? You'd be doing the same thing as in these examples, just more times

[elder ridge]

So then we get back to this

Just making sure; is everything making sense?

[neon lagoon]

For the most part, I’m understanding the 1 and 0 and carrying over but the 2^(0) + 2^(1) etc is where I’m getting lost

[elder ridge]

ok

That is the hard part

The idea is that the the result of this sum is actually n ones in binary

as 2^4 is 1 followed by 4 zeros etc.

[elder ridge]

this is a tiny bit wrong; the sum ends at 2^(n-1)

this may help

[neon lagoon]

okay a little, yeah, when you draw it out like that

[elder ridge]

cool

Now what happens when I add 1 to that?

[neon lagoon]

10000000

[elder ridge]

exactly!

[neon lagoon]

oh okay cool

[elder ridge]

what's that in binary?

not binary

normal numbers

[neon lagoon]

128

[elder ridge]

which is 2^7 as in binary it was a 1 with 7 zeros

wait

uhh