help-26

[prisma lake]

I have tried to solve this by dividing 22 by 2 and using the remainder as an exponent for the last digit but the remainder is 2. Im stuck

[sinful flint]

,rotate

[sinful flint]

!status

[topaz sinew]

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

[prisma lake]

2

[sinful flint]

!show

[topaz sinew]

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

[prisma lake]

Ok, well all the work was done on that space in the picture. The 22 is the root index and the 2 is part of the following chart. 22/2 is 11 with no remainder. For previous questions I did the same thing, got a remainder and used this chart to find the integer.

[iron rain]

,rotate

[prisma lake]

when can i ping helpers

[pseudo bear]

Fifteen minutes after posting your question, you can ping @Helpers once.

[prisma lake]

ok

[pseudo bear]

Have you ever done a square root on paper using a method that looks a lot like long division?

[prisma lake]

no, but for a very simmilar question to the one I showed, I had a method that worked.

[pseudo bear]

Well, one hint I'd give is to find out how many digits the result has. Is 10^22 is higher than their number? If so, is 100^22 higher?

[prisma lake]

im sorry can you elaborate? which result? and which number?

[pseudo bear]

The result is the answer you're expected to give.

Their number is the number you're given in the problem.

The one that starts with 73786....

[prisma lake]

The answer I got was 1 somehow

ill check their number

[pseudo bear]

The answer to which question? The question on your paper or the question about how many digits?

[prisma lake]

The answer to the whole question, I got 1 somehow. there are 20 digits in the number. something I have never seen before, a number with less digits than the root.

[pseudo bear]

Well, if the 22nd root of a number is 1, then 1^22 is that number.

But 1^22 isn't that long number, so the 22nd root of that number can't be 1.

What do you mean you've never seen that before?

2^10 is 1024, which is a lot less than 10 digits.

You've likely seen that all the time.

[prisma lake]

Im saying for this type of question, I think im overthinking this

[pseudo bear]

That's why I recommended finding out how many digits the result has.

[gusty kindle]

Isn't that SoM

spirit of math work

[prisma lake]

yea

[pseudo bear]

The answer is the 22nd root of a number.

That means that the answer to the 22nd power is the number you started with.

So, if the answer is 12, 12^22 is the long number they give you in the problem.

That means that you can try the smallest two digit integer, 10, to see if you need less than two digits or not.

[prisma lake]

ok, like 10^22?????

[pseudo bear]

Right. Is 10^22 lower than the answer?

Or equal to it?

If so, you need at least two digits.

Otherwise, you have to go lower than 10.

So, you'd have one digit.

[prisma lake]

Id have to go lower

[pseudo bear]

OK, so it's a one-digit answer.

Now you were getting the last digits of other exponents.

[pseudo bear]

Like here ^

[prisma lake]

yup

[pseudo bear]

You can also do that for the last digit of x^22.

[prisma lake]

thats what I was using for the other questions

[pseudo bear]

So, like 1^22 gives you 1 as the last digit.

Do you know Euler's theorem?

Or Fermat's little theorem?

If not, that's OK.

[prisma lake]

nope

[pseudo bear]

OK, so you can do 2^22 = (2^2)^11 using the exponent rules.

[prisma lake]

also do you want to see what I was doing for the other questions

[pseudo bear]

OK.

[prisma lake]

,rotate

[pseudo bear]

Why did you divide by 4?

[prisma lake]

because of the chart. the last digit is 2, and numbers in the chart for the 2 column repeat 2 numbers.

[pseudo bear]

Where is the chart for an exponent of 41?

[prisma lake]

so thats where the division comes in, allowing you to use the remainder calculate which number

[pseudo bear]

I'm still a bit lost. You said because of the chart. Which chart?

[prisma lake]

this one, im sorry i suck at explaining stuff

[pseudo bear]

The line below the last typed in row here ^?

[prisma lake]

im sorry?

[pseudo bear]

Well, you filled in the chart and then you added a row below the chart.

You wrote 1 1 4 4 2 1 1 4 4 2 just below the chart.

Is that what you're referring to?

[prisma lake]

that is the amount of numbers that repeat

so i divided by 4, as 4 is under the 2 column. this is very hard to explain

[pseudo bear]

I don't think that'll work.

[prisma lake]

thats what I was taught and it works

[pseudo bear]

Yes, and if you need to get 2 times 2, 2 + 2 = 4 gives the correct answer. Are you sure it works in general?

[prisma lake]

not fully sure

[pseudo bear]

You have rows for x^2, x^3, etc.

I'd recommend making a row for x^22.

You can simplify it quite a bit.

Here's how.

Let's say you have 7^22 and you need the last digit.

You start with 7^1 = 7.

Then, you square that to get 7^2 = 49 = 9.

Then, you square that to get 7^4 = 9^2 = 81 = 1.

Then, you square that to get 7^8 = 1^2 = 1.

Then, you square that to get 7^16 = 1^2 = 1.

If you square it again, you get 7^32, but 32 is higher than 22.

Then, you figure out which exponents add up to 22.

So, like 16 + 4 + 2.

Then, you do 7^22 = 7^(16 + 4 + 2) = 7

[prisma lake]

thats what I was trying to say, you dont need to. I can show another example. for example lets say you have 273^66. As you can see in the chart, for the threes column, the amount of times numbers repeat are 4. so I can do 66/4 = 16 R 2. then from the top of the 3 column I can look at the second one. that is the last digit

[pseudo bear]

You can only do that if the pattern repeats in a cycle.

Like 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4.

That forms a cycle.

Oh, I see what you're doing.

One moment.

Yes, you have 4, 8, 6, 2, 4, ... and it'll repeat every 4 because you get the pattern by multiplying a number by 2 to get the next number.

[prisma lake]

as the exponent grows, the numbers repeat, thats what the number at the bottom is. for example the pattern for 3 is 3,9,7,1. so with the remainder you can find out the units digit

[pseudo bear]

So, if 4 goes to 8 the first time, it'll do the same the next time, since 4 times 2 is the same thing in both cases.

OK, I see what you're doing now.

If you see a 4 and then you see another 4 later, it'll do the same pattern after both of them.

So, you can divide by 4 and see what the remainder is.

[prisma lake]

yea

[pseudo bear]

OK, yes, what you're doing makes sense.

I mean, you can divide by the distance between the 4s.

OK, so what are the 22nd powers of the digits?

[prisma lake]

the units digit for the big number?

[pseudo bear]

Right.

22/4 = _ r 2.

So, you can use the x^2 row, right?

[prisma lake]

20

[prisma lake]

wait why are you dividing by 4, you divide by the amount of times it repeats, in this case its 2

[pseudo bear]

Well, in your chart, you have a row for x^2 last digits, x^3 last digits, etc.

And then, like x^6 is the same as x^2, right?

The last digits for x^6 all match the last digits for x^2.

[prisma lake]

yeah I didnt even know that

[pseudo bear]

Well, the way you can see it is that the 0 column repeats every 1 row. The 1 column repeats every 1 row. The 2 column repeats every 4 rows. And so forth.

The repeats are every 1, 1, 4, 4, 2, 1, 1, 4, 4, 2.

[prisma lake]

yes those are the numbers at the bottom

[pseudo bear]

So, you can take the LCM.

To get a multiple that works for all of them.

Like with the 0 column, it repeats every 1 row.

Which means that it also repeats every 5 rows or 6 rows or whatever.

I mean, if you look down 5 rows, it'll be the same number.

Same with column 3. It repeats every 4 rows.

Which means that it also repeats every 20 rows or 24 rows.

[prisma lake]

yea..

[pseudo bear]

So, the idea is that if it repeats every 6 or something, it also repeats every 2 * 6 or 3 * 6 or 4 * 6.

So, you can use any multiple of how often it repeats.

So, what you want to do is to find the smallest number that's a multiple of all of them.

Which is 4.

4 is a multiple of 1.

4 is a multiple of 2.

4 is a multiple of 4.

So, every single column will repeat every 4.

Does that make sense?

[prisma lake]

yes

[prisma lake]

every 4 rows yes?

[pseudo bear]

That's called the least common multiple because it's a multiple of all of them (common to all of them) and it's the least one.

Right.

[prisma lake]

yeah LCM

[pseudo bear]

So, what you can do is to say that x^1, x^2, x^3, x^4 are all the rows you need to get any row.

Because the numbers going across the page in each row repeat every four rows.

[prisma lake]

im following..

[pseudo bear]

So, you can say x^22 has 22. 22/4 = 5 r 2.

So, to get the x^22 row, we can just copy the x^2 row.

So, x^22: 0, 1, 4, 9, 6, 5, 6, 9, 4, 1.

Now, what's the last digit of the long number they gave you?

[prisma lake]

4

so 6

[pseudo bear]

OK, and 4 is in column 2 or column 8.

[pseudo bear]

From the x^2 row here ^

Does that make sense?

[prisma lake]

but wouldent it be 6?

[pseudo bear]

You mean column 6?

[prisma lake]

in the 4 column, and the x^2 row the # is 6

[pseudo bear]

No, not in the 4 column.

In the column that has a 4 written.

Because 4 is the last digit.

And those get written in the boxes in the table.

Like x^2: 0, 1, 4, 9, 6, 5, 6, 9, 4, 1.

Remember how you filled in that table.

[prisma lake]

yeah

[pseudo bear]

You did the squaring and you wrote down the last digit.

What this problem is telling you is that they took an integer to the 22nd power and got a long number.

The last digit of that long number is 4, so you want to find where you wrote 4 for the last digit.

[prisma lake]

yeah i just picked a random number ending in the digit for the column i wanted to fill and i filled the answers units digit

[pseudo bear]

Right.

So, we're doing x^22, which means we're using the x^22 row of your table, which is just a copy of the x^2 row.

We look up the last digit of our x^22 number, 4.

We find it in two places: x^22: 0, 1, 4, 9, 6, 5, 6, 9, 4, 1.

Does it make sense why I'm doing that?

[prisma lake]

gimme a sec to digest (im a very slow learner)

[pseudo bear]

OK.

[prisma lake]

ok good

[pseudo bear]

OK, so our answer will either end in 2 or 8.

So, maybe it'll be 132 or 568.

[prisma lake]

but from before dont we know its 1 digit answer

[pseudo bear]

Yes.

So, it'll be exactly 2 or exactly 8.

[prisma lake]

right

[pseudo bear]

If you're allowed to use a calculator, you can do 2^22 or 8^22.

If not, you can use the repeated squaring I did earlier.

[prisma lake]

ok so its 8

it doesent show the full answer

[pseudo bear]

Yeah, it's probably too many digits for the calculator.

[prisma lake]

but it shows 7.378697629

x10^19

also, that was a lot. what would i put on my page as a "full solution"

[pseudo bear]

Well, you'd show that it was only one digit with that 10^22 thing (which is 1 followed by 22 zeroes) being more than the number they gave you.

Then, you'd say that 22 / 4 = 5 r 2, so you use the x^2 row.

Then, you'd point out that the last digit of the long number they gave you shows up in column 2 and 8, so the answer must end in either 2 or 8.

[prisma lake]

ok thanks a lot, that was a long chat

[pseudo bear]

You're welcome.

[prisma lake]

one more question, you might have answered this, but why did the previous question work, and the one before that.

[pseudo bear]

7 worked for the same reason. You found that 41/4 = 10 r 1, so you use the x^1 row. Then you look up the last digit of the number they give you in the x^1 row, and you find that only in column 2.

Then, you point out that 10^41 is longer than the number, so it must be a one-digit number.

The only one-digit number that ends in 2 is 2, so that's the answer.

6a is the 10^power thing being too high, so there's only one digit.

6a and 6b, I mean.

Then for 6c, 35/4 = 8 r 3, so you use the x^3 row and you look up 7 (the last digit of that long number).

[prisma lake]

i just double check that wow

[pseudo bear]

That's in column 3, so the answer must end in 3.

And it's one-digit, so it's exactly 3.

[prisma lake]

tysm this was so useful

[pseudo bear]

You're welcome.

One thing, though.

Make sure not to use x^0.

[prisma lake]

yes

[pseudo bear]

That row is all 1s, which isn't as useful.

Use row x^4 for that.

Sometimes, the repeating part of something starts only after a few things go by.

Like 453.3333333 or something.

[prisma lake]

use when remainder is what?

[pseudo bear]

When it's 0.

Like if the exponent was 24.

You'd use x^4.

Because x^0 isn't part of the cycle.

The cycle starts with x^1.

And it repeats every 4.

So, it's like x^1, x^2, x^3, x^4, then x^5, x^6, x^7, x^8, etc.

You can see that by noticing when the first repeat happens.

The x^1 row that they filled in for you is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

And then you see that repeat in x^5.

And that's the first repeat.

[prisma lake]

this is different to what they showed, is there a way I could send the video

[pseudo bear]

What site is the video on?

[prisma lake]

brightspace spirit of math, you need a login (which means you need to be enrolled) to watch.

idk if there is a way to save the video

[pseudo bear]

Oh, I have a login, but I'm not a paid member.

But that's something to know.

Like when something repeats over and over, it doesn't always start out with something that repeats.

Like if I have some numbers.

1, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5....

Notice that 3, 4, 5 repeats forever.

But the first two numbers there aren't in that cycle.

So, what you want to do is if you want the 55th number in the sequence, you notice that the cycle has 3 numbers in it.

You do 55/3 = 18 r 1.

Then, that 1 is important as we've seen before.

What you do is to find the first number in the cycle that also has a remainder of 1.

1, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5....

That's the first number in the cycle that has a remainder of 1.

So, the 55th number in the sequence is also 4.

[prisma lake]

so 4 is the 55th number?

[pseudo bear]

Right.

[prisma lake]

wow thats crazy how that works

[pseudo bear]

Yeah, any time you get into a fixed-length cycle that lasts forever, it works like that.

[prisma lake]

that was extremely helpful, tysm again.

[pseudo bear]

You're welcome.

[prisma lake]

.closee

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[topaz sinew]

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[low monolith]

can sum1 help me with these

[low monolith]

i don't understand each postulate there is in triangles

[ivory sorrel]

Is this on congruence of triangles?

[low monolith]

yes

[ivory sorrel]

Let's start with problem 1?

[low monolith]

okay

[ivory sorrel]

What do you think?

[low monolith]

they seem similar or alike

same angles and stuffs

[ivory sorrel]

yes, but can you determine if they are congruent

that is can you superimpose them on one another

[low monolith]

yes they are congruent

[ivory sorrel]

Well, they are similar, but they are NOT congruent

[low monolith]

what how

they're same size and shape

[ivory sorrel]

How do you know they are the same size

[low monolith]

idk they're just seem alike with each other

[ivory sorrel]

When two lines are of equal length in geometry, they're marked with perpendicular lines

like here notice the small dash?

[low monolith]

yes

[ivory sorrel]

that means that those lines are of equal length

[low monolith]

then what about the dashes that are III II

does that show that non of the angles are not equal

[ivory sorrel]

Lines with identical markings( number of dashes) are of equal length

[low monolith]

can u explain a bit further

[ivory sorrel]

okay, let me draw some diagrams

So here AB=DE

CB=EF

and DF=AC

[low monolith]

so the I on both figures shows that they're the same as well as II and III

[ivory sorrel]

yes

[low monolith]

okay I get it now

but how do I know if they're congruent

like #1

[ivory sorrel]

Do you know the various congruence criterions ?

[low monolith]

what's criterions

[ivory sorrel]

congruence theorms?

conditions

like side -side - side

side - angle - side

[low monolith]

those are postulates right?

AAA SSA ASS ASA etc.

[ivory sorrel]

sure, yes

AAA is for similarity

[low monolith]

yeah I know them but kinda confused about the differences of each

[low monolith]

im getting more confused

[cosmic furnace]

Bro no helpers are helping me either

Yo i can help you tho

[cosmic furnace]

What are you stuck on?

[low monolith]

this

[ivory sorrel]

With which part exactly

[low monolith]

identifying them

[ivory sorrel]

https://youtu.be/jWHOF6cFbpw?si=Xt4cAthvaJXMtygN you might want to watch this

[low monolith]

i love oct

thanks

how about this tho

[ivory sorrel]

Well, there are still two triangles, no?

[low monolith]

Side - Angle - Side

[ivory sorrel]

Well, no

SSA

Side-Side Angle

[low monolith]

there's no such thing as SSA tho

then that means it's not congruent

[ivory sorrel]

oops, my bad

sorry

[ivory sorrel]

I think so, yes

[low monolith]

are these correct then

[ivory sorrel]

I believe so

[topaz sinew]

@low monolith Has your question been resolved?

[low monolith]

how about this

[topaz sinew]

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[next rain]

I don’t understand how we did this step

[vernal island]

well if you multiply -cos(x) by 1 you get -cos(x), and if you multiply -cos(x) by -cos(h) you get cos(x)cos(h)

[next rain]

Ohhh right

I see it

Okay thank u

.solved

[topaz sinew]

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[topaz sinew]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[sharp dew]

https://www.youtube.com/watch?v=bBC-nXj3Ng4&ab_channel=3Blue1Brown

[sharp dew]

the video cannot no longer be displayed

https://www.3blue1brown.com/lessons/bitcoin

im so sad

[glass maple]

what is the actual reason for occupying the channel tho

[sharp dew]

I wonder if there's any other avenue can I watch the video

.close

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[glass maple]

he might have a github repo of his videos

[sharp dew]

I should post it on discussion.

[glass maple]

at least there would be a github of his manim code

idk if he has a video attached with each manim anim tho

[sharp dew]

I'm so sad, these crypto giants claiming stuff they have nothing to do with.

[glass maple]

video got taken down by a crypto company

[pseudo bear]

Go to the URL to get it in your address bar.

[sharp dew]

.reopen

[topaz sinew]

✅

[pseudo bear]

Put web.archive.org/ in front of it.

Press enter.

[sharp dew]

It works, I’m crying

.close

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Channel closed

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[sharp dew]

thank you

[pseudo bear]

You're welcome.

[topaz sinew]

Available help channel!

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[sharp dew]

How should I describe 2^256 in English

[sharp dew]

2 with a power of 256

[modest glen]

2 to the power of 256

[sharp dew]

what are other synonyms

[modest glen]

I don't think so?

[thick lily]

"big"

that's how i'd describe it

[sharp dew]

The approximate value of 2^256 should be attainable via the application of log table.

[thick lily]

1 with 256 0s behind it in base 2

[sharp dew]

shouldn't log table only provides values with base 10.

[thick lily]

who has a log table

you keep that under your rollodex?

or behind the abacus

[sharp dew]

you are right. Is it possible to approximate the value of it by manipulating it into log with a base of 2.

Is that what you suggest?

and by doing so, log table would not be needed.

[thick lily]

what's wrong with 2^256 as it is

no reason to bring logs into this

[sharp dew]

How would you approximate its value then?

[thick lily]

Why would I?

[opal vault]

sure you can get its number of digits in base 10 computing floor(log_10(2^256)) + 1

but not sure what else you could do

[odd forge]

hmm

did you take natural log both sides

[whole geode]

You can simply use the change of base formula

[odd forge]

yea

make it to log base 10

[whole geode]

log_10(x) = log_2(x)/log_2(10)

[opal vault]

I mean

log_10(2^256) = 256log_10(2)

[opal vault]

so tomato tomato

[sharp dew]

Can I deduce that it is a 76 digits number

I just took 0.301 as 0.3 for calculating convenience

[opal vault]

and that convenience cost you a digit

[sharp dew]

How do you know

[opal vault]

,calc 256 * log(2)/log(10)

[thorny flame]

Result:

77.063678889979

[opal vault]

that's how I know

[sharp dew]

I thought you can “feel” the value being wrong.

And I would like to learn that then

[opal vault]

also

[opal vault]

I told you to get the number of digits

after taking the floor you must add 1

so it has 78 digits in base 10

[sharp dew]

Why would you take the floor, it is unnecessary and a bit redundant, no?

[opal vault]

redundant?

[sharp dew]

Yes, you can still get the value without taking so

[opal vault]

floor literally means "cut off the decimals" for positive numbers

that's what you implicitly do already

[sharp dew]

I see

[opal vault]

also

if you want the leading digit

[sharp dew]

Of course I do

[opal vault]

notice that the remainder is 0.06...

[sharp dew]

Ohh

[opal vault]

below log(2)

[sharp dew]

I see

[opal vault]

so leading digit is 1

[sharp dew]

I do not see how the floor and plus one method is working in terms of approximating the value

Why should I add one to the value after taking the floor.

[opal vault]

say x has n digits

[sharp dew]

Doesn’t it potentially leads to miscalculation

[opal vault]

no

I will prove it to you

say x has n digits in base 10

that means 10^(n-1) <= x < 10^n

which means n-1 <= log_10(x) < n

ok there we go

mmh wait

frick

if x has n digits

then the power of 10 below x that has n digits

has n-1 zeros

[opal vault]

Ok now we're good

I'm just confusing myself over and over

so

n-1 = floor(log_10(x))

n = floor(log_10(x)) + 1

[sharp dew]

It works perfectly well with my tiny number exhibition

[outer portal]

115 quattuorvigintillion 792 trevigintillion 89 duovigintillion 237 unvigintillion 316 vigintillion 195 novemdecillion 423 octodecillion 570 septendecillion 985 sexdecillion 8 quindecillion 687 quattuordecillion 907 tredecillion 853 duodecillion 269 undecillion 984 decillion 665 nonillion 640 octillion 564 septillion 39 sextillion 457 quintillion 584 quadrillion 7 trillion 913 billion 129 million 639 thousand 936?

[topaz sinew]

@sharp dew Has your question been resolved?

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[neon iron]

can someone help me understand what the arc length formula is?

[neon iron]

hello?

can someone help me

<@&286206848099549185>

[mystic jay]

of circle? (the radians one) ?

[neon iron]

btw was i supposed to use that ping?

[neon iron]

yes

[mystic jay]

do you understand the formula for circumference of a circle?

[neon iron]

yes

2 pi radius

right?

[mystic jay]

yes

now do you see why

[neon iron]

?

[mystic jay]

the arclength is = theta/360* of the circumference ?

[neon iron]

i dont get it

[mystic jay]

try looking at the arclength as a portion of the circle

the arclength covers theta

[neon iron]

ok

[mystic jay]

while the full circle covers 2pi radians

right?

[neon iron]

so the arc lenght is the portion

[neon iron]

yes

[mystic jay]

so

the ratio of the length of the arc to the circumference

is the ratio of the angle it covers to 2pi radians

right?

[neon iron]

yes

[mystic jay]

so

if the arclength is

k

k/(2pir) = theta/(2pi)

yes?

[neon iron]

i dont get it

[neon iron]

could u explain this bit again

[mystic jay]

so the ratio

of red length to blue length

is the ratio of theta to 2pi

yes?

[neon iron]

wait what is the central angle?

[mystic jay]

theta

[neon iron]

i get everything else

[mystic jay]

that oval thing is the symbol for theta

[mystic jay]

yes

[neon iron]

oval? wait the tiny thing in the middle of the portin?

portion?

kk

[mystic jay]

yes

[mystic jay]

so you get this

right?

[neon iron]

yep

[mystic jay]

so

[neon iron]

wait

what does the oval represent

[mystic jay]

it rpresents angle

[neon iron]

oh ok like 45

degrees

kk

[mystic jay]

yes

[neon iron]

yep got it

[mystic jay]

so

arclength/2pir = central angle/2pi

yes?

[neon iron]

yes

but what is 2 pir

circumference?

[mystic jay]

length of circumference

[neon iron]

kk

[mystic jay]

so multiplying by 2pir

we get

arclength = central angle (in radians) * r

[neon iron]

got it but what is radians and what is 2 (pir)?

[mystic jay]

radians

is the unit of angle

in which 360* = 2pi radians

[neon iron]

radius?

[mystic jay]

it is defined so that that 1 radian has arclength of 1 radius

[neon iron]

oh ok

[mystic jay]

ok

[mystic jay]

do you get this?

now

[neon iron]

so the arc length is the portion of the section = to the angle of the portion?

[mystic jay]

into radius

[neon iron]

?

x radius?

[mystic jay]

yes

[neon iron]

ok so the arc length is the portion of the section = to the angle of the portion? times radius?

[mystic jay]

yes

[neon iron]

and thats the arc method?

[mystic jay]

thats the arc length formula

[neon iron]

ok so how do i use it for this problem

[mystic jay]

do you know how many radians 90 degrees is?

[neon iron]

idk

90?

[mystic jay]

360 degrees is 2pi radians

right?

[neon iron]

yes

[mystic jay]

so

90 degrees = 360degrees/4 = 2pi radians/4 = pi/2 radians

yes?

[neon iron]

???

[mystic jay]

90 degrees = (1/4) * 360 degrees

yes?

[neon iron]

ok 360/4=90 = 2pi radians/4 =

what does the pi/2 radions mean

[mystic jay]

2pi/4

radians

=pi/2 radians

[neon iron]

so is it 3.14/2?'

[mystic jay]

yes

[neon iron]

oh ok so the answer is that?

[mystic jay]

yes

they would expect 1.57 ig tho

[neon iron]

oh ok

ok i go tit right thx but could u summarize what you said like everything so that i could write it down?

[mystic jay]

uhmm

i am bad at englsih

stuff

[neon iron]

like a few sentences

[neon iron]

thats alright

no prob

i can rewrite it

like just tell the all of the formula and the steps

[vestal totem]

no.

[mystic jay]

ratio of arclength of to circum ference is ratio of angle to 2pi
so we get
arclength = angle (in radians) * radius
so
arclength = 90 degrees (in radians) * 1
90 degress = 360/4 degrees = 2pi/4 radians = pi/2 radians
so
arclength = pi/2
which is 3.14/2 = 1.57

[vestal totem]

!15m

[topaz sinew]

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

[neon iron]

thx so much

[vestal totem]

All you need to know here is that an angle in radians is by definiton $= \frac{\text{arc length}}{\text{radius}}$

[thorny flame]

Percy

[topaz sinew]

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[stark crater]

Hi

[stark crater]

I have this de power series sol

It's my teacher's sol

And my solution is very close to it but it's different in the constants. My guess it's abt expanding the series

[chilly walrus]

your teacher re indexed the series

[stark crater]

Yeah.. I've marked c1 constant. I think it should be c1x not c1x^0

[chilly walrus]

$\sum_{n=0}^\infty c_n x^n = c_0 + \sum_{n=1}^\infty c_n x^n$

[thorny flame]

artemetra

[stark crater]

Yeah I got all of that

Can u open the pics?

I marked a circular red mark on the constant c1 in both my teacher's and my solution

I think that what makes the 2 solutions different

I wonder if the mistake from the teacher's side

[chilly walrus]

i don't think it's a matter of a mistake but rather consistency

if you start with 0-based index use it till the end

but honestly I can't read all of that rn, sorry

[stark crater]

Fair enough..

Thanks for helping out

[topaz sinew]

@stark crater Has your question been resolved?

[topaz sinew]

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[grave hedge]

can someone help me with part d? how did they work out the values of 6.4, 11.6, 15.4?

[deep forum]

calculator maybe

[grave hedge]

how? what do i press?

[craggy pond]

They just set up the equation to solve for t

P was given, so they plugged it in, and manipulated the question algerbraically til they isolated t

[grave hedge]

yeah but how did they work out 6.4, 11.6, 15.4

[craggy pond]

the expression

[timber vault]

a calculator gives 2.6, periodicity of cos gives infinitely many more solutions

[deep forum]

yes periodic solution

[timber vault]

cos(t) = cos(t+2pi)

[deep forum]

what about arccos tho

[glass maple]

u might want to commit general solutions of each trig

to memory

[timber vault]

arccos is inverse cos function

[deep forum]

how do you inverse the period

[glass maple]

what do u mean>

[timber vault]

uh

[glass maple]

u are not inversing the period

[timber vault]

yeah i just mean you can add any int multiple of 2pi to the answer a calculator gives

[deep forum]

2.6 + 2pi = 8.4 tho

[grave hedge]

so to work out the 6.4, it'll be 2.6+2pi?

[glass maple]

thats not how the periodicity works?

[timber vault]

there's a scale factor in this q

[glass maple]

u are missing solutions if u only add 2pi

[timber vault]

oh right yea

[timber vault]

this is wht i mean

[topaz sinew]

@grave hedge Has your question been resolved?

[grave hedge]

how did you get to 9k?

[timber vault]

same as this from line 4

[grave hedge]

Okay I get it now

[grave hedge]

Thank you

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[neon iron]

I was wondering if my algebra is correct, I have no premium so I have to guess it myself

[neon iron]

This is regarding the derivative of x^arcsinh(x)

[mortal thunder]

You're all good >.<

Except replace y with y' from line 3 maybe

[neon iron]

Thank you, I was wondering back then why was wolfram alpha giving me a different answer

so I really have no idea what to do and that's what I came up with

[neon iron]

oh yeah I forgot about that

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[wispy pier]

Hi bro !

[leaden swallow]

how do i proceed here?

[leaden swallow]

hello!

[wispy pier]

! status

[topaz sinew]

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

[leaden swallow]

I don't know where to begin

[wispy pier]

Start by writing the equation of PR and QS

[leaden swallow]

done

[wispy pier]

Then Calculate T

Done ?

Now we will find line TA , DRS of TA is the cross product of DRS of PR and QS and it passes through T

[leaden swallow]

okay

[wispy pier]

If you generate the line

You can represent all parameters of A in respect to a constant

And use the distance condition to determine it

You need further assistance?

[leaden swallow]

ah okay i get it

btw is this question really difficult or is it with me only?

@wispy pier

[wispy pier]

Not that difficult

Once yk how to

[leaden swallow]

oh okay

maybe i got anxious just by looking at it

.close

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[strange basin]

needs checking as it may be wrong

[topaz sinew]

@strange basin Has your question been resolved?

[mortal thunder]

u = 12.16 m/s

Now, you need v_f after the 1.6s of falling which is,

v = 12.16 + 9.8(1.6)

Now, total s = (v² - 0²)/2g

[strange basin]

ham letmetrythat

[mortal thunder]

Your final s should be 39.54 approx

[strange basin]

is my answer wrong

which part of my answer is wrong

[mortal thunder]

,calc 0.59.81.2385*1.2385

[thorny flame]

Result:

7.516023025

[mortal thunder]

I suppose you miscalculated s in your solution

[strange basin]

so

u is correct

and then from there which part is wrong

[mortal thunder]

t's also right. Recalculate s

[strange basin]

Ok

I still don't get it

could u show ur working for s

[pliant pecan]

hallo

[strange basin]

hi

[topaz sinew]

@strange basin Has your question been resolved?

[pliant pecan]

hi

[strange basin]

<@&286206848099549185>

[topaz sinew]

@strange basin Has your question been resolved?

[strange basin]

.close

[topaz sinew]

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[neon iron]

In the following graph, AC=AD and BE=9, EC=7.
Find DE.

[neon iron]

<@&286206848099549185>

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[nocturne obsidian]

I don't understand 7 & 8

[nocturne obsidian]

How do I even start to attempt this question?

[pseudo bear]

Draw the lines.

Or just find the slopes.

Tangent of an angle will give you the slope.

So, arctangent will take a slope and give you an angle.

[nocturne obsidian]

Oh so like the tan of the gradient?

[pseudo bear]

No, tan(angle) = gradient.

arctan(gradient) = angle.

[nocturne obsidian]

Oh I ment like that

[pseudo bear]

Oh, OK.

[nocturne obsidian]

Mb

[pseudo bear]

If the gradient is infinite, it's either the straight up or straight down angle.

[nocturne obsidian]

Right....

Ok so for example for 7c

The gradient is half

So arctan(1/2) = 26.57

[pseudo bear]

,calc atan(1/2) * 180 / pi

[thorny flame]

Result:

26.565051177078

[nocturne obsidian]

Basically rounded to the 2nd decimal place

[pseudo bear]

Yes, looks good.

[nocturne obsidian]

Alright so that's Basically it?

[pseudo bear]

Note that arctan will give you the angle with the positive x axis.

[nocturne obsidian]

Yea

[pseudo bear]

If you want the angle from something else, you have to adjust.

[nocturne obsidian]

Makes sense

[pseudo bear]

But that's basically it.

[nocturne obsidian]

Is there anything else to note down?

[pseudo bear]

No, as long as you got arctan(gradient) = angle and the thing about infinite gradients, that should be it.

Oh, one second.

[nocturne obsidian]

?

[pseudo bear]

,calc tan(45 deg)

[thorny flame]

Result:

1

[pseudo bear]

,calc tan(225 deg)

[thorny flame]

Result:

1

[pseudo bear]

Note that the tangents are the same 180 degrees apart.

Because the slopes are the same.

[nocturne obsidian]

Yea I've learnt the unit circle

[pseudo bear]

So, I guess you need to take into account the quadrant.

[nocturne obsidian]

?

How so

[pseudo bear]

Well, if you have a line from (0, 0) to (1, 1), that's at a 45 degree angle from the positive x axis.

[nocturne obsidian]

The question is only asking for the angle

[pseudo bear]

If you have a line from (0, 0) to (-1, -1), that's at a 225 degree angle from the positive x axis.

But the slope is the same for both.

[nocturne obsidian]

Nono i get that, but in what circumstance do I need to specify the quadrant

[pseudo bear]

Hmm, I don't know given the question.

[nocturne obsidian]

It's only asking for the angle as far as I know

[pseudo bear]

It's using a line rather than a ray.

Do you know about reference angles?

[nocturne obsidian]

It might be a different term that I know but please do explain

[pseudo bear]

Well, reference angles tell you how far in degrees an angle is from the x axis.

Like if you have an angle of 179 degrees, that's 1 degree away from the x axis.

[nocturne obsidian]

Mhm

[pseudo bear]

Same if you have an angle of 181 degrees.

Or 1 degree or 359 degrees.

[nocturne obsidian]

Ohh I get it

Yes I already know this

[pseudo bear]

I don't know if it's asking for the actual angle or how far in degrees the angle is from the positive x axis.

Because it says "Find the angle the line makes with the positive direction of the x axis".

[nocturne obsidian]

No i it means the gradient should be positive

The line should go right instead of left

[pseudo bear]

,calc atan(tan(0.5))

[thorny flame]

Result:

0.5

[nocturne obsidian]

??

[pseudo bear]

OK, so it looks like atan gives you the angle in quadrant 1 or 4.

So, the heading-to-the-right angle.

[nocturne obsidian]

.

Yea yea

[pseudo bear]

The only thing I'm not sure of is if it wants the angle or the absolute value of the angle.

Like if it's -1 degree, that's 1 degree away from the positive x axis.

[nocturne obsidian]

I think your making it more complicated than it needs to be

[pseudo bear]

Probably.

[loud ingot]

I have a question.

[nocturne obsidian]

What is it?

[pseudo bear]

If you mean a math question, #❓how-to-get-help will show you how to get a help channel.

[loud ingot]

What is the topic you are studying?

[pseudo bear]

Oh.

[nocturne obsidian]

Coordinate geometry & linear relations

[loud ingot]

I am guessing you are in middle school?

The question is worded weirdly ngl

[nocturne obsidian]

idk if 11th is middle school for you but for me its secondary

[loud ingot]

Guess sketching the line is the best way to do it

[nocturne obsidian]

i was just asking what i would do after it

[loud ingot]

Middle school is like 5-8

Well once you have the sketch then it's just trigonometry I assume

[nocturne obsidian]

and then i find the elevation right?

Alright im stuck on 8e

same question but difficult is the equation

[thorny flame]

Dev

[nocturne obsidian]

what do i do next?

nvm i got it

[topaz sinew]

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[prisma lake]

Only 8, i think i have the answer but i have doubts

[prisma lake]

!status

[topaz sinew]

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

[prisma lake]

4

I got the answer 1936^127776

[nocturne obsidian]

which question?

[prisma lake]

8

im on 4 for status

[nocturne obsidian]

i got

[thorny flame]

Dev

[nocturne obsidian]

basically what i did was root 85184

Which gave me 1936

[thorny flame]

Dev

[nocturne obsidian]

so

[little pine]

,calc 1936^2

[thorny flame]

Result:

3.748096e+6

[nocturne obsidian]

huh?

[little pine]

yea it's not the same

[nocturne obsidian]

What

oh

oops

[little pine]

I got that answer too

,w Solve[85184^85184 = 1936^x, x]

[nocturne obsidian]

OOh nvm i did smt very wrong

mbb

[prisma lake]

cuz when you make the base 44 you can raise it to 1/2 (44 turns into 1936)

[thorny flame]

Results provided by WolframAlpha

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

Requested by sepdron

[prisma lake]

all good

[little pine]

wolfram agrees too
ignore the imaginary part

[prisma lake]

i dont understand i

i

[little pine]

I did 85184*log_1936(85184)
and that got me the power

[prisma lake]

i did smth diff

i prime factorized 85184 to get (44^3)^85184
then power of a power to get 44^255552
then (1936^1/2)^255522
which equals 1936^127776

not the most effective but its what i was taught

[little pine]

ah that's smart
that's probably the intended way
I did the log thing to get a shortcut that 85184 = 1936^1.5
1.5 is the log value

then same idea

[prisma lake]

both work 👍 🙂

for efficiency your method is better

ok thanks guys!

.close

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[little pine]

yea but also need a calculator

np!

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[prisma lake]

idk how to make that into normal form

[thorny flame]

verDerber

[prisma lake]

there we go

[topaz sinew]

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[indigo bone]

Hi, can anyone tell me what (ii) wants?

[ashen pecan]

Calculate the change of variable and use that to express the old derivatives in terms of the new ones

[viral lantern]

I think thats just a roman numeral

ii for 2

iii for 3 iv for 4 and so on

[ashen pecan]

Ahh. I thought you meant iii

[indigo bone]

I actually solved iii, not sure how to decide ii

[indigo bone]

I mean the question 😂 not the meaning for ii for 2 and iii for 3

[viral lantern]

yeah i just realized that lmao

[indigo bone]

May I know what you mean? You mean what I did in iii?

[ashen pecan]

Yes. Exactly what you did

[indigo bone]

I wonder how to tackle ii, I asked my tutor and she also said not sure what to do for ii

[ashen pecan]

I know you want to draw characteristic curves like how you do for first order equations but idk if I was taught it for second order

[indigo bone]

Yea

[topaz sinew]

@indigo bone Has your question been resolved?

[topaz sinew]

@indigo bone Has your question been resolved?

[indigo bone]

<@&286206848099549185>

[topaz sinew]

@indigo bone Has your question been resolved?

[peak spruce]

Have you studied both 1st order and 2nd order PDEs ?

[topaz sinew]

@indigo bone Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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[plain abyss]

I need help in my math

[sinful flint]

!da2a

[topaz sinew]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[plain abyss]

Does anyone know about…?

d=rt

can anyone help me to solve

[sinful flint]

!status

[topaz sinew]

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

[plain abyss]

2. I have begun but got stuck midway.

[hoary burrow]

First, can you find the time dick needs to give jack a head start on

[cedar phoenix]

Ez

Yes

Time taken for both

[hoary burrow]

You are not op😭

[plain abyss]

I have find the dick rate and jack rate
dick is 8 yards/second
Jack is 5 yards/second

[cedar phoenix]

Then absolutely value the difference and multiply by jack speed

Wait

[hoary burrow]

Now how much time does dick need to give a head start jack before starting to run

[cedar phoenix]

Jack takes 33 seconds more

[hoary burrow]

Bro you're not OP😭

Ok but yes so Dick needs to give Jack a 33 second head start

[dim plume]

he is overpowered tho

[cedar phoenix]

(440×33)/88

Ans

[dim plume]

get em 2015 doggo pfp

[cedar phoenix]

33 I ment

[plain abyss]

15

[hoary burrow]

Ok welp that works ig

[plain abyss]

is like that

[hoary burrow]

In this case it's simpler

[cedar phoenix]

165 yards

Correct answer

[hoary burrow]

You can just multiply the speed of jack by the time dick gives him a head start on

[plain abyss]

how to calculate?

so 5 yards * 55

?

[hoary burrow]

5 yards/second * 33 seconds

[cedar phoenix]

So how much time headstart should Dick give jack to complete the race

Tell me

Denzino u ain't helping

[hoary burrow]

Welp he already knows the answer anyway

[cedar phoenix]

Ok

[hoary burrow]

Since you kinda just like

[cedar phoenix]

Welp

[hoary burrow]

Did that so

Might as well end it here

[plain abyss]

I need the calculation

[hoary burrow]

This

[cedar phoenix]

Ok so how much time

SO Think

how much time would dick have to give jack

[hoary burrow]

Helpful

[cedar phoenix]

no wait

a better way

is

jack will complete the race in the 88th second right?

bruh ur so slow at responding chinese guy

or whatever language that is

[hoary burrow]

Is your native language Chinese

I can try explaining in Chinese

[plain abyss]

yep

[hoary burrow]

Ok

[dim plume]

https://tenor.com/view/social-credit-social-credit-score-meme-john-xina-gif-23649557

[plain abyss]

some I not very understand

cause I need to use the equation to solve

[cedar phoenix]

Jack --> race --> time --> how much?

[hoary burrow]

Jack的速度是5yards/second

[cedar phoenix]

u understand that?

[plain abyss]

yeah

[hoary burrow]

Dick在88秒后才会完成比赛

但jack要55秒

[plain abyss]

Dick是五十五秒

Jack 还是88秒

[hoary burrow]

阿对不起

[cedar phoenix]

🥷 ⌛ -- > 88
👨 ⌛ --> 55

👨 ⌛ + 33 = 88

🥷 speed = 5 yard/s

🥷 speed x 33 = 165 ⌛

got this

chinese

[hoary burrow]

如果dick等33秒才跑

dick和jack会一起完成比赛

这你理解吗？

[pearl fog]

bro wtf is this channel

[plain abyss]

理解
所以calculation 就是

5 yards 乘 33

然后拿到 165

[plain abyss]

yes

[hoary burrow]

对

[plain abyss]

原来

[deep forum]

Dick gives 33 seconds of headstart
Jack runs 440yard/88seconds
How much does Jack run in 33 seconds?

[hoary burrow]

A bit late ig

[plain abyss]

等下我还有其他问题要问