help-0

[paper hull]

can i get some help?

[paper hull]

its homework due tmre

tmrw

for tuitions

<@&286206848099549185>

[lone heart]

@paper hull Has your question been resolved?

[gray isle]

that are so many questions there
is there a specific one you need help with

[paper hull]

quite a lot ill show u which ones im struggling with

thats it

[mortal mantle]

I can help with this one real quick

[paper hull]

alr ty

[mortal mantle]

Have you learned how to calculate the slope of a line

[paper hull]

i dont think

a lot of this is a lot higher level than me

im grade 7 and this is a lot higher

in my country

[mortal mantle]

So you weren't taught this stuff but you have homework on it ?

[paper hull]

basically

we have to figure it out

and try it

but if u dont do it

she gets mad

and tells ur parents

which i dont want to happen obv

[mortal mantle]

Well you would have to learn the concepts for these then

https://youtu.be/9bm1_IJ00lQ

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/slope-of-a-line-2

If you watch those 2 videos it will give you the knowledge to do that question

This will be used a lot more throughout math so it's better to learn the concept for it now

[paper hull]

oh wait

i know hpw to do it

like

calculating slopes

rise/run and x2- x1 over y2- y1

[mortal mantle]

Yes

That's what you do foe those questions

Slope = m

Fir your other question, it's jist asking for you to graph it. They give you the x axis and y axis range. Then you just plot your points on the graph

@paper hull

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[quaint ivy]

This is the prompt for problem 14. Is there a simpler way for me to find the Maclaurian series other than brute calculating the first five derivatives? I assume it has something to do with the "perform multiplications, divisions, and so on" hint of the prompt, but I'm not sure how to do that

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@quaint ivy Has your question been resolved?

[quaint ivy]

<@&286206848099549185>

[amber iron]

what do you need help for

no, the simpler way is to find the patterns in the coefficients

you know how to do it?

[quaint ivy]

I don't lol

[amber iron]

alright then write out the series for f(x) in summation form

[quaint ivy]

I'll try with that, thank you

.close

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[glossy oxide]

Does someone know how to do this

I tried the ratio test

Got one

The gauss's test looks like it gets to complicated so its probably not the way to go

Ik that if you insert instead of e something smaller than e

Its convergence

If you insert something bigger than e

Its divergent

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@glossy oxide Has your question been resolved?

[ruby summit]

I am not sure

My guess would be to make an infinite sum of a geometric series where the common ratio would be $\frac{e}{n}$ and the starting value is e.

[ocean seal]

Bman

[ruby summit]

@glossy oxide

[glossy oxide]

Well

[ruby summit]

Ohh nevermind you are changing n

[glossy oxide]

Ye its real freaky

[crisp grove]

what are you trying to find? the limit or just it's convergent or not

[glossy oxide]

Does it convergence or not

[crisp grove]

have you tried doing $|a_n|^{1/n}$?

[crisp grove]

tell me what is the value of $\lim_{n\to\infty} \frac{n!}{n^n}$

[glossy oxide]

Ill then gen a nth root of n! And idk whats that

[glossy oxide]

Das a 0

[crisp grove]

yeah and what's $\lim_{n\to\infty} \left(\frac{n!}{n^n}\right)^{1/n}$

[crisp grove]

off

[glossy oxide]

Im guessing a 1 or a 0

[crisp grove]

no

also don't guess

[glossy oxide]

That'll be a 0^0

[crisp grove]

ok, I think there are other ways to do it as well

do you know that a necessary condition for a sum to converge is that the terms must go to zero as n tendo to infinity?

[glossy oxide]

Yes

[crisp grove]

you need to use the fact that $n!\sim \sqrt{2n\pi} \left( \frac{n}{e} \right) ^ n$

[crisp grove]

that's the stirling's approximation of n!

for large n

[glossy oxide]

Oh that makes it much simpler

[glossy oxide]

Ok i see this must equal 1/e

[crisp grove]

it is

[glossy oxide]

And if i prove that its just a lil jump from that

But idk how to prove its 1/e because if i try to

Write a n^n-n^n

In the upper part of the fraction

So that i can get a 1 out of the fraction

I end up with a e to the 0

[lone heart]

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[molten elk]

How do I prove this?

[molten elk]

I don't understand how I would be able to prove this using the notion of a normed vector space

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[molten elk]

<@&286206848099549185>

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@molten elk Has your question been resolved?

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@molten elk Has your question been resolved?

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[alpine sable]

Whats the memory that storages the BIOS that is the software that makes inventory of the harware?

[bleak ridge]

I mean it's just stored in a chip on the motherboard

I'm not sure how this is a math question though

[alpine sable]

its informatics question

i think the answer is ROM

[raw shard]

this isn’t a math question

@alpine sable close this channel

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[alpine sable]

does anyone know how to program a calculator

[alpine sable]

like can you take out the mother board and how would I connect it to my pc?

<@&286206848099549185> 🙂

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[charred flint]

you can do that with some graphing calculators with a USB cable

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[rough owl]

need help

[buoyant kayak]

cool

[rough owl]

ummm

[raw shard]

close the channels

[rough owl]

Can I ask help for my assignments then?

[raw shard]

if it’s not a test

still close the other channel

[rough owl]

okay

[raw shard]

it would be nice if you sent a question and closed the other channel

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[odd lion]

help

[alpine sable]

With?

[odd lion]

power bank offers two types of interest accounts. The first account offers 6% compounded monthly, while the second account offers 6.5% interest compounded semi-annually. Which account would you choose if your goal is to grow your 120,000 peso savings and not withdraw from it for 10 years?

@alpine sable

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@odd lion Has your question been resolved?

[glass lichen]

You only need 1 channel..

[odd lion]

okay

[sly mantle]

@odd lion pls dont multipost

.close

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[normal turtle]

can i get some help on this question?

[lone heart]

@normal turtle Has your question been resolved?

[bleak ridge]

Did you not learn about this form of equation?

If not I'd just derive the Cartesian form

Tbh

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[royal falcon]

Hwlp

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[spark salmon]

im trying to find the shortest distance between these two vectors. could anyone let me know if i did this correctly?

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@spark salmon Has your question been resolved?

[devout summit]

Why are the parameters of r_a and r_b the same?

Shortest distance you get this way is not necessarily the minimum.

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[brazen hawk]

i need help on a and B

[foggy otter]

You'd create a equation to model the cost of each plan and then set them equal to each other

[brazen hawk]

ik

but wuts the equation

@foggy otter

[bold token]

you can set x as the needed minutes

[brazen hawk]

ik its

15 + 0.08x = 3 + 0.12x

[bold token]

then find x

[brazen hawk]

x = 300

how do I solve part b

[foggy otter]

multiply 15 by 30 and plug in

[brazen hawk]

plug in how

[foggy otter]

what does x represent in your equations

[brazen hawk]

uh

[bold token]

yeah, use the equation u just made

[brazen hawk]

idk

[bold token]

in the equation, the x is the minutes right?

[brazen hawk]

ye

its minutes

i would put it in twice or in its simplified equation?

[bold token]

so in b, it is given that there is 30 minutes in each call, then ---

[bold token]

wdym by that

simplified equation

[brazen hawk]

lik15 + 0.08x = 3 + 0.12x

make that

[bold token]

you made two equations right?

[brazen hawk]

simplified

i made 1

[bold token]

yeah but that's Plan A = Plan B

in b, ur finding which is cheaper

and each equations from Plan A and Plan B has x as the minutes

[brazen hawk]

wait

i dont udnertsand

[bold token]

in the question b, you don't need to connect the two equations

[brazen hawk]

so then

[bold token]

you plug in the x's separately in Plan A(15+0.08x) and Plan B(3+0.12x)

then find which is cheaper

[brazen hawk]

OH

then you put the

15 x 30

[bold token]

yes

[brazen hawk]

into both of those?

[bold token]

yeah

[brazen hawk]

ty

my last question is this

[bold token]

have you encounter "working together" problems before?

[brazen hawk]

nope

this is a quiz

[buoyant kayak]

you're not allowed to cheat on this server

[brazen hawk]

its a

test we are allowed to work together

[magic geyser]

[bold token]

idk what to do 😕

[buoyant kayak]

you are definitely not allowed to cheat on tests

[bold token]

ayo you didnt help me yesterday 😡

[magic geyser]

?

[bold token]

the probability problem, but sure I blame my knowledge abt it

[magic geyser]

you should just have stayed in school

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@brazen hawk Has your question been resolved?

[buoyant kayak]

@brazen hawk you might as well close this channel, nobody is going to help you with a test

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@brazen hawk Has your question been resolved?

[lone heart]

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[short sapphire]

Please help plsss

set-builder notations represents (-2, 10].

[short sapphire]

I'm stucked here

[gray isle]

based on the phrasing of the question its multiple choice,
what are the options and what exactly are you confused by?

[short sapphire]

@gray isle

[gray isle]

and what exactly are you confused by?

[lapis ingot]

( means it doesn't include -2 and ] means it includes 10

[short sapphire]

So what

is

the letter?

[gray isle]

what letter

[short sapphire]

the answer

[gray isle]

#❓how-to-get-help

[short sapphire]

I'm kinda stucked on this problem because the question is came out of nowhere

[gray isle]

we don't give answers away like taht here

[lapis ingot]

well < means strictly less than and > mean strictly greater

[gray isle]

and what exactly are you confused by?

[lapis ingot]

and equal or less and strictly or greater means that it also can be equal and not just strictly greater or less

[lapis ingot]

do u understand now

[short sapphire]

ye

.close

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[dry echo]

Just a quick question.
Should the sign be reversed if I square both sides of an inequality?

[gray isle]

depends

[dry echo]

On what?

[gray isle]

signs and/or magnitude of what you originally had

[dry echo]

Interesting

Are there any resources I can read about this?

I wanna visualize that

[gray isle]

you could consider some examples

7 > 3
7 > -3
7 > - 16
-7 < - 3

[dry echo]

oh

That certainly helps

I see it now

thank you!!

.close

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[alpine sable]

I don't understand b)

in the textbook, the answer for b) just says 4, 3

but i dont get it

[bleak ridge]

Constant of variation is how much the y changes for each x

[alpine sable]

OHH

omg tysm

.close

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[rustic tendon]

i made an integral from using these 2 curves,, and did it on my calculator and im still getting it wrong please help, thank you uwu.

Dox — Today at 9:22 PM

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@rustic tendon Has your question been resolved?

[lone heart]

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[alpine sable]

hi

[hollow vapor]

If 250 is 8% of the purchase price then what is the actual sale price?

[alpine sable]

is the ans 1195

[alpine sable]

250 divided by 8 times 100

[hollow vapor]

Ye

[alpine sable]

is it 1195?

[hollow vapor]

You got it

Yep

[alpine sable]

oh so thats the answer

alrighty ty

oh

it was wrong

[hollow vapor]

Wait how

[alpine sable]

we had to add 250 ig

[hollow vapor]

Oh

Im so sorry

[alpine sable]

all good

[hollow vapor]

I want to erase myself im so sorry

[alpine sable]

dw all g

over here do i do 1445 divided by 5, over 3125?

nvm

.close

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[alpine sable]

How do I find x. I dont know if i should use the theorems or not

[gray isle]

I dont know if i should use the theorems or not
use whatever theorems you want

[alpine sable]

idk which one to use

[gray isle]

consider first connecting A and O
and B and O

the consider the relation between the central angles and arc measures,
basic angle sums
properties of circles
and some triangle theorem(s)

[alpine sable]

thanks

.close

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[orchid forge]

For question 2, I got the answer x=4.5 but on the markscheme it said the answer is x=-3, can somebody explain how this is possible?

This is my working.

Oh no its flipped.

There we go.

[tight locust]

Thats not how logarithms work haha.

[orchid forge]

Wait it's not?

[tight locust]

b*log(a) = log(a^b)

[jagged imp]

to be specific this is where you fucked up

[orchid forge]

Oh.

[tight locust]

Lmao

[orchid forge]

I had to bring it to exponents?

[jagged imp]

and you should use the log law endtimes said

[orchid forge]

Wait so if I can apply any of these log laws I HAVE to apply them?

Because I thought they are the same thing I don't have to change it.

[tight locust]

But its not the same thing on both sides

One of the sides has a factor of 2 in front

[orchid forge]

Yeah but that's because I multiplied by 2 to get rid of the denominator right?

[tight locust]

So you cant just cancel out the logarithm because of the extra factor

[orchid forge]

Ohhh.

I have to bring the coefficient to the exponent before I can cancel out the logs?

[tight locust]

Yes

Then it's perfectly fine.

[orchid forge]

Ohh.

Ok tyvm.

I have semester exams next week and I am so fucked.

Lmaooo.

I have to study for HL chem, SL bio, HL econ, SL maths, and english and japanese.

[tight locust]

Sounds fun

I have Econ and Stats

[orchid forge]

Oof.

Do you take IB?

[tight locust]

I'm in college lmao

[orchid forge]

OH.

Well uh did you take IB?

[tight locust]

Nah they didn't have it at my school

[orchid forge]

Oh.

I honestly regret taking IB.

Yeh anyways ty for the help.

.close

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[neat laurel]

can someone pls help me solve this?

[gray isle]

what have you tried

[neat laurel]

i tried using change of y/change of x, and the cross multiplying it
so b-0/1-1=-1/5, but the book says b should be 5 and i got 0 solving it

[gray isle]

b-0/1-1
notation is confusing also where's that coming from

[neat laurel]

i assumed (1,0) is a point for the line, so i thought using that might work

idr how to solve it anymore lol

[vale wigeon]

(1,0) is a point on the graph of y = 1/x?

is that what you're saying you assumed?

[gray isle]

also why are you choosing some random point

instead of what they're asking for

[vale wigeon]

to solve this problem all you need to know is the definition of average rate of change

[true jackal]

sorry to disturb But can I please Ask a question?

[gray isle]

#❓how-to-get-help

[vale wigeon]

@true jackal go to a channel in the Math help (available) category.

@neat laurel are you still here y/n

[true jackal]

yea but no one has arrived to help

[vale wigeon]

be patient, and also do not occupy more than one channel.

[gray isle]

ironically multiposting and helper spamming works against that

[true jackal]

Sorry

its just that it was very urgent

[neat laurel]

sorry my laptop died

[vale wigeon]

have you brought it back to life?

[neat laurel]

yes

[neat laurel]

cause idk how to solve it

[gray isle]

do you know the formula for aroc?

[vale wigeon]

to solve this problem all you need to know is the definition of average rate of change

[neat laurel]

ok

[vale wigeon]

do you know the formula for the average rate of change? Y/N

[neat laurel]

yeah

changee of y/ change of x

[vale wigeon]

okay, so can you write out the average rate of change of f over the interval [1,b]?

in terms of b, obviously.

[neat laurel]

oh wait

im not sure what u mean

[vale wigeon]

i mean exactly what i said

[neat laurel]

i thougnt it was -1/5 cause the question says that

[vale wigeon]

yes, but that's not what we care about right now

our goal is to construct an equation in terms of b

so that we may solve it for b

-1/5 will be on its right-hand side

[gray isle]

can you state the change in y from 1 to b

[vale wigeon]

but we want to make the left-hand side

[neat laurel]

ok

[vale wigeon]

can you state the change in y from 1 to b

[neat laurel]

i solved it

thc

thx

b = 5

[neat laurel]

obviously, but if someone doesnt know how to solve it and theyre confused, they might not immediately understand

but ty for ur help

.close

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[vale wigeon]

you don't need to thank me for things i didn't do

[lone heart]

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[brazen oak]

Alright so i'm helping a younger friend of mine with their math studies and so far it's been pretty straightforward until (ii) of this question, where i keep getting 109.636 (to 3dp), and according to the jumbled answer key, this answer does not exist, which has left me confused.

Would love to know another interpretation of this question, i'm losing ego by the minute

[spice aurora]

which part do u need help?

for part 1 you have paid off 15% of the cost

[brazen oak]

I had specified (ii),

would like to know if the answer of 109.636 is correct and simply not placed on the answer key, or i have misunderstood what the question was asking

[spice aurora]

oh ok

[brazen oak]

yep, 5680 * 0.85

[spice aurora]

let me check

that is correct

[brazen oak]

Yeah, alright phew, I thought all the math ability i have learnt has just left my brain

Thanks!

[spice aurora]

np

[lone heart]

@brazen oak Has your question been resolved?

[alpine sable]

wait

dirt ur here

@brazen oak its me kyen

[alpine sable]

and it isnt correct

[spice aurora]

?

[alpine sable]

the answ is wrong

its not in the options

[spice aurora]

wdym not in the options?

[alpine sable]

there are a set of options given

that question is from me btw

#help-1 no one answered 💀

[spice aurora]

he did not mention that

[lone heart]

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[alpine sable]

oop

anyways there are a set of options soo

the ans was wrong whatever they got

[lone heart]

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[civic pagoda]

can somebody please help in simplifying

[civic pagoda]

please somone

[rough owl]

I can help

@civic pagoda

[civic pagoda]

sure give it a try

[rough owl]

x/32y

[civic pagoda]

yeah but how exactly ?

[rough owl]

mutiply

[raw shard]

(3x/12)(y/(8y^2)) = (3x/12)(1/(8y))

[rough owl]

@raw shard I need help

[civic pagoda]

did I do right ?

[raw shard]

no

[magic geyser]

don't tag people to say that u need help when u have a channel opened lol

[rough owl]

I meant for him

not for me lol

[civic pagoda]

how then ?

[raw shard]

what i sent is all the steps

[civic pagoda]

ok

[civic pagoda]

Thanks

.close

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[austere jetty]

Does this mean my system dont have a solution?

[austere jetty]

this came from AX=B, then LUX=B, THEN L(UX)=B// UX=Z// LZ=B

To end up doing UX=Z

but i dont know if it has no solution

because every non square matrix is gonna end up with a row full of zeroes

[lone heart]

@austere jetty Has your question been resolved?

[lone heart]

@austere jetty Has your question been resolved?

[alpine sable]

<@&286206848099549185>

[lone heart]

@austere jetty Has your question been resolved?

[austere jetty]

🥺 anyone?

[alpine sable]

Do you know what back-substitution is?

Give that a try

Or equivalently, multiply it all out and see what happens,

[austere jetty]

I don't know about back substitution

The thing is

I can solve the equation

but

the fact that there is a row full of zeroes wouldn't in theory mean that it is an incompatible system?

[alpine sable]

Imagine this, if you truncate the matrix so that it only has 6 rows, that won't change the result of multiplication by a vector for the first six entries in the resulting vector

And truncating it to only 6 rows gives you a reduced matrix with full rank, so what does that tell you

[austere jetty]

that it is in fact a compatible system?

[alpine sable]

Yeah
You can think of it geometrically too
It's a 7x6 matrix multiplied by a 6x1 vector, which you can think of as mapping a set of points in R^6 to one in R^7
Going up a dimension won't squish your vector if the matrix has linearly independent columns, which it does
But the last row is all 0s, so you also shouldn't gain a dimension
So the only way this system will work is if a_1 works out so that that last entry in the right hand side vector is 0

[austere jetty]

So

I have to find a value for a1 that makes the division 0 right?

Even tho that parameteer doesn't affect the others solutions?

[alpine sable]

It should make that expression 0 exactly
Cause if it weren't 0, then you would have something nonzero equal to 0

Multiplying out the left-hand side just for the last row gives you 0x1+...+0x6 = 0

So the right hand side should match too or else you have 0 = something nonzero

Which is definitely not true

[austere jetty]

yh thats what I thought

I was half right then

Somehow I was worried by a1 not having any influence over the others solutions

So in the case a1 wouldn't be there, it wouldn't have solution then right?

[alpine sable]

Yeah if it were just some number not equal to zero there

[austere jetty]

I see

[alpine sable]

Cause if I have a matrix that sends a point in R^6 into R^7 and makes the last coordinate 0, a point with last coordinate not equal to 0 could never have gotten there via that matrix

[austere jetty]

That makes sense

This clarifies everything, THANK YOU!!

hope you have a nice day 🙂

.close

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[lone heart]

@mortal goblet Has your question been resolved?

[lone heart]

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[tawny spear]

I need to prove that left side=right side

can anyone please help me with identities

[amber iron]

multiply left side by sinx/sinx

[tawny spear]

so 1/cscx-sinx * sinx/sinx?

but then what would that get me to?

[amber iron]

secxtanx

[tawny spear]

wait so what would the product be?

[wooden flint]

Anyone know how to do this

[amber iron]

0+0

[late bridge]

post in a free one

[tawny spear]

after we get that product then we would use an identity to change to secxtanx?

[sand pawn]

#help-5

[late bridge]

yes, you'll end up with sinx/(1-(sinx)^2) which you can simplify using pythagoras

[tawny spear]

thanks

.close

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[subtle coyote]

Need help solving these.

[lone heart]

@subtle coyote Has your question been resolved?

[subtle coyote]

<@&286206848099549185>

[lone heart]

@subtle coyote Has your question been resolved?

[crude falcon]

@subtle coyote what atr you having trouble with?

Are*

[lone heart]

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[dreamy raft]

hey guys I'm back, I decided to just abandon the other question because it was too hard and was taking too much time, but would someone be able to assist me with this one? Last question

[lone heart]

@dreamy raft Has your question been resolved?

[dreamy raft]

<@&286206848099549185>

hol up

I think I'm on to something

HAHAHA

.close

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[alpine sable]

let f be even function and g be odd function.
is function f/g an odd, even, both or neither of them?

[buoyant kayak]

do you have work thus far?

[alpine sable]

I know that f(x) = f(-x) = f(x)
and g(-x) = -g(x)

[buoyant kayak]

definitions of even and odd functions, yes

[glass lichen]

Apply that for f/g

[buoyant kayak]

[glass lichen]

Ie consider (f/g)(-x)

[alpine sable]

f(-x)/g(-x) = f(x)/-g(x)

[buoyant kayak]

and what does that mean?

[alpine sable]

both can be changed, so its even and odd function?

[slim fog]

(f/g)(-x)=f(-x)/g(-x)=f(x)/-g(x)=- f(x)/g(x)=-(f/g)(x)

therefore odd

[buoyant kayak]

don't do people's work for them

...especially when they're on the right track

[slim fog]

sorry

[alpine sable]

oh, I forgot that I can just do this:
(f/g)(x) = f(x)/g(x)

what if I try this:
let f be odd function:
what type of function is f²(x)?
f²(x) = f(x)*f(x)

f²(-x) = f(-x)f(-x) = -f(x)*f(-x) = -f(x)*-f(x) = f(x)f(x) = f²(x)
so f²(x) is an even function.

[glass lichen]

Yep

[alpine sable]

Yeah!!!

[glass lichen]

Wait sorry, messages just loaded in

f^2(x) is always even if f is even or odd

[alpine sable]

lets try (f + g)(x):
let f be even and g odd function.

(f + g)(-x) = f(-x) + g(-x) = f(x) - g(x) = (f - g)(x)

in this case, this is neither even or odd.

this is one is a bit tricky 🤔

is it not odd and not even?

.close

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[south rock]

In the speed chess competition involving both Year 12 and Year 13, there are nine more competitors from Year 12 than from Year 13. Each competitor must play every other competitor, and draws are not allowed – the game is replayed until someone has won. The winner of a game gets one point and the loser none.

In total the Year 12 players gained nine times as many points between them as did the Year 13 players.

Find the greatest possible score for a Year 3 player.

[lone heart]

@south rock Has your question been resolved?

[alpine sable]

I think it might be enough to consider the complete graph from this situation, and also the bipartite subgraph of that where all year 12s are playing year 13s

@south rock

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@south rock Has your question been resolved?

[lone heart]

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[simple elm]

K(x)=190000*e^(0,15x)

[simple elm]

The capital K grows with time x years according to the formula above

When has the capitol grown to 300 000?

I got to e^(0,15x)=1,6

But i dont know how to solve the x

[warped sleet]

have u done logs before?

[simple elm]

Not much

Im lost because of the constant in front of x

I have never done one of those before with constants in the exponent

[warped sleet]

well to take x down from being an index you should take the natural log of both sides

[simple elm]

Okay

Like so?

[junior ore]

from the first step e

u dont have to bring the x to the front yet

u can just take the nat log of both sides

and when u do this the e will be canceled out as ln is log base e, so u ll be left with 0.15x = ln1.6

i think it says those numbers

[simple elm]

Like so?

[junior ore]

booya

yes u correct

[simple elm]

Okay

Thanks

[junior ore]

welcome

[simple elm]

New question

Write an exponential fuction with the base e that meets the following requirements :

Start value at 3000kr, increase of 17%/year

I wrote y=3000*1.17e^x

Is that correct?

[warped sleet]

y did u put e in the equation?

[simple elm]

Because having a base of e is a requirement

[warped sleet]

that makes it a bit more complicated

thats a weird question if it says u must give it with base e

i would try to rearrange it so it takes the form 3000e^y

so the function 3000*1.17^x=3000e^y

then solve for y

[lone heart]

@simple elm Has your question been resolved?

[simple elm]

But i dont need to solve the y

[warped sleet]

u do if u need base e

[simple elm]

Okay now im confused

[warped sleet]

the answer to the question asked is 3000(1.17^x) but you said it needs to be in the form 3000e^y

if you solve 3000(1.17^x)=3000e^y for y in terms of x then u can sub it into 3000e^y to give answer with base e

[simple elm]

So i need to solve 1.17^x = e^y

[warped sleet]

yes

are you 100% certain they ask for base e

because thats v weird

[simple elm]

Yes i am

How do you go about solving something with unknown exponents on both sides?

I only have done it on one side before

[warped sleet]

u will get one in terms of the other

[simple elm]

e^y should just become ln e

And the other side would be x * ln 1.17

[warped sleet]

to solve it i would take natural log of both sides so ln(1.17^x)= y

[simple elm]

I got x=6,4

[warped sleet]

its not solvable

you can only get one in terms of the other

im just gonna type out my steps

[simple elm]

So the function is done at y=3000*1.17e^x ?

[warped sleet]

no thats incorrect

3000 growing exponentially at a rate of 17% is 3000(1.17)^(years passed)

what were doing is trying to make it base e

[simple elm]

Okay how do we go about doing that? Doing ln 1.17?

[warped sleet]

for base e we need 3000(1.17)^x in the form 3000e^y

so we needa solve 1.17^x=e^y for y

ln(l.17^x)=ln(e^y)

ln(1.17^x)=y

sub y into 3000e^y

so 3000e^(ln(1.17^x))

do u mind me asking what level in school u r because i think its a misworded question

[simple elm]

I dont understand

This is swedish maths, course 3b

[warped sleet]

yeah i dont have a clue what level that is im from uk lmao

which step did i lose u on

[simple elm]

The step where we magically solve e^y

[warped sleet]

ln(e) is 1

[simple elm]

And the step where we rewrote 1.17^x to base e at e^y

How did the exponent go down then?

[warped sleet]

wdym

it didnt

[simple elm]

ln e^y and then as you wrote it it just became y

[simple elm]

Here

[simple elm]

And here

[warped sleet]

the natural log is log base e

log base e of e is 1

[simple elm]

Oh

So the function ends with x*ln 1.17= y?

Thats so weird

I dont get it

I dont get how this has a base of e

[warped sleet]

base e means e to the power of something

[simple elm]

But we dont have an e in the fuction

[warped sleet]

e^(ln1.17^x)is base e rather than 1.17^x

we did we arrived at 3000e^(ln(1.17^x))

[warped sleet]

here

[simple elm]

Thats so confusing

I still dont get it

[warped sleet]

thats why i think its worded wrongly

[simple elm]

“Write your own exponential function with the base e and that meets the following requirements : has a start value of 3000kr, has an increase of 17% per year”

Thats basically what it says

[warped sleet]

idk how the swedish education system works but converting that to base e is probably like 18yo/ final year of school type level

idk how to explain the solution any further but if u cant follow it id say that u havent been taught most of the stuff like it in school so u shouldnt be expected to solve

[simple elm]

Im not in highschool im taking a math course to be able to apply to economical/biological educations in university

I need to have a grade in those to meet the requirements of application

So i didnt learn this in highschool

Because my class only had level 1 maths, and the rest was voluntary

[warped sleet]

oh ok sorry

[warped sleet]

have u followed me through this stage

[simple elm]

Yes

But to me it doesnt make any sense because we are left with x*ln1.17=y

And thats not a base e and its super weird to have 2 different variables on both sides

[warped sleet]

were not going to solve for x or y to be just some number

[simple elm]

And how is that an exponential function

[warped sleet]

the answer for each will contain the other

[simple elm]

its supposed to be like y=C *a^x

[warped sleet]

yes

two variables which are dependant on eachother

what were doing here is trying to find a value for y so substitute into 3000e^y which is the form we need to give the answer in

[simple elm]

so y=3000e^(ln1.17x)?

Oh

[warped sleet]

^x

but yes

[simple elm]

How is that even possible

We have 2 exponents on top of each other

An exponent on top of an exponent

How does that make sense

[warped sleet]

if x=1 for example it would be 3000e^ln1.17

if x=2 its 3000e^(ln(1.17)^2)=3000e^(ln1.3689)

[simple elm]

Okay

I have never seen exponents on top of exponents

[warped sleet]

its not some crazy complicated topic u do its just the same process as one exponent

[simple elm]

Okay

y’(x)=0,9e^(0,3t)=7,0

I got t=7

Is that correct?

[warped sleet]

how did u solve t in an equation with two variables

was a y'(x) provided

[simple elm]

y=3,0*e^(0,3t) i made a derivative from that into y’= 0,9e^(0,3t)

From the original function i was supposed to get the derivative at x=4 because of the 1st question so i derived it and put in the x and got 3

Next question was when is the derivative at 7mm/week

So i put in y’(x)=7

And got out t=7

[warped sleet]

was the first question to differentiate with respect to t or with respect to x

[simple elm]

First question was decide the speed of growth at t=4,0

Thats it

Second question is “when is the speed of growth 7mm/week?”

For the 1st one i got 3mm/week, 2nd one i got t=7

[warped sleet]

for second question did u set ur derivative equal to 7 and solve for t

[simple elm]

Yes

That was exactly what i did

[lone heart]

@simple elm Has your question been resolved?

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[umbral abyss]

dont want the answer just how to do it

is that allowed

[tired kettle]

Would you agree that sqrt(ab) = sqrt(a) x sqrt(b)

[umbral abyss]

i have no idea what that is

[alpine sable]

ok

so basically

i is the squareroot of an imaginary number

correct?

[umbral abyss]

yes

[buoyant kayak]

negative*

[magic geyser]

^

[alpine sable]

yeah

mb

negative is what i meant

basically, you can rewrite √-169

[buoyant kayak]

also skyline was saying
$$\sqrt(a\cdot b)=\sqrt{a}\cdot \sqrt{b}$$

[ocean seal]

a disappointing son

[buoyant kayak]

latex sucks?? that root is supposed to be over the quantity (a*b) but i'm not gonna have texit resend the message now lol

[umbral abyss]

ah got it

[magic geyser]

sqrt(a) *b?!?!?

[alpine sable]

as √169*-1

which is the formula that the latex shows

$$\sqrt(169\cdot -1)=\sqrt{169}\cdot \sqrt{-1}$$

[ocean seal]

DoomKing

[alpine sable]

so this is how it looks in a neater way

now, what is √-1 equal to again?

[umbral abyss]

much better

[buoyant kayak]

i missed the {} on the first sqrt, that's why it didn't render correctly lol

[umbral abyss]

do a lot of people come here asking for answers

or just me

[alpine sable]

we won't give you the answers

[buoyant kayak]

very popular server lol

[alpine sable]

we will guide you to them

[umbral abyss]

i know

just saying

[magic geyser]

$\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$

[ocean seal]

alepk

[alpine sable]

can we focus guys

[umbral abyss]

yes myb

[alpine sable]

or take your latex war somewhere else

[magic geyser]

:(

[alpine sable]

so what is √-1 equal to

[umbral abyss]

square root of -1?

[alpine sable]

yes, answer is in the problem statement

[umbral abyss]

i

[alpine sable]

yep

so now put i instead of √-1

and you get

$\sqrt{-169} = \sqrt{169} \cdot i$

[ocean seal]

DoomKing

[umbral abyss]

i dont understand

arent i and -1 the same thing

[alpine sable]

that's the point

[buoyant kayak]

no

[alpine sable]

oh wait

[buoyant kayak]

sqrt(-1) = i

[alpine sable]

not -1

i^2=-1

[umbral abyss]

meant to say that

[alpine sable]

not i

basically you swap in i for the place of √-1

just like plugging in a variable, except this time it's reversed

[umbral abyss]

so the square root of 169 times i is the answer

+5

[alpine sable]

yep, but that isn't fully simplified

the root of 169 has a whole value

[umbral abyss]

31 i

13 i*

[alpine sable]

that is ONE of the answers

[umbral abyss]

right

[alpine sable]

tell me, what is -1 * -1

this isn't any trick problem, literally what is -1 * -1

[buoyant kayak]

that doesn't apply here, you aren't solving for a variable

just simplifying

[umbral abyss]

so its D

thats the only option

[alpine sable]

look at the answers, two of them are correct

[buoyant kayak]

no

one of them is

[alpine sable]

+-13?

[buoyant kayak]

.

[buoyant kayak]

yes

[umbral abyss]

ty

[alpine sable]

ah wait

sorry im overthinking

yeah it's D

god i space out way too much

yeah ignore what i was saying at the last bit

[umbral abyss]

i should really know how to do this im in ap classes

but my alg teacher is like super bored and monotone all the time

impossiple to stay awake

[alpine sable]

abuse khan academy if you need to

it's a god send gift

[umbral abyss]

impossible*

[alpine sable]

anyways, i need to go eat

have a nice day

[umbral abyss]

ill keep that in mind

[lone heart]

@umbral abyss Has your question been resolved?

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[alpine sable]

Given that 0 <= x,y,z <=1.Find max of :

[lofty axle]

What have you tried?

[alpine sable]

i cant try anything, i think this exersice should have x+y+z = ...

[lofty axle]

How about a derivative? Derivatives are pretty swell.

[alpine sable]

sr but i didnt study about that

[lofty axle]

So what tools do you have?

[severe sluice]

maybe take the gradient?

oops

[lofty axle]

What class is this for?

[alpine sable]

me have Cauchy-Schwarz, Cauchy

me also have 0<=x<=1 => (x-1)(x-0) <=0

that's all to use for this exercise

[lofty axle]

You're optimizing with Cauchy-Schwarz?

[alpine sable]

it cant be optimized because there is z^2020 and y^4 i think

[lofty axle]

I mean finding min/max. That's optimization.

What class is this for?

[alpine sable]

wdym

[lofty axle]

Is this for a class? Or did you just decide you wanted to find the maximum of this function on [0,1] using Cauchy-Schwartz for fun?

[alpine sable]

it's for my class

[lofty axle]

Right. Which class? "Optimization of Polynomials by Cauchy-Schwarz"?

[buoyant kayak]

lmao

[lofty axle]

If we don't know what tools you can use, we can't help you. The name of the class would give us some hint of that, since all you've told use you can use is CS, which is quite restrictive.

[lone heart]

@alpine sable Has your question been resolved?

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[olive inlet]

Help

My answer is 46
I just wanna confirm if it's alright

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@olive inlet Has your question been resolved?

[olive inlet]

.close

[lone heart]

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[subtle cedar]

What’s 2x squared = 16

[subtle cedar]

What’s x

Wait it’s 2

HA WE WERE BOTH WRONG

[devout summit]

$(2x)^2=16\implies x=\pm 2$

[ocean seal]

Euclid31415

[subtle cedar]

.close

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[waxen owl]

How do you find the anti derivative of 2^u? It evaluates to 1/ln(2) times 2^u online. But idk how to do it

[gray isle]

express 2 as e^(ln(2))

to explicitly get an exponential function with base e

which should be a lot easier to integrate

[waxen owl]

Thx

.close

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[ocean glacier]

I'm making an elastic collision system in desmos and I want to trace the path my object will take. However, I need to convert the equation of a point into the equation of a line and I'm not sure how to do this.

[ocean glacier]

https://www.desmos.com/calculator/e89ulqrxyi

[lone heart]

@ocean glacier Has your question been resolved?

[lone heart]

@ocean glacier Has your question been resolved?

[lone heart]

@ocean glacier Has your question been resolved?

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[inner grotto]

Hey, so I have 4 vectors (a1,a2,a3,a4) and I need to prove that they're a basis of Q^4. From what I know you have to find their rank(I don't know if it's called rank in English) and I don't know what comes after that

[inner grotto]

Here's how far I've come

If my calculations are correct, this is the rank but I don't know how to prove that it's a basis of Q^4

[velvet pelican]

my way (which is probably not the best) would be to show that you can show the 4 basis vectors of Q^4 as linear combinations of your vectors, which i think directly follows from them being linearly independent

[lone heart]

@inner grotto Has your question been resolved?

[inner grotto]

Oops

I'm here

[inner grotto]

I don't exactly understand what you mean by that

Could you specify or show me?

[velvet pelican]

every vector in Q^4 can be written as a linear combination of the basis vectors

so if you can show that we can write the basis vectors as linear combinations of these 4 vectors

you can show that they form a basis of Q^4

maybe someone else can explain it better than me

[inner grotto]

If it's not too much trouble, could you write it down somewhere?

[velvet pelican]

sorry, dont have a notebook with me rn

[inner grotto]

Alright, well thanks for the help anyways! ^^

.close

[lone heart]

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[ocean seal]

-Lil Galil-

[stable venture]

@ me if you have written something

[lone heart]

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[stable venture]

.

[gray isle]

don't use photomath

[stable venture]

why?

[gray isle]

because its bad

[stable venture]

aight, but the answers also agree with photomath, do you know what i have done wrong?

[gray isle]

the answers probably have something like sec^2(x) instead of tan^2(x)

[stable venture]

nope, one sec ill send them

ignore the +1

[gray isle]

so yeh. 1/cos^2(x) is sec^2(x)

and tan^2(x) and sec^2(x) differ by a constant

[stable venture]

i dont understand, it is still not equal to this

[gray isle]

and tan^2(x) and sec^2(x) differ by a constant

considering the constant of integration