help-27

[twilit comet]

if you can't type that fast

[graceful cipher]

i applied quotient rule and got $(x^2 + a^2)^{\frac{3}{2}} - x(x^2 + a^2)^{\frac{1}{2}} * \frac{3}{2} = 0$

oh shit i found the mistake

i didnt apply chain rule

[twilit comet]

$\frac{u'v=uv'}{v^2}$

[woven radish]

ren

[twilit comet]

yea exactl

[graceful cipher]

the denominator is always non zero, so i ignored it

is it safe to do?

[woven radish]

therealtdp

[twilit comet]

no

[graceful cipher]

where am i wrong

[twilit comet]

and btw what if a = 1 and x = -1?

then?

[graceful cipher]

?

what happens?

i dont see a problem?

i think the denominator is $(x^2 + a^2)^3$

[woven radish]

therealtdp

[graceful cipher]

.close

[devout snow]

Channel closed

Closed by @graceful cipher

Use .reopen if this was a mistake.

[devout snow]

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.

[blissful oriole]

Does anyone know how to do (1/2)^-2

[heavy current]

what property about negative exponents do you know about?

[blissful oriole]

Must have skipped a lesson or two

This must be what happens when you dive into pre calc

While not taking any math for 2 years

It equals 4 I have no clue how they got there

[heavy current]

do you know how exponents distribute to a fraction?

like (2/5)^2

[blissful oriole]

I kind of just assumed it would be 2/5 x 2/5

[heavy current]

that would be right, but we want to use exponent properties

So exponents distribute to fractions, that is (2/5)^2 = (2^2)/(5^2)

= 4/25

[blissful oriole]

Ok, and do negatives just follow a whole different rule?

[heavy current]

sort of, you can still apply this though

(1/2)^-2 = (1^-2)/(2^-2)

now you need to know another property about exponents, which is that

a^(-n) = 1/(a^n)

[blissful oriole]

Hm

[heavy current]

actually, you can omit the step about disturbing the exponent altogether

[heavy current]

by just applying this from the getgo

in your case, the “a” is 1/2 and the “n” is 2

[blissful oriole]

Ah ok

[heavy current]

so the rule tells us that (1/2)^(-2) should equal 1/[(1/2)^n]

which you can simplify I presume

[blissful oriole]

Ok so it ends up at 2 and we then we raise it to the power of 2 again to get 4?

[heavy current]

yes, that seems right

[blissful oriole]

Ok good thank!

[devout snow]

@blissful oriole Has your question been resolved?

Channel closed

Closed by @blissful oriole

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.

[rain otter]

Can someone check my work for part B and C

And help me with part A and D?

I have absolutely no idea how to do it

[zenith summit]

@rain otter can u send the full question please?

[devout snow]

@rain otter Has your question been resolved?

[rain otter]

this is the full question

@zenith summit

[zenith summit]

on the graph

wait

im being slow

gimme a min

[rain otter]

alright

[zenith summit]

@rain otter i agree with ur part b

looks right to me

[rain otter]

Part B and C Im decently confident about

I just have no idea how to do part A and D

[zenith summit]

okl its cos u said u wanted someone to check part b and c

ill take a look at a and d now then

[rain otter]

Alright, thanks so much

[zenith summit]

its going to be a bit confusing to explain

okay

so part a

on your graph i want you to draw the line y=-1

and then picture what the volume of revolution would look like if its rotated around y=-1

(dw im not gonna leave it as vague as this but i want to challenge you a bit)

@rain otter should i tell you or can u picture it

[rain otter]

yeah I drew that

[zenith summit]

so if you was to rotate your R around that line

its the same as doing a volume of revolution around the x-axis

but you have to account

for the cylinder

that will also be made

[rain otter]

right

[zenith summit]

with radius 1

so just work out volume of both and then add

[rain otter]

so the outer radius - (-1) - the inner radius - (-1)

integrate that?\

[zenith summit]

idk exactly what u mean by that sorry

elaborate?

[rain otter]

To find the volume, integrate e^y - (-1) - (0 - (-1) until the intersection point

and then integrate (5-y - (-1)) - (0 -(-1))

and integrate taht

add both

multiply by Pi

[zenith summit]

its your answer to part c + the volume of the cylinder that is formed

[rain otter]

how do I find the volume of the cylinder formed?

[zenith summit]

you know the radius

and the length

(the length is from your 2 x intercepts)

then apply the volume of a cylinder eqn

pi * r^2 * l

[rain otter]

so 1 = r and x-int = 1 and 5?

[zenith summit]

yeah so your l would be 4

[rain otter]

But don't I use the shell method to integrate it?

[zenith summit]

you would get the same answer

wait

no

[rain otter]

so pi * 1 * 4

[zenith summit]

i have made a mistake

now im confused

im so sorry

[rain otter]

its alr

[zenith summit]

<@&286206848099549185>

the volume of the cylinder formed would be 4pi right?

[zenith summit]

try integrate it via the vol of revolution method

you would still get 4pi

integral from 1 to 5 of 1 with respect to x

all multiplied by pi

would be 4pi

so i wasnt bugging

and add that to ur part c answer (assuming u was correct for part c)

[rain otter]

ok, but my answer to part c is 112.030

the total for Part A + B + C + D is 130.055, which is given in the stem

so if I were to add 4pi to 112.030, it would exceed the total

which means I'm wrong with part C

[zenith summit]

i guess

[rain otter]

right

[zenith summit]

or the answer to part d is very small

[rain otter]

And since the upper curve of integration changes, I would need to split the integral for part C

[zenith summit]

4pi +112.03 is less than 130.055

[rain otter]

maybe

that makes my part C correct

Wait do u mind checking my Part C just in case?

Im so sorryy

[zenith summit]

im a bit rusty but ill take a look rq

[rain otter]

thanks so so much

[zenith summit]

u did square ln x and (5-x) right

[rain otter]

no because I'm just taking the area

I did square the total of the antiderivative of ln(x) and (5-x)

and multiplied it by pi

[zenith summit]

volume of revolution around x axis is pi * the integral of y^2 though

[rain otter]

yeah

it is also area^2 integrated

[zenith summit]

i dont know if this will get you the same thing

ill check rq

[rain otter]

so can I take the area and square that and multiply it by pi right technically?

alr

[zenith summit]

ill check but i doubt it tbh

[rain otter]

okay

[past scaffold]

Most beautiful handwritten integral signs I have ever seen haha

[zenith summit]

yeah @rain otter

u cant do what u did

[rain otter]

ok

[zenith summit]

i did it the other way and ended up with 8.746 which is equally sus

[rain otter]

I have to square it

[zenith summit]

wtf type of questions are they giving you guys holy

@uncut hornet bro check this question

unless im being braindead

[rain otter]

Ikkkk and I have a test over all this today

[rain otter]

I got 97.397

[zenith summit]

trust your answer not mine

honestly good luck

i gtg now

sorry i couldnt be of more help

[uncut hornet]

i cba helping w volumes of revolution

[rain otter]

thats alr, thanks so much for ur help, truly

[zenith summit]

@rain otter .closed or .solved when ur done btw

[rain otter]

.closed

[zenith summit]

.closed

.solved

<@&268886789983436800>

[dire forge]

.close

[devout snow]

Channel closed

Closed by @dire forge

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.

[solemn sinew]

How to solve this problem without the graph?

[devout snow]

@solemn sinew Has your question been resolved?

[devout snow]

@solemn sinew Has your question been resolved?

[devout snow]

@solemn sinew Has your question been resolved?

[devout snow]

@solemn sinew Has your question been resolved?

[steep sinew]

(don't mind me, I'm still working on it)

sin(2pi/3)
= Im(e^(2ipi/3))
= Im(e^(2ipi * 1/3))
= Im((e^2ipi) ^ 1/3)
= Im((-1) ^ 1/3) 
= -Im(1 ^ 1/3)

we want the negative imaginary component of the 1st 3rd root of unity

(where 0th = 1)

we know they're spaced evenly

=> form an equilateral triangle

oh wait you could also do it over the taylor series

[steep sinew]

anyway, this is the 30-60-90 triangle

guess what: two of these make an equilateral triangle

therefore, the short side is 1/2 the hypothnuse

[steep sinew]

the other is therefore sqrt(1² - 0.5²) = sqrt(0.75) = sqrt(3/4) = sqrt(3) / 2 the hypotenuse

the hypothenuse is one

the shorter side therefore 1/2

the longer, the one we want, sqrt(3) / 2

[devout snow]

@solemn sinew Has your question been resolved?

[devout snow]

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.

[stoic mantle]

How would you go about factoring a question that is x^8 + x^4 + a constant in the same manner that you would factor a question such as x^4 + 9x^2 + 20 being (x^2 + 4) (x^2 + 5)

[magic pine]

set x^4 = y

the polynomial can then be written as y^2 + y + a, which you can use the quadratic formula for

[stoic mantle]

What about the x^8

[magic pine]

well x^8 = (x^4)^2

hence the y^2 in the polynomial

[stoic mantle]

Can you make an example if possible?

[magic pine]

start with x^8 + 2x^4 + 1 = 0
set y = x^4 -> y^2 = (x^4)^2 = x^8, so x^8 = y^2
then we can substitute into the equation
y^2 + 2y + 1 = 0
solve using the quadratic formula to get
(y+1)(y+1) = 0
sub back in
(x^4 + 1)(x^4 + 1) = 0

[stoic mantle]

Thank you

How would you go about using completing the square to factor a polynomial that starts off with a degree of 3 or more

[solid bolt]

do you have an example in mind

[stoic mantle]

No I do not, my teacher just said it would be on the test but we do not have any examples

[devout snow]

@stoic mantle Has your question been resolved?

Channel closed

Closed by @stoic mantle

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.

[shut oak]

How to solve this question?

[shut oak]

In the given figure, ABCD is a square and BHGF is a rectangle. If BE = BH, prove that the square ABCD and the rectangle BHGF are equal in area.

The figure is in the image

[solid bolt]

what have you tried

[devout snow]

@shut oak Has your question been resolved?

[shut oak]

1)Area of triangle ABE=1/2 AREA OF SQUARE ABCD[STANDING ON SAME BASE AND BETWEEN SAME PARALLEL LINES]
2)AREA OF TRIANGLE ABE=1/2AREA OF RECTANGLE BHGF[SAME AS ABOVE AS BH=BE]
3)AREA OF SQUARE ABCD=AREA OF RECTANGLE BHGF[FROM (1)&(2)]

I tried this

is this correct?

[shut oak]

.close

[devout snow]

Channel closed

Closed by @shut oak

Use .reopen if this was a mistake.

[devout snow]

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.

[nocturne relic]

does anyone have an idea on how to understand which one of these two functions goes to +infinity faster as n->+infinity?

[nocturne relic]

id need to understand which one is bigger between 11/2 and log(4/3,3) but i have no idea on how to do that without a calculator

[topaz axle]

oh that's 4/3

[magic pine]

i can tell you the right one goes to infinity faster for large n, but over that interval im not sure

[topaz axle]

looks like n/3

[magic pine]

oh

i thought it was n/3 too haha

[uncut crow]

me too

[topaz axle]

it's probably n/3

[nocturne relic]

nope its actually 4/3 i dont have the best handwriting

[uncut crow]

you can bound log_(4/3)(4)

don’t need to get a good approximation

for example, is it less than 10?

[nocturne relic]

the fact is that i need it to calculate the complexity of a function and i need to know exactly which one is bigger and by what margin but it seems impossible without a calculator

[uncut crow]

no it’s possible without a calculator

i claim log_(4/3)(4) < 10

can you see why?

we need something a little different for the problem but it’s just an example

log_(4/3)(4) < 10 is true because 4 < (4/3)^10

[nocturne relic]

yea that makes sense

[uncut crow]

knowing log_(4/3)(4) < 5 would solve the problem right?

[nocturne relic]

yea it does

[nocturne relic]

thats exactly what i was doing rn after you said this

it makes a lot of sense, thank you :D idk why i didnt think of that

[uncut crow]

[nocturne relic]

.close

[devout snow]

Channel closed

Closed by @nocturne relic

Use .reopen if this was a mistake.

[devout snow]

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.

[manic tundra]

Help😅

[manic tundra]

I need formule for volume and surface

Pls 🙏

Someone

I just need to know how to get the length of a line underneath 45°

Do I use sin,cos,tg,ctg or something else

[twilit comet]

trig?

yes probably

[twilit comet]

this question isn't very clear but it definitely will require trig; rephrase since i can't really understand wdym

[manic tundra]

I need to get formula for the length of the line under the 45°

When I know that I can use PT to get everything else

[devout snow]

@manic tundra Has your question been resolved?

[manic tundra]

No

[devout snow]

@manic tundra Has your question been resolved?

[devout snow]

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.

[restive river]

Is this correct

[restive river]

.close

[devout snow]

Channel closed

Closed by @lusty nimbus

Use .reopen if this was a mistake.

[devout snow]

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.

[ocean socket]

the question was to calculate the five number summary for the set of data in the image. i was wondering if somebody could check my working and let me know if i did all my calculations correctly or if i made any mistakes.

[ocean socket]

i’m aware that this is simple maths but i really need to double check with somebody

[devout snow]

@ocean socket Has your question been resolved?

[ocean socket]

<@&286206848099549185>

[ocean socket]

<@&286206848099549185>

[devout snow]

@ocean socket Has your question been resolved?

[ocean socket]

<@&286206848099549185>

[restive river]

yo

this is quartiles?

[ocean socket]

yes

five number summaries basically

[edgy dirge]

Yep, it checks out. Ur right!

[ocean socket]

thank you sm i appreciate it

[edgy dirge]

Np!

.close

[ocean socket]

.close

[devout snow]

Channel closed

Closed by @ocean socket

Use .reopen if this was a mistake.

[devout snow]

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.

[marble quail]

Determine the matrix X such that it solves the matrix equation

Since A does not have an inverse thus i can't move it over to the RHS to solve for X. How do i go about solving this?

[stone stump]

what size would X need to have

[marble quail]

2x3

[stone stump]

ok

lets say the first column of X has entries (x1, x2)

what can you say about those

[marble quail]

I'm not sure sadly

[marble quail]

I don't understand the question?

[stone stump]

what is A*(x1,x2)

[marble quail]

= x1 + x2 ?

[stone stump]

what happened to the rest of A

[marble quail]

Is this what you mean?

@upper schooner

[wicked turtle]

you seem to be assuming that x1 = x2, and similarly for the y's and z's

[upper schooner]

Also this would be the first row that you would get

[marble quail]

I'm mainly interested in the steps to solve it

Normally i'd take the inverse and solve for X but that isn't possible

[upper schooner]

There’s the second and third one too, which is what was asked for

[marble quail]

$x_1+x_2 \
2x_1+3x_2 \
x_1+2x_2$

[woven radish]

Merineth

[marble quail]

Like so?

[stone stump]

yes

and that is supposed to equal the first column of B

[devout snow]

@marble quail Has your question been resolved?

[devout snow]

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.

[marble quail]

I'm given 3 vectors v1,v2,v3

and i'm supposed to find all vectors that are perpendicular to v1 v2 and v3

why on the final step of gaussian elimination

Does the answer become t(4,-1,3,-.1) ?

.close

[devout snow]

Channel closed

Closed by @marble quail

Use .reopen if this was a mistake.

[devout snow]

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.

[livid carbon]

Let a be a non-zero complex number such that |a| $\neq$ 1. Let P be the point a in the complex plane, and let Q be the point $\frac{1}{\bar a}$. Let $C_1$ be the circle ${z : |z| = 1$} and let $C_2$ be any circle passing through P and Q. Show that $C_1$ and $C_2$ intersect orhtogonally. [Two circles are said to intersect orthogonally if the tangents at a point of intersection are perpendicular to each other.]

[woven radish]

Normed

[livid carbon]

I've made the diagram but not able to show that the circles intersect orthogonally, can someone help?

[devout snow]

@livid carbon Has your question been resolved?

[strange arch]

won't be available in a sec, but the procedure is:

determine a general circle formula for all circles that pass through a and 1/a-

then determine the intersections of the given unit circle and that variable circle

at these two intersection points, you can show orthogonality via the direction vector

or normal vector

either would work

[livid carbon]

Ahh alright

Let me try

[strange arch]

the normal vectors of a circle are directly pointing outwards, so since you have it in radius form

that makes it more straightforward

than e.g. x=sqrt(1-y²)+2

[strange arch]

if you're unsure how to get the circle formula you can also look up how to construct a circle from two given points

[devout snow]

@livid carbon Has your question been resolved?

[devout snow]

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.

[pine trellis]

i've thought about simply arranging the pears in consecutive order

ie boxes of 0+1+...+10

however this is 55

not sure where to go from here

[torn vessel]

so, this shows that 11 boxes would be necessary this way and 12 isn't possible when packing the pears. But 11 doesn't divide 60 so the apples wouldn't be evenly distributed. So what is the other maximal option?

[pine trellis]

10 im guessing

but then how would i arrange the pears in 10 boxes

[devout snow]

@pine trellis Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

[devout snow]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[plucky grove]

Heyy, how do I make the function f(x) = ax^2+bx+c and f(x) = a(x-x1)(x-x2) into this function? a(x-m)^2+n?

[plucky grove]

Is it even possible

[restive river]

vague question.

[plucky grove]

how so?

x^2-4x+3 for the ax^2+bx+c

and for a(x-x1)(x-x2) = -(x+2)(x-3)

Now how do I turn these both into a(x-m)^2+n?

[brave vapor]

By Completing the square

[plucky grove]

😭 could I please get a formula of how

Cause i've been trying to do that for like 40 minutes

[brave vapor]

It does not have a formula, it has multiple steps which you can find on YT

You can also try searching for converting quadratic equation to vertex form

[devout snow]

@plucky grove Has your question been resolved?

[devout snow]

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.

[onyx pivot]

The W point is the center of the PQRS square, and the U point is the center of the RS side. The segments TW , UW and VW divide this square into three equal parts (in terms of square area). What is the length of the segment SV if the side of this square is 1?

[onyx pivot]

The answer is 5/6 but I don't understand really why

<@&286206848099549185> if something isnt clear let me know

[devout snow]

@onyx pivot Has your question been resolved?

[onyx pivot]

<@&286206848099549185> i think i need to find a way to calculate the area of PQVT in order to calculate VSUW area but i dont know how to calculate the PQTV area by using some formulas or anything, like im completely blank in terms of it i only know that the distance PQ is 1 and the height is 1/2 but im missing something i guess, i know that only PQTVW = VSUW = WURT = 1/3

its not a test btw

if anyone is wondering

its 2 years old and from a competition

[faint zinc]

Hi

[onyx pivot]

hi

[faint zinc]

Ok so, we'll need to express the areas in terms of the sides

[onyx pivot]

okay

[faint zinc]

We want SV, so let's call it x. This means PV is 1-x, we are assuming that we have symmetry about WU, which doesn't seem to be actually stated

We know that WU is 1/2

[onyx pivot]

U is the middle

so WU is 1/2

[faint zinc]

So the area of the pentagon PVWTQ is the area of triangle VWT and the rectangle PVTQ

[onyx pivot]

wait

ive done it

i think so

and it simplifies to 6x=5

so x =5/6

[faint zinc]

Extend WU into the line VT and it intersects at a right angle, let's call this point A. WA = 1/2 - (1-x) = x - 1/2

So the area of the triangle is 1/2 WA * VT = 1/2 * (x - 1/2) * 1

Or x/2 - 1/4

The area of the rectangle is 1 * (1-x) = 1-x

So we get 3/4 - x/2 for the area of the pentagon

This is equal to the area of the trapezoid WUSV

This will give you one equation in x

[onyx pivot]

i see i see

[faint zinc]

Then you just solve

[onyx pivot]

thanks

[faint zinc]

Yw

[onyx pivot]

any idea about this?

theyre both the same

P square is 45cm^2

[faint zinc]

Have to help my fellow pokepfps

[onyx pivot]

ofc i need to get smart someday

[faint zinc]

Can you translate the full question?

[faint zinc]

You already speak one language more than I do.

[onyx pivot]

In every of these two identical isosceles triangles with a right angle, inscribed a square like shown on a picture. If the square P has 45cm^2 area, then the R area is?

[faint zinc]

Oic

Ok, so you have a lot of similar triangles here

We have in particular that by symmetry, P goes halfway to the edge

So the total area of the triangle is twice that of P

Next, for R the three smaller triangles all have hypotenuses that add up to the overall hypotenus

Sorry, my bad,

The smaller triangle hypotenus+ 2 longer triangle edge

[onyx pivot]

uhhh

[faint zinc]

Let's say the side length of the big triangle is x, and the medium y, and the small z. so we have x√2 = 2y + z√2 and x = z + y√2

Which upon reflection is the same equation twice, hmmm

Oh we also have z √2 = y from the sides of R

So x√2 = 3y

[onyx pivot]

i dont get it

[faint zinc]

There aren't any points labeled

So let's make some

[onyx pivot]

okay

[faint zinc]

R diagram:

Top left A
Bottom left B
Bottom right C

R square starting from top and going clockwise: QRST

We know that RS = ST, so BS √2 = CS

And we know that AC = AQ + QR + RC

So AQ = AB/3 * √2

We know that 1/2 AB^2 = 90 from the previous so AB = √180 = 12√5, I believe.

[onyx pivot]

seems somehow logical

[faint zinc]

So AQ = AB/3 * √2 = 4√10

[onyx pivot]

wait

isnt sqrt180 6sqrt5?

[faint zinc]

This is wrong yeah

Mental math + I am sick, made an error

Thanks for spotting

[onyx pivot]

sure

[faint zinc]

QR = 2√10 then

So QR^2 = 40

I'm going to crawl back into bed for a little while and drink some more tea

[onyx pivot]

i understood only that (2sqrt10)^2=40

i need to read it like 30 times

[faint zinc]

Remember that QR is the side of the square

I wrote AQ before, which is equal to QR, because I got them mixed up.

[onyx pivot]

okay

i have a question

why is BSsqrt2 = cs

[faint zinc]

BS = CS

On this image

I was talking about the R one

[onyx pivot]

oh

yeah

[faint zinc]

I guess R was a bad choice for point name

My b

[onyx pivot]

xD

np

okay next thing

And we know that AC = AQ + QR + RC

why does this

work

[faint zinc]

This is just the line segment AC broken up into 3 shorter segments joined end to end

[onyx pivot]

i dont understand

:(

[faint zinc]

One sec

[onyx pivot]

thats what i have rn

[faint zinc]

All of what I wrote is referring to this figure

[onyx pivot]

ohhhhhhh

wait a sec then

why do we know that RS = ST and then BSsqrt2 = CS? @faint zinc

like rs = st i understand

but the 2nd part not really

[faint zinc]

Because of the triangles around it

Triangle BST and triangle RCS are similar and have a relative scaling factor of √2

[onyx pivot]

RS = RC = CS?

huh

[faint zinc]

RS = RC = ST

And ST = BS √2

[onyx pivot]

why RC

[faint zinc]

Isoceles right triangle RCS

[onyx pivot]

so thats just how it works?

that AQ = QR = RC?

i dont understand

thats where im stuck at

in my drawing

@faint zinc

[faint zinc]

Sorry, zonked out currently. AQ = QT (triangle AQT) and QT = QR (square)

That's why AQ = QR = RC

All of the triangles are 45-45-90

Which is why any of this works

[devout snow]

@onyx pivot Has your question been resolved?

[devout snow]

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.

[solar goblet]

Randomly choose 3 vertices from a regular dodecahedron. Calculate the probability of picking 3 vertices of a non-isosceles right triangle

[solar goblet]

i dont know where to start

this is my sketch of a dodecahedron

what i do know that for the vertices to not be isosceles, the 3 chosen points must not be adjacent

but what about the condition for them to create a right triangle?

[spare crypt]

hmm that seems hard to count all the cases of

from the picture it looks like these are on top of eachother and would make a rectangle to give right triangles

[solar goblet]

oh right

and there are 5 sides like that

so, 20/1140?

[dense lynx]

so u want to simplify the problem

a regular dodecahedron has very nice symmetry so the first thing u should do is to fix a single point, then your problem is is to randomly pick 2 other points and find the prob. these 3 points outline a non-isosceles right triangle

(strictly speaking, this is optional. but it's useful as i alrd see u made a counting error in the number u posted above)

[solar goblet]

the opposite sides make a rectangle

and there are 4 ways of picking 3 vertices from it

and since there are 10 rectangles in our dodecahedron

so, 40/1140?

[dense lynx]

again no

that's why i'm suggesting the simplification approach above

but if u really want to do it ur way, then carefully count how many edges a dodecahedron has

[solar goblet]

hmmm

wouldnt the prob be different for each sides?

[dense lynx]

take a close look at the diagram u have

doesn't it look kind of the same no matter what vertex u view it from

[solar goblet]

oh yeah i suppose so

[dense lynx]

indeed a "regular dodecahedron" is one of the platonic solids so its properties r very nice

[solar goblet]

so lets say i pick a fixed point

now could you hint me of how to find the prob of picking 2 other vertices that create a right triangle?

[spare crypt]

here's the points that are symmetric compared to the red fixed points

[devout snow]

@solar goblet Has your question been resolved?

[devout snow]

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.

[gentle mantle]

could someone explain the logic to me on this one?

[gentle mantle]

its a circit and the probobility for the device to work in on the rectangle

[devout snow]

@gentle mantle Has your question been resolved?

[dense lynx]

each of the 3 segments (left, middle, right) must work for the entire device to work
for a segment to work, at least 1 of its 2 components must work

so, for a single segment (let's say the left-most one)
P(the segment works) = P(at least 1 component works) = 1 - P(both components fail) = 1 - (1 - 0.9)(1 - 0.95) = (1 - (0.1)(0.05))

and u repeat this thinking across the entire circuit

[devout snow]

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.

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

[jagged bone]

lost

[topaz beacon]

https://youtu.be/VkRYjSa3BlM?si=Jxn4GNSVPFBXJ-hJ check this video out

[devout snow]

@jagged bone Has your question been resolved?

Channel closed

Closed by @jagged bone

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.

[heavy current]

do you know the definition of n choose k?

[strange arch]

try writing out (n over 3)

and show that the product of its terms must be even

[jagged bone]

yeah n!/(n-k)!k!

[jagged bone]

ok

[solid osprey]

plug in k=3, and see what you get

[strange arch]

notice that n! = n * (n-1) * ... * 1

and (n-3)! = (n-3) * (n-4) * ... * 1

meaning n!/(n-3)! = n * (n-1) * (n-2)

[jagged bone]

how does plugging in 3 show its even though

[strange arch]

is this part clear

[jagged bone]

oh yeah cause (n-3)! cancels

[strange arch]

yes

so now we're asking

is n * (n-1) * (n-2) / (3 * 2) even?

[solid osprey]

try it first, youll get (n)(n-1)(n-2)/6, and since n is even just say n=2m

[strange arch]

since 3! = 3 * 2 * 1 = 3 * 2

[solid osprey]

try to see where to go here

[strange arch]

and now you can directly show that it's even

[strange arch]

yeah directly refactoring, inserting n=2m or using induction all prove it 🦇

[jagged bone]

so plug in n as even number and solve it would result in a even expression

[strange arch]

yea but you could also directly see it here

since from among the terms n, n-1 and n-2

one of them is divisible by 3

and two are divisble by 2

thereby the total product is still even

since at least one factor 2 remains

[jagged bone]

how do you know its divisiblity

[strange arch]

because they are three consecutive numbers

which means one of them is multiple of 3

since if you look at all natural numbers

you see that each third number is divisible by 3

[solid osprey]

oh, you could imagine as even×odd×even/even which is still even

[strange arch]

yop

[jagged bone]

oh that makes sense

[devout snow]

@jagged bone Has your question been resolved?

[devout snow]

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.

[peak kiln]

Can you send the graph too?

[devout snow]

Channel closed

Closed by @turbid ocean

Use .reopen if this was a mistake.

[devout snow]

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.

[bronze willow]

I already solved the differential equation but I wanna ask what do I have to do with the extra small questions in the question itself

[bronze willow]

I checked the answers and I got it correct

But the answer doesn't show how it came to be, thus skipping out the questions that has to be [shown]

Pinging helpers every 15 mins

[devout snow]

@bronze willow Has your question been resolved?

[bronze willow]

<@&286206848099549185>

[devout snow]

@bronze willow Has your question been resolved?

[bronze willow]

<@&286206848099549185>

[devout snow]

@bronze willow Has your question been resolved?

[bronze willow]

<@&286206848099549185>

[bronze willow]

<@&286206848099549185>

[bronze willow]

<@&286206848099549185>

[bronze willow]

<@&286206848099549185> All of you are genuinely so slow that I have another question I have to ask here

[solid bolt]

!vol

[devout snow]

Helpers are just people volunteering their time to help you. Be polite and patient.

[merry gust]

@SandAnth what is your problem?

[bronze willow]

-Is my method of solving the differential equation correct, that's it

[merry gust]

@sandanth What is your problem?

[bronze willow]

I'm sorry I have to be that way, I've been waiting for 2 hours

[bronze willow]

Do not forget this

[bronze willow]

Question 11 and question 14

[merry gust]

Hold on, I am reading the question

[restive river]

Most people in this discord are full time students and dont have much free time to spare 😭 Everyone does get answered eventually though

[bronze willow]

2 hours man

[restive river]

Wait til you find out it takes months to get answered on math stack exchange

[bronze willow]

Must be complicated I bet

[merry gust]

I cannot solve question number 14 as I don't know calculus. But ques 11 seems to be under my jurisdiction. @sandanth

Have you thought of anything up until now?

[restive river]

Is this working to do w the first part of the question?

Is that what youre struggling with?

wait its all one question

mb

misread

[bronze willow]

I guess I'd consider the 1st part to be finding the general equation

2nd part is basically extra questions surrounding the general equation

But I cannot process the function of the components itself

[restive river]

Yeah so youve found the equation n it looks right

[bronze willow]

Confirmed it with the answer in the book yes

Note that the answers do not show the steps of each questions

If it did I would not have been here in the first place

[restive river]

Do you need help with the next parts then?

[bronze willow]

Yes I do

[restive river]

Showing that it reaxhes those values under those conditions

so for the first one, consider what happens when t -> infinity

or just any large number

As that will represent the process repeated many times

[bronze willow]

1-e^(-kt/A) tends to 1 right?

[restive river]

Yes as when t gets large, e will tend to 0

so its 1-0

[bronze willow]

Man I'm stupid sometimes

Did not see the word "exceed"

[restive river]

Dont call yourself stupid

u done the hardest part of the question

[bronze willow]

I guess so

Theres still a bit more at the bottom

[restive river]

yss the half volume bit

[bronze willow]

Which variable is considered the volume?

[restive river]

its referred to as the depth mb

Half depth

And x represents the depth

[bronze willow]

What would it mean about the half depth

x/2?

[restive river]

I think x refers to the depth at any given point, so the time taken for that value to half is x/2 yes

[bronze willow]

How would you show that k is that value then?

[restive river]

Okay so basically we’ve established that w/k is the value after a long time t

We can consider that the maximum value of x

[bronze willow]

Omg I have not taken that into consideration

If x has to be half w/k has to be multiplied by 1/2 is it?

[restive river]

yes

so you will get

w/2k = w/k(1 -e^kt/A)

where you can just start off by cancelling out w/k

giving you 1/2 = 1-e^-kt/A

then from there basic rearranging then ln

[bronze willow]

Got the answer

Lets go!!!!

[restive river]

congratss

[bronze willow]

Still have this one tho

[restive river]

yep looks right

[bronze willow]

Im not so sure myself

Is it?

[bronze willow]

I dont even know where to begin with this one

I wish there were answer steps to this because I literally cannot comprehend how to form equations off this

<@&286206848099549185>

Pinging every 15 mins from noe

God I hate word questions like this

[old frigate]

i got 1.36minutes is that correct?

using ratio

[bronze willow]

You have to use calculus

Question 15

228 mins?

Ok yknow what

[restive river]

rate of change in concentration

your concentration is initially 1kg/100litres

or 10g/litre

As a function of time

your concentration would be 10,000/1000+5t where t is number of minutes

[bronze willow]

Questions needed help on: 14 and 15 (these are definitely the only ones I need help on)

Question 14:
Am I doing this correct?
If else, state what I am doing wrong

Question 15:
What should I do first in order to form the differential equation?

Answers are given, but not the steps tp it (I hate this book for that)

[restive river]

^ As t increases, your total volume of water increases and conc. decreases

wait

[bronze willow]

Dont forget that that water flows out the same rate

That's what stumping me in the first place

[restive river]

dv/dt = 5 ltr min^-1

[bronze willow]

Thats it?

[restive river]

one sec

water flows out

uhh

You would have to assume that the mixture loses sodium hydroxide

constantly then

[bronze willow]

This is about the table salt and not the water right?

[restive river]

Yes as the actual volume of water wont be changing

Youll just lose sodium hydroxide

And how much you lose is to do with the concentration

To begin with you have 10g/litre

And if you lose 5l of water in a minute, you would lose 50g in the first minute

Its gonna be an inversely proportional relationship

take concentration as a function of time

dc/dt being proportional to 1/m where m is mass of sodium hydroxide

wait

no

my mind fried

the final equation should follow something like c = c0 e^-At

c0 being initial concentration

A being some constant i cant think of rn

[bronze willow]

Hol on

Before the general solution

Whats the differential equation you came up with?

[restive river]

I cant think of one rn, my minds exhausted 😭

I just know how the shape of the graphs gonna look

dm/dt = dc/dt * v i think

so dm/dtv = dc/dt i think

not certain

[bronze willow]

Might have to ask around some more

[restive river]

wait im@overcomplicatig it

one sec

[bronze willow]

Hmm

Lets say the salt at a certain time, t is s

it'd be ds/dt

[bronze willow]

For the differential equation

Since water is added to the saltwater at a rate of 5 litres min^(-1), then the amount of salt is going to be diluted at the same time at a rate of 50 grams min^(-1)

And if the saltwater solution is also going down at the same rate, the amount of salt going out of the tank is gonna be another 50 grams min^(-1)

Both of these are going through the same time, t

So -100t

Or -0.1t in kg

[restive river]

I just tried it and i got 0.2278 which is short by quite a bit 😭

Probably a unit error

i took dc/dt = -5c

wait thats only the mass

try dc/dt = -5c/1000

might be different

Yeah that gives the answer

over complicating it for what 😭😭

my apologies

[restive river]

The dilution of the mixture is to do with the removal of sodium hydroxide

Not the addition of water

The addition of water is just to counteract the loss of water

To keep the volume constant

The waters going to be a constant volume of 1000 litres

And the loss of sodium hydroxide per minute is 5c

So the decrease in concentration at any given momement in time is -5c/1000

change in mass/volume

change in concentration

[bronze willow]

Dang I see now

Alright then, thanks for the help

[restive river]

Ywah im sorry for overcomplicating it to begin with 😭

[bronze willow]

No worries about it

Then there's this question left

[restive river]

gove me a second

[devout snow]

@bronze willow Has your question been resolved?

[royal carbon]

Hello

[bronze willow]

only 1 question left

[bronze willow]

<@&286206848099549185>

whatever

I had help and I thought the answer was weird, but ngl it seems legit so I'm just gonna count it as an error in the book

anyways, thank you to everyone who helped me

.close

[devout snow]

Channel closed

Closed by @bronze willow

Use .reopen if this was a mistake.

[devout snow]

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.

[restive river]

this might be a dumb question but i dont know how to solve this

[upper jetty]

Here you can use the cosine relations (sorry if it's called something else, not native language, don't know the english terms).

[restive river]

wait all i have to use is cosine rule?

[restive river]

OHHH

i didnt know

well thats easy

[upper jetty]

Seems that way, yeah.

[restive river]

ok thanks

[upper jetty]

[restive river]

.close

[devout snow]

Channel closed

Closed by @wild crest

Use .reopen if this was a mistake.

[upper jetty]

@restive river might also have to use the sine relations as well.

[restive river]

oh

ight

thanks again

[upper jetty]

[devout snow]

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.

[quasi mountain]

I have tried looking up how to do this one million times and I have answered one of these questions right only because i guessed and somehow got it right but this website has never gave me trouble until now becuase it never taught me how to find the p value it just always says "use technology" 🤬 does anyone know how???

[devout snow]

@quasi mountain Has your question been resolved?

[quasi mountain]

<@&286206848099549185>

[quasi mountain]

.close

[devout snow]

Channel closed

Closed by @quasi mountain

Use .reopen if this was a mistake.

[devout snow]

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.

[grave acorn]

Hi Math help!

[grave acorn]

I’m working on a set of homogenous and 3 variable system of equations

The question is #36

The final solution was 0,0,0

But I don’t get what I essentially did that was wrong?

[restive river]

do you still need me to help

[grave acorn]

Also when dealing with three variable system of equations. Idk when the let z = c. Do we always eliminate x first?

I get diff answers depending on the first variable I eliminate

[devout snow]

@grave acorn Has your question been resolved?

[graceful cosmos]

Why do you think that's incorrect?

[graceful cosmos]

You shouldn't

[grave acorn]

Like for example

If I set z to c

My solution will be different from someone

Who sets x to c

And idk if mine is incorrect as a result

[graceful cosmos]

Indeed, that would make one of those solutions incorrect

No matter the method, the solution should be the same

[grave acorn]

The solution in purple is what my prof gor and the one underneath it is the textbook answe

But according to the prof both r right

She did a diff procedure

[grave acorn]

Idk what I did that was incorrect

[graceful cosmos]

Gotcha, there's a family of solutions.

If both works are correct, then this is actually the same family, but different descriptions of it

,w matrix row reduce {{5,2,3,0},{3,1,-2,0},{4,-7,5,0}}

[woven radish]

Results provided by WolframAlpha

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

Requested by kaynex

[graceful cosmos]

Your work is correct, the only solution is (0,0,0)

@grave acorn

[devout snow]

@grave acorn Has your question been resolved?

Channel closed

Closed by @grave acorn

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.

[sick tendon]

this is a non calculator question on a timed test

is there even a fast way to do this

i feel like the question was also vague

[patent marsh]

We can’t help with tests. It’s against the rules of the server

[sick tendon]

its a practice test

this is a revision

to see what i have done wrong

and practice for the real one

[glad patio]

It's MCQ so the fast way is to not add exactly, just estimate to the nearest 50, 418 is wrong because that is the 'rest' that is evenly distributed, not the amount at S Paulo hospital specifically

nearest 100 would probably do if mental maths is not your strong suit

[sick tendon]

its like

i took too long to interpret the question

and jsut kind of guessed

ill try again

[glad patio]

Yeah Qs like this are kinda horrendous, a lot of aptitude tests many moons ago when I was applying to airlines had Qs like this, the more you do the easier it gets

In the early stages, write the key numbers on a notepad as you go to help keep track

That way if you get lost you dont have to start from the beginning

[sick tendon]

.CLOSE

.close

[devout snow]

Channel closed

Closed by @sick tendon

Use .reopen if this was a mistake.

[devout snow]

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.

[drifting zinc]

I'm trying to write this with polar coordinates

[drifting zinc]

are the bounds correct?

I'm not getting the correct final answer

[acoustic leaf]

you may want to double check the bounds on theta

[drifting zinc]

I thought that might be wrong but I'm looking at the graph and the angle does go from 0 to pi/4

[acoustic leaf]

only if you're strictly in the first quadrant

[drifting zinc]

oh i see.. so is it -3pi/4 to pi/4?

that still doesnt give the correct answer

[devout snow]

@drifting zinc Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[drifting zinc]

.reopen

[devout snow]

✅

@drifting zinc Has your question been resolved?

[devout snow]

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.

[weak cove]

Why?

What log properties do you know?

I would go 1-by-1 on the options

simplifying

to see if they're actually equal or not

Show your work

[devout snow]

@placid frost Has your question been resolved?

[devout snow]

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.

[devout snow]

Please don't occupy multiple help channels.

[zinc pewter]

Have any clearer calculation method?

[kindred agate]

do you want the limit of the top limit

[zinc pewter]

yes

[kindred agate]

well, let's try to bound it between two other limits

so what is the absolute minimum that cos x can be

[zinc pewter]

0?

[weak cove]

I closed your other channel. Stick to 1 channel only

[kindred agate]

cos x

you drew a graph of cos x over there

look

whats the minimum

[boreal ingot]

try to form
smth <= x+cosx / x <= smth
using facts abt cos

btw is the 2nd image the solution?

[zinc pewter]

YES

[kindred agate]

this is a specific case of a generalized limit method when there's a rational function and there's a cosine or sine there somewhere and it's going to infinity

anyways

whats the absolute lowest value of cosine

you drew a cosine graph

[zinc pewter]

1

?

[zinc pewter]

not I drew

tbh

my teacher sent to me one

[lilac patio]

the cos x/x limit can be ascertained via squeeze theorem

[zinc pewter]

wow

[kindred agate]

no

minimum

least

lowesat

lowest

[zinc pewter]

-1

[kindred agate]

correct

and 1 is highest

so those are strictly less than or equal to cos x for the first one, and >= cos x for the second one

so we can rewrite the original limit

[lilac patio]

-1 <= cos x <= 1
-1/x <= cosx / x <= 1/x
lim x to infty -1/x <= lim x to infty cosx / x <= lim x to infty 1/x
0 <= lim x to infty cosx / x <= 0

[kindred agate]

we are doing x+cosx

/x

cosx/x is trivially zero when you go to infinity

[lilac patio]

you can separate the function as x/x + cosx / x

[kindred agate]

yeah but that cant always be done with limits of this form

[lilac patio]

oh wait they already did that in the board

[kindred agate]

we wanna learn the general lesson of "sin and cos are negligible at infinity in a rational function with x's on the top or bottom

[kindred agate]

so we can restate the equation as (x-1)/x<=(x+cosx)/x<=(x+1)/x

and these are both trivial

so we can apply squeeze theorem

[zinc pewter]

Ok

Sound interesting

[kindred agate]

alright

so what is lim x->inf of (x-1)/x

and then (x+1)/x

[zinc pewter]

it's 1 right?

[kindred agate]

yep

[zinc pewter]

now (x-1)/x<=(x+cosx)/x<=(x+1)/x
becomes 1<=(x+cosx)/x<=1?

[devout snow]

@zinc pewter Has your question been resolved?

[devout snow]

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.

[zinc pewter]

.

[restive river]

Does anyone know how to solve this, a guy needs it done

[strange igloo]

this too

[blissful herald]

this channel is occupied my guy

[strange igloo]

i sent the other picture as well

[weak cove]

Are you guys taking a test together?

[weak cove]

no @restive river did

[blissful herald]

💀

[strange igloo]

both questions are my math phomeowkr

[blissful herald]

lmao

[strange igloo]

they are

[weak cove]

Why did a different account open and post the question for you

[restive river]

wait iam tryna help great888

help him instead

[weak cove]

bruh

[restive river]

I was tryna help him in the first place

mb

[blissful herald]

so there are 6 rectangles in this shape

[strange igloo]

yes

[blissful herald]

and you want each rectangle to be painted only partially

upto 10 inches

ans the length is given as 27

so find the area of paint for one rectangle

and multiply it by 6

[strange igloo]

thses are the other slides btw

i already did that

[blissful herald]

so what is your question

[strange igloo]

the question

its so difficult

i ddid absolutly everything