help-27

[scenic surge]

alr lemme try

kinda stuck

m i on the right path?

wait a min

am i being stupid

earlier

when we did the

factorized form

we got something like ax^2 - a(x1 + x2)x + x1x2

i can j plug in no?

like that

[craggy escarp]

im sorry, i was away

yes, that works!

[scenic surge]

is there an easy way to do this

instead of this

[craggy escarp]

Unfortunately, you got them dimensions wrong

[scenic surge]

shit

[craggy escarp]

If I were you, I would just set up my 2 equations

And solve them simultaneously

[scenic surge]

what 2 equations r u referrin to

i dont get it

[craggy escarp]

The first equation is for the perimeter

And the second is for the diagonal

[scenic surge]

oh and for diagnol

mhm

let me try

[craggy escarp]

2(L+W)=12

and

W²+L²=20

Works wonders!

[scenic surge]

bet brb

[scenic surge]

im tryin to solve the second equation

and i dont know

where to go from here

[craggy escarp]

Oh my xD

Why are you complicating it!

[scenic surge]

shit

idk

[craggy escarp]

You have the perimeter equation: L+W=6

[scenic surge]

oh

6^2

wait

wym

i did that

[craggy escarp]

And the diagonal equation: L²+W²=20

You have a system

L+W=6
L²+W²=20

From the first get L = 6 - W

And substitute in the second to find W

[scenic surge]

fuck

[craggy escarp]

lol

[scenic surge]

$l^2 - 6l + 18 - \sqrt{5} = 0$

[woven radish]

Calc II Victim

[craggy escarp]

Where the hell are you getting square roots from??

[scenic surge]

broooooooooo

lemme show u

[craggy escarp]

No

you have L²+W²=20

not sqrt(20)

[scenic surge]

waity ni

it is

sqrt(2)

sqrt(20)

doe

look

oh fuck sqrt(20)^2

[craggy escarp]

But but but the pythagoran theorem says

[scenic surge]

fuck

fuck

[craggy escarp]

a²+b²=c²

[scenic surge]

fuckf

cuk

omgh

giigfbfgbugfgr

[craggy escarp]

lol

😋

You must be exhausted

[scenic surge]

$(l - 4)(l - 2) = 0$

[woven radish]

Calc II Victim

[scenic surge]

im getting this now

pls be correct

[craggy escarp]

Yeees

[scenic surge]

so

its

4 x 2?

the dimensions?

[craggy escarp]

Not yet

You found 2 values for the length

Either 2 or 4

For the length itself 2 values

you did not find the width

[scenic surge]

right

but

how would i know

which is the correcvt value for length

do i try both

and see

[craggy escarp]

exactly

L=2 -> W=?

L=4 -> W=?

Some contradiction must emerge to remove one of the possibilities

[scenic surge]

yo i think i fucked up....

coz

w = 4-6 = -2 and w = 2-6 = -4...

why are both negatives

[craggy escarp]

Oh my gaaaad

I told you you're exhausted

lol

[scenic surge]

oh i see tghe mistake

[craggy escarp]

its 6 -

[scenic surge]

yes im slow j clocked it lmao

mhmm

now both

seem right to me

[craggy escarp]

give me the 2 "answers"

[craggy escarp]

The pairs of solutions (L,W)

Yes

But do you accept both?

Or select one of them?

[scenic surge]

first one

[craggy escarp]

Why!

[scenic surge]

nvm

my dumass thought

that the length > width for rectangles

[craggy escarp]

Yes right

that's it

lol

[scenic surge]

oh wtf

[craggy escarp]

you're not dumass

[scenic surge]

i searcjed up

it says thats not the case

[craggy escarp]

No no, it is

L>W

cuz if W>L

then that W is the L

[scenic surge]

ah

[craggy escarp]

and L is the W instead in reality

[scenic surge]

bet

[craggy escarp]

if that makes sense

[scenic surge]

ye ngl imma just take a break

im tripping

ty doe

[craggy escarp]

you're welcome, you did good!

[scenic surge]

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[devout snow]

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[sand jetty]

I have done that got me to nothing

[magic thicket]

it's (y^2/3)^y = y^(y^2/3). Parentheses matter

then assuming y != 1 or -1, we get 2y/3 = y^2/3

ok I didn't put parentheses but i figured it was kind of obvious that it's y^(2/3)

since you're actually doing the computations, you should notice that

[sand jetty]

yeah, i had put that before

in the image i sent you

that why I removed the parentheses because I thought something was wrong

I dunno what to do after this

[magic thicket]

y^(1/3) = 3/2

assuming y != 0

[sand jetty]

I solved it, ty

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[proper tusk]

Need help on factoring this. I think i did the first part right but i dont know what to do from here

[devout snow]

@proper tusk Has your question been resolved?

[lavish oar]

is the remainder zero?

@proper tusk

[proper tusk]

Yes

[lavish oar]

oh then just use the property

quoteient * divisior

are it's factor

[proper tusk]

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[bleak siren]

In Discrete / continuous random variables, does Var ( aX +- b ) = a^2Var(X)

[bleak siren]

In Discrete / continuous random variables, does Var ( aX +- b ) = a^2Var(X)

[frosty cradle]

yes

[devout snow]

@bleak siren Has your question been resolved?

[devout snow]

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[crimson niche]

I have a question about complementary in probability. Is it just the the items in the sample space that didn't show in the outcome?. Also If you were in a multipul choice and you have 4 choices. Why is the complementary of getting 11 correct answer is "Getting at least one incorrect answer" or "Getting at most 10 correct answer"

[wicked turtle]

11 correct answers out of 11 total?

[crimson niche]

yes

[wicked turtle]

in that case "Getting at least one incorrect answer" or "Getting at most 10 correct answer" mean exactly the same thing

you could word it either way

[crimson niche]

yeah it's just different wording

[wicked turtle]

oh you're saying why is either wording correct?

[crimson niche]

yes

[wicked turtle]

because you either got all 11 correct, or you did not

and if you did not, you got at least one wrong

conversely, if you got at least one wrong, then you did not get all 11 correct

so the complement of "got all 11 correct" is exactly "got at least one wrong"

that's how you show equality of events (or sets in general) - show that each is a subset of the other

[crimson niche]

The complement of guessing 18 correct answers on a 18-question true/false exam is ...
A. guessing at least 1 correct answer.
B. guessing at least 1 incorrect answer.
C. guessing no incorrect answers.
D. guessing 18 incorrect answers.

Why would C not be right here?

[wicked turtle]

which do you think is right?

[crimson niche]

It's B

[wicked turtle]

right

[crimson niche]

Oh

wait

I didn't read it right

[wicked turtle]

the question is a bit vague, i mean is it an option to not guess at all?

like normally you could leave some blank

[crimson niche]

I thought C meant Guessing all answers incorrect

[wicked turtle]

they seem to assume that is not the case here

[crimson niche]

Which could be complementary right?

[wicked turtle]

the complement of getting 18 out of 18 correct is getting at least one wrong

so B

basically read complement as "NOT"

as in the event of NOT getting 18 out of 18 correct

[crimson niche]

So for example the complementary of getting even number is not getting an even number

[wicked turtle]

yes

which is the same as getting an odd number

since numbers are either even or odd

[crimson niche]

Yeah I got it

thank you

[wicked turtle]

sure, gl

[crimson niche]

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[proper warren]

upon reaction to treatment, a spherical-shaped cancer tissue has a radius that is decreasing at the rate of 2 mm per day. Find the rate at which the its surface area is changing when the radius is 10mm

[proper warren]

i just want to know what do I need to find

is it the surface area?

[void helm]

the rate at which surface area is changing

im guessing per day

[proper warren]

so Ill be using this formula

right?

[void helm]

yes

[proper warren]

alright, thank you so much

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[plush bluff]

I have a simple question, but I am not sure. I have an equation like 3^{x}+4x=1 and I want take the logarithm of both sides. Will it be correct and appropriate?

[sonic smelt]

It won't really help with solving the equation

[plush bluff]

does the equation save the roots? would this be an equivalent expression?

[sonic smelt]

,w solve 3^x + 4x = 1

[woven radish]

Results provided by WolframAlpha

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Requested by A Lonely Bean#7998

[sonic smelt]

Yes it does

One is trivial and the other is not

You may want to look into lambert w function for the non trivial solution

Search it up

[plush bluff]

and log2( 3^x + 4x)=log2(2)

[sonic smelt]

... = log2(1)* ?

[hollow mantle]

if you want to use logs to get x = 0 first substract 4x both sides

so u have xln3 = ln(1-4x)

[plush bluff]

I'm asking about the logarithm of both parts of the equation

[hollow mantle]

xln3 = ln1/ln(4x)

xln3=0

x=0

[sonic smelt]

You can take log

But it will do nothing

[hollow mantle]

it gets u to the x=0 solution

[plush bluff]

will it change the roots?

[sonic smelt]

ln(1 - 4x) is not ln(1)/ln(4x)

[sonic smelt]

No

[hollow mantle]

oh shit, i mixed things

sry

[sonic smelt]

,w solve ln(3^x + 4x) = 0

[woven radish]

Results provided by WolframAlpha

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Requested by A Lonely Bean#7998

[sonic smelt]

As you can see

The roots remain untouched

[sonic smelt]

log2(0) is not 0

[plush bluff]

x must be >0

[sonic smelt]

x could be 0

Plus that has nothing to do with what I said

[plush bluff]

i mean for R

[sonic smelt]

3^x + 4x - 1 = 0
Does not mean that
ln(3^x + 4x - 1) = 0

[plush bluff]

i see

let's move 1 to another side

[sonic smelt]

Instead do ln(3^x + 4x) = 0

[sonic smelt]

Yes, that will be correct

[plush bluff]

if i have 3^{x}+4x-2=0

ok I understand

[devout snow]

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[lofty monolith]

for part e

i dont get why you wouldn't equate the graph to 8

since it intersects once

[feral agate]

you would do exactly that

[low holly]

<@&268886789983436800>

[lofty monolith]

ms says u equate to -8

but i dont get why

[feral agate]

oh

because of the modulus

[low holly]

|g(x)| = 8 is true whenever g(x) = 8 or g(x) = -8

[feral agate]

the function doesn't reach positive values

[polar chasm]

Did you edit the ping? Im not sure if it works when it's edited

[low holly]

oh maybe not

[polar chasm]

<@&268886789983436800>

[low holly]

<@&268886789983436800>

[polar chasm]

oh good

[lofty monolith]

that was fast

anyway i dont get why u cant equate to 8

[lofty monolith]

this makes sense

[low holly]

you can

[feral agate]

.

for the domain given

[low holly]

you'll just get a solution outside of the bounds

[feral agate]

yea

[lofty monolith]

ohhhhhhhhhhhhhh

[feral agate]

for the domain given g(x) can only = -8, not 8

[lofty monolith]

oh wait so i can do it both ways

and then eliminate

the invalid one

[feral agate]

you don't need to

its obvious from the graph that g(x) can't reach +8, only -8

in the domain

[lofty monolith]

oh

oh ive shown that graph

i was confused by this

the graph in part d i mean

[low holly]

that's the graph of |g(x)|

[lofty monolith]

bc dont u have to use that

its fine though i understand mostly

thanks

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[fickle abyss]

Hey

[fickle abyss]

I need some help in approximation of an expression

Shouldn't this just approch to zero?

[pastel pasture]

Is this the

Electric field of a disc

[fickle abyss]

Ring

[stuck field]

The second one is a ring.

[pastel pasture]

Ah

[stuck field]

First one is a point mass or sphere.

[fickle abyss]

Point mass

[stuck field]

You can use binomial.

Approximation.

[pastel pasture]

If x >>> R then assume x^2 + R^2 = R^2

[fickle abyss]

But the second term should be KQ/X^2 too

[pastel pasture]

x is only compared to R

We don't know how big or small x is so

[pastel pasture]

Are you sure

kQx/R^3 seems a lot more reasonable for an approximation

[fickle abyss]

Noo i mean if we take common x^2

[fickle abyss]

You mean X^2?

[pastel pasture]

Oh I misread

[stuck field]

Perseus you're reading wrong.

[pastel pasture]

Yeah

Sorry

[stuck field]

You have to first take lcm and then binomial.

Not binomial directly.

[fickle abyss]

Why can't we do like this?

.close

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[gaunt yoke]

i need the method, i know how to do depreciation value but not the other way around.

[keen nacelle]

write it out algebraically

is that a word?

[gaunt yoke]

yep

okay i can try that

[keen nacelle]

6000x^7 = 1396.51

work from there

[gaunt yoke]

naaah man idk

im not good at this

[gaunt yoke]

brother help me

[devout snow]

@gaunt yoke Has your question been resolved?

[gaunt yoke]

no

:(

.close

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[sudden lynx]

Hi

[sudden lynx]

I don’t understand the part on the right

[rare zodiac]

2(4y+3t)

2 is a common factor

6 is 3x2 and 8 is 2x2x2 so we took the common factor, which is 2

[sudden lynx]

I’m talking about the right part

I understand the part on the left

But the right

[main gull]

It asking for the property that was applied

I'm pretty sure if you clicked on it, it displays a list

Or it's one of the ones where you type it all in

[sudden lynx]

It displays a list

But I’m trying to figure out which one it is

[main gull]

So from 6t + 8y, to the next line, did you fill out the box?

[sudden lynx]

No but Ik the answer

I said I’m trying to figure out the left side

[main gull]

And I'm trying to not give out answers, so did you figure out what the blank on the left side is?

[sudden lynx]

YES

It’s 8t

8y

[main gull]

So then from 6t + 8y to 8y + 6t, what mathematical property did you apply?

[sudden lynx]

Commutative?

Addition

[main gull]

Do you know what commutative property of addition does?

[sudden lynx]

Kind of

But do u mind not teaching me rn

Because my dad wants me to show me the IXL

In 15 mins

So I have to be who

Quick

So can u just to tell Answer please

[main gull]

No

[sudden lynx]

Bro

[main gull]

Because that's not the purpose of the server

[sudden lynx]

Please I beg

[main gull]

If you want answers, this isn't the server for you

[sudden lynx]

Please

<@&286206848099549185>

[devout snow]

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

[sudden lynx]

Yeah I don’t have time

[main gull]

Also if you read #❓how-to-get-help

• When asking for help, do not insist on getting just the answer; we are here to help you learn, not do the work for you.

[sudden lynx]

Bro I would be taught if I had time

But I really don’t

It’s 2 questions

[main gull]

And that's our problem how?

[sudden lynx]

Did I say it was your problem

No

[raw knoll]

Alright uh the thing on the right is indeed confusing

[sudden lynx]

Ikr

Do u know?

[main gull]

I told you how to do it

[sudden lynx]

Ok then teach me

[main gull]

You select the proper property that you applied

[sudden lynx]

💀

Thanks bro

[main gull]

6t + 8y to 8y + 6t, what mathematical property did you apply?

[sudden lynx]

Commutative addition?

[main gull]

Are you sure? Do you know commutative property of addition does?

[sudden lynx]

Kind of

[raw knoll]

Oh wait

[sudden lynx]

It’s distributive ?

[raw knoll]

So for the right

When u fill it up

Is it variable only

Or variable x number

Or number

[sudden lynx]

It’s the property

[main gull]

Going from 6t + 8y to 8y + 6t, you swapped the positions of the terms, what mathematical property lets you do that?

[sudden lynx]

Am I wrong?

[raw knoll]

Hey

[sudden lynx]

Distributive?

[raw knoll]

I think the answer is asking for what the left answer is

[sudden lynx]

No

The right

Left is easy

[raw knoll]

Yeah the right is asking what the left is

[sudden lynx]

I’m so confused

[raw knoll]

I don't think it's asking for the thing u used

[sudden lynx]

Hello

[main gull]

Please stop interrupting if you don't know what it means

[main gull]

Yes it is

[raw knoll]

Alright if u say so

[main gull]

The right side is asking for what property was applied

[sudden lynx]

Yeah

So…

[sudden lynx]

Is it commutative

Addition

?

[main gull]

The reason why I'm not saying yes or no is because you should be 100% confident in your answer. During tests, and if you weren't part of a math help server, you should know for a fact what it should be without second guessing

[raw knoll]

For example line 3 it says factor, which is what 3t is, a factor

[sudden lynx]

Ok the answer is commutative addition

[main gull]

Then yes, it's that

[sudden lynx]

And for the 2nd it’s distributive

[main gull]

Because it's a list, which you can't see

[main gull]

What are the other options?

[sudden lynx]

Commutative and associative

Addition and multiplication

It’s distributive though

[raw knoll]

Oh okay my bad then

[main gull]

So out of commutative, associative, and distributive, which one is the most logical that was applied to the last part?

[sudden lynx]

Distributive

[main gull]

Yes

[sudden lynx]

Ok

Great my think lagged

I need some more help

[main gull]

Same process as the last one

If you know what goes in the blanks on the left, the right side is the property that was applied

[sudden lynx]

I think the first is associate multiplication

On the right

I understand left

[main gull]

What did you put in the blank on the left?

[sudden lynx]

4t

Then 9

Then 11

[main gull]

Looking at the difference between 9(4t + 5y) + 2(5y + 4t) and 9(5y + 4t) + 2(5y + 4t), what changed?

[sudden lynx]

Just 4t and 5y switching

[main gull]

And what property lets you switch the terms?

[sudden lynx]

Which means it’s accosiative?

[main gull]

You should look into commutative and associative property

[sudden lynx]

Ik

So it’s distributive

Then

This is year 10 things

Btw it’s kinda hard to understand as I’m year 9

Never been taught this

[main gull]

Just 4t and 5y switching
You're saying that is distributive?

[sudden lynx]

No associative

That was my first thought

[main gull]

You should google resources like this

[sudden lynx]

Commutative multiplication

Then

[main gull]

9(4t + 5y) + 2(5y + 4t) and 9(5y + 4t) + 2(5y + 4t)
Pay attention to the signs, is 4t and 5y getting added or multiplied?

[sudden lynx]

Multiplied

By 9

[main gull]

All that happened was just swapping the 4t and 5y, nothing with the 9

[sudden lynx]

Yeah

[main gull]

So is 4t and 5y getting added or multiplied?

[sudden lynx]

Added

[main gull]

So then what property let the 4t and 5y swap?

[sudden lynx]

Associative addition

[main gull]

Refer to this, what does associative property do?

[sudden lynx]

Add in any combination

[main gull]

Are you sure?

[sudden lynx]

No when adding you can group numbers in any combination

[main gull]

So then

All that happened was just swapping the 4t and 5y
What property was applied?

[sudden lynx]

Associative multiplication

[main gull]

Look at the chart I sent

You said associative does this

adding you can group numbers in any combination

All that happened between 9(4t + 5y) + 2(5y + 4t) and 9(5y + 4t) + 2(5y + 4t), was that 4t and 5y swapped places

[sudden lynx]

So it’s commutative addition

[main gull]

What property in that chart demonstrates that you can swap places with two numbers?

[sudden lynx]

Identify property

Ok it’s getting late now my dad’s gonna check

Dw not your fault

Mine

But I’m dead

[main gull]

It's not a hard question, it's reading comprehension. Look at that chart, look at what was done between between 9(4t + 5y) + 2(5y + 4t) and 9(5y + 4t) + 2(5y + 4t). You stated that 4t and 5y swapped places. Looking at that chart, what property demonstrates that you can swap places with two numbers?

[sudden lynx]

Hello?

It’s not hard for you

We both have different brains

[main gull]

I gave you the info that you needed

[sudden lynx]

This is the first time ever I’ve done this

[main gull]

You just need to apply it

[sudden lynx]

I tried

But I still don’t know

[main gull]

As I asked, what property, in this list demonstrates that you can swap places with two numbers?

[sudden lynx]

Identity

[main gull]

Is there any swapping with that?

[sudden lynx]

Yes

[sudden lynx]

Actually no

Commutative

[main gull]

Does that have to do with swapping?

[sudden lynx]

It’s commutative

[main gull]

Are you sure?

[sudden lynx]

Yes

[main gull]

Then that's your answer

[sudden lynx]

But idk if it’s addition or multiplication

[main gull]

Is 4t and 5y getting added or multiplied?

[sudden lynx]

Multiplication

[main gull]

Are you sure?

[sudden lynx]

Yea

[main gull]

9(5y + 4t) + 2(5y + 4t)

Where do you see multiplication between just only 5y and 4t?

[sudden lynx]

U don’t

It’s addition

But the 2nd part is distributive

I think

[main gull]

Yes

[sudden lynx]

Ok

Thanks

There’s one more question

First one is associative multiplication

[main gull]

Are you sure?

[sudden lynx]

And 2nd is commutative multiplication

[sudden lynx]

Yes definitely for the 1st

[main gull]

Yes that's right

[sudden lynx]

2nd one too?

[main gull]

Yes

[sudden lynx]

Thanks

Thanks u saved my life

Bro there was another one

This one

I don’t understand

[devout snow]

@sudden lynx Has your question been resolved?

[supple knot]

Start with quotient of z and 3 first

[devout snow]

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[sudden lynx]

Hi I need help

[sudden lynx]

I would hate to get it wrong

[mighty knoll]

well this should be right

[sudden lynx]

U think

?

Or u know

[mighty knoll]

you did, in fact, double the quotient of b and d, and then subtracted that from c

[sudden lynx]

If I get this wrong I will throw my phone out the window

YYYESSSSSS

HERESS DONE ITTTTTY

[mighty knoll]

let's goo :D

[sudden lynx]

THIS TOOOOOKKK MMMEEE TWEOPP HOOURS

YYIPPPEEEE

THANKS

[mighty knoll]

no problem xD

[devout snow]

@sudden lynx Has your question been resolved?

[devout snow]

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[restive river]

Help please

[mighty knoll]

So, d is the child's dosage, and a is the adult dosage. If Ben's dosage is half of the adult's dosage, then d = a/2

[restive river]

ohhh

i see

[mighty knoll]

$\frac{1}{2}a = a(\frac{c+1}{24})$

[woven radish]

imTyp0

[restive river]

i did a/2 for the on the right

makes sense noiw

and now i solve for c

[mighty knoll]

c actually

[restive river]

mhm

thanks man

[mighty knoll]

you want Ben's age

No worries!

[restive river]

❤️

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[marble nest]

for this one ik that u have to factor it and then solve each of the factored things made

idk how to explain it well

WAIT NVM'

.CLSOE

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[solid trail]

@mighty knoll

[solid trail]

Given $f(x)=\frac{2x+3}{kx-2}$, find the value(s) of $k$ such that $f^{-1}(x)=f(x)$ has solutions.

I considered that the function equals its inverse only at $f(x)=x$, which means $kx^2-2x=2x+3$ and $kx^2-4x-3=0$.

Using determinant we have $16+12k > 0$ and $k > -\frac{4}{3}$, but it's not the right solution (or thought process). How not?

[woven radish]

sed

[split tusk]

you have the wrong implication
if f(x)=x, then yes f(x)=f^{-1}(x), but this is not an only if

if a \neq b and f(a)=b and f^{-1}(a)=b, then f and f^{-1} intersect at (a,b) and (b,a) which is not on the line y=x

[lucid moss]

You were almost there with the realization that $f^{-1}(x)=f(x)$

[woven radish]

alll

[solid trail]

I also have this piece of information

I'll just take off and think about this for a few minutes

[lucid moss]

This looks like a different question

[devout snow]

@solid trail Has your question been resolved?

[solid trail]

Alright so

When can I use f(x) = x to solve f⁻¹(x) = f(x)?

[split tusk]

never

its guaranteed to give all the solutions iff there dont exist a,b such that f(a)=b and f^{-1}(a)=b but thats not really helpful

if f(x)=x we have that f(x)=f^{-1}(x) but for any a,b where f(a)=b and f^{-1}(a)=b we also have f=f^{-1} (including when a \neq b in which case f(x) \neq x)

look at f(x)=1-x^3. f and f^{-1} intersect at 5 distinct points only one of which lies on the line y=x

so you cant just be solving f(x)=x

its sufficient but not necessary

[solid trail]

Right I figured

You can use f(x) = x if f is strictly increasing, but not when it's strictly decreasing

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[sand jetty]

I have to prove the following:

[sand jetty]

I got to the following, but for some reason it feels that something is off, if my logic was correct then gcd(xn + 1, n) would be true for any x > 0, which is probably true

could anyone help me?

[devout snow]

@sand jetty Has your question been resolved?

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[junior swan]

you need help

[urban hornet]

Yes

[junior swan]

alright

[devout snow]

@urban hornet Has your question been resolved?

[urban hornet]

<@&286206848099549185>

[lucid moss]

Have you attempted the problem?

[urban hornet]

Yes but I'm not getting in the form of y(py^2+1)(qy^2-1)

[lucid moss]

Please show all your work

[urban hornet]

y(2sqrt2cos(2x) y^2 +6 sin^2(2x) y^5

[lucid moss]

That's an expression, but you haven't provided any context

The question gives two equations and two unknowns (p and q)

Your answer should involve both equations and an attempt to link them together

Ok, and if that's correct, what next?

[urban hornet]

I don't know what to do after this

[lucid moss]

what else do we know y'' equals>

?

[urban hornet]

I don't know

[lucid moss]

Go to the question and literally write down every piece of information it gives you

[urban hornet]

.close

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[jolly swan]

this is always true?

[silk hill]

yes, you can prove it with substitution

Also you forgot to write the constant of integration, never forget c

[jolly swan]

okay, I noticed that people say that from experience they identify a substitution, does this mean that this way you can identify a substitution?

[silk hill]

Yes, with more problem-solving, identifying which substitution to use, becomes easier.
It is always a good question to ask, "Which substitution going to simplify this integral? "

[jolly swan]

basically that is substitution? just skip the steps

[silk hill]

It is the step

[jolly swan]

thx

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[lyric hornet]

Quick question, real simple: What is the line that goes through two parallel lines, specifically two parallel lines in particular, I just kinda forgor ;-;

[lyric hornet]

I've scoured the internet for an answer

but NOTHING

I swear I'm not insane rihgt?

it had a name i swear to God

[silk hill]

Transverse ?

[lyric hornet]

Transversal!

thanks man

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[devout snow]

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[carmine swallow]

How would I know if a triangle is SSA or SAS

[carmine swallow]

like how would I know which one 7 and 8 are

[magic pine]

draw them

[carmine swallow]

idk how to

[magic pine]

draw a triangle and label the sides a, b and c (doesn't matter which is which)

and then label the respective angles A, B and C

it should be clear what type of triangle you have from that

[carmine swallow]

@magic pine

did I do this right

[magic pine]

your first triangle is correct

your second isnt

[carmine swallow]

what did I do wrong

idk how to draw triangles

[magic pine]

just check your given data and what you drew

[carmine swallow]

I just put the values in the same place as the first one

[magic pine]

the value of "a" should be opposite of angle A

[carmine swallow]

so where would it be

[magic pine]

opposite of angle A

[carmine swallow]

so where I have side c?

[magic pine]

where you wrote 46

i am now noticing your first triangle is labeled wrong

your a and c are also flipped on that one

[carmine swallow]

how should it be

I dont know how to draw triangles just solve

[magic pine]

take your triangles

and just change where you wrote "c" and "46"

and for the top one change where you wrote "a" and "12"

and that's correct

again, your sides should be opposite of the angles

so angle "A" should be on the other side of the triangle to the side "a"

kind of like how your angle B is on the other side to side "b"

[carmine swallow]

give me a sec

how about now

[magic pine]

if this is what you drew then yes

[carmine swallow]

I followed this

[magic pine]

your triangles look fine

i would suggest writing the angles inside the triangle though

[carmine swallow]

ok

now what do I do

[magic pine]

look at what is given to you in order

for example

for your first triangle you have

a side

an angle

and another side

so that is an SAS triangle

[carmine swallow]

ok

how about the second

[magic pine]

you tell me

[carmine swallow]

a angle side side

[magic pine]

yes, or side side angle

which is what

[carmine swallow]

ssa

so it just depends on the order?

[magic pine]

yes

[carmine swallow]

is there a way I can do that without drawing it

[magic pine]

well one way is to just imagine the triangle

[carmine swallow]

ok thank you

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[meager hollow]

ok so

[meager hollow]

suppose i had a sphere

something like this

and it was cut along that blue line

and the radius of the sphere is R

and the yellow shaded part that was cut off

has an outer surface area of pi x R^2

how would i find the area of the flat part of the cut off section

like this blue part

sorry for the trash drawings

[sonic smelt]

Are you sure it's pi * R^2?

[meager hollow]

thats what the question says

[sonic smelt]

Or I am just misunderstandingwhat you said there

Could you show the question?

[meager hollow]

its a phy question

i need the flat surface area for somethign else

ok ill show it

they say the area of that flat part is 3pi x R^2/4 but idont see how

just read these parts ig

[sonic smelt]

Without calculus, right?

[meager hollow]

id prefer without calculus but if thats the only method then sure go with that

[sonic smelt]

Hmm, hold on I will try and come back if it works

[meager hollow]

ok thanks

[sonic smelt]

Alright

Let's say the cut surface is some distance s away from the center of the sphere

So, what I did was revolve y = sqrt(R^2 - x^2) around the x-axis from s to R and find its surface area

According to the formula it should be $2\pi\int_s^R\sqrt{R^2-x^2}\sqrt{1+\frac{x^2}{R^2-x^2}}\dd{x}$

[woven radish]

A Lonely Bean

[sonic smelt]

You will see that the integrand can actually be simplified to just R

So it's $2\pi\int_s^RR\dd{x}$

[woven radish]

A Lonely Bean

[sonic smelt]

Or 2piR(R - s)

And we were given that this should be piR^2

So we just say 2piR(R - s) = piR^2 and solve for s

You should get that s = R/2

[meager hollow]

what is y here?

[sonic smelt]

y = sqrt(R^2 - x^2)

[meager hollow]

no what is it representing

[sonic smelt]

Wait I'll show

[meager hollow]

could u show a diagram

it would make more sense that way

[meager hollow]

okay

[sonic smelt]

If you are wondering what it looks like then it's

,w graph y = sqrt(1 - x^2)

[woven radish]

Results provided by WolframAlpha

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

Requested by A Lonely Bean#7998

[sonic smelt]

Something like this

But I cut it

This part, basically

[meager hollow]

is x supposed to be s or ?

is this

[sonic smelt]

Yeah that's what I meant by s

[meager hollow]

so what is x supposed to be

[sonic smelt]

Ah

x is the distance from the center as a variable, visually speaking

It goes from s to R

[meager hollow]

ah ok i see

[sonic smelt]

Continuing, we got that s = R/2

[meager hollow]

so y is essentially these small white heights?

[sonic smelt]

Meaning the radius of the cut surface should be sqrt(3)R/2, you can get this using the Pythagorean theorem here

[sonic smelt]

Yes

They represent the radii of each circle that we are dividing that shape into you could say

[meager hollow]

ohhh ok

[meager hollow]

which formula is this...?

[sonic smelt]

Generally you will see it as $2\pi\int_a^by\sqrt{1 + (\dv{y}{x})^2}\dd{x}$

[woven radish]

A Lonely Bean

[meager hollow]

ive never done area integrals or anything

is this a formula for sphere area or something?

[sonic smelt]

Once you plug in y = sqrt(R^2 - x^2), yeah

But generally it's the surface area of the shape that you get by revolving a graph around x-axis

[meager hollow]

ohk so if s = r/2

we can find the 'radius' of the flat circle to be root 3 x R/2 ?

[sonic smelt]

Yes

[meager hollow]

and so area would be 3 pir^2/4

ahh

nice

is there a way to do without integrals

[sonic smelt]

I thought of considering the angle that you get when you connected the center of the sphere and the circumference of the cut surface, but didn't really make much out of it

[meager hollow]

ah okay

once i reach area integrals i guess this will be doable then

thank you so much!

.close

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[polar oyster]

I am trying to model the relationship of 2 things. For X between +6 to -6, the relationship is a sine wave. I created an equation for this and it works fine. However, this equation doesn’t work for X between 9 to 6 and -6 to -9. This is because the relationship looks more like a square at these values (look at my drawing). How should i model these areas?

[restive river]

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

Use this function

[polar oyster]

My relationship is not an exact square, does it still work for that?

Also, I have no idea what that is

how would I input that on desmos?

[devout snow]

@polar oyster Has your question been resolved?

[polar oyster]

it becomes more square like the larger the number gets

[devout snow]

@polar oyster Has your question been resolved?

[devout snow]

@polar oyster Has your question been resolved?

[polar oyster]

imma give up gn

[devout snow]

@polar oyster Has your question been resolved?

[devout snow]

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[lapis lichen]

Hello can you please help with question 1.6

[devout snow]

@lapis lichen Has your question been resolved?

[supple pasture]

Do you know what are the restrictions on D?

[lapis lichen]

No

No

[supple pasture]

Then I'll assume that D has the same y-coordinates as B

And by the way, what does $\hat{EDB}$ mean? I don't use this type of notation

[woven radish]

Math Is Fun

[devout snow]

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[lunar parcel]

Help pls: 0 =<a1 =<a2=<……=<an=<1 Prove: a1 + a2^2 + …… + an^n >= na1a2….an

[lunar parcel]

<@&286206848099549185>

[small quartz]

Each of the terms on the lhs is at least $a_1 \cdot a_2 \cdots a_n$

[woven radish]

Cain

[small quartz]

Right?

@lunar parcel

$a_i^ i \geq a_1 \cdot a_2 \cdots a_i \geq a_1 \cdot a_2 \cdots a_n$

[woven radish]

Cain

[lunar parcel]

Yes

[small quartz]

You have $n$ such terms, so you get the answer

$\sum_{i=1}^{n} a_i^i \geq n a_1 \cdot a_2 \cdots a_n$

[woven radish]

Cain

Cain

[lunar parcel]

Why so?

[feral agate]

add up all the inequalities

[grizzled yew]

Clever

[feral agate]

$a_1\ge a_1 \cdot a_2 \cdots a_n, a^2_2\ge a_1 \cdot a_2 \cdots a_n, a^3_3\ge a_1 \cdot a_2 \cdots a_n\cdots$

[woven radish]

kheerii

[lunar parcel]

a1 >=a1a2…an ок, but why a2^2 >=a1a2…an?

[small quartz]

see this again

$a_i^ i \geq a_1 \cdot a_2 \cdots a_i \geq a_1 \cdot a_2 \cdots a_n$

[woven radish]

Cain

[lunar parcel]

I understood everything

Thanks

[small quartz]

You are welcome 🙂

[lunar parcel]

.close

[devout snow]

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[crystal kite]

how to get to the answer from the book

[crystal kite]

they are both correct

[devout snow]

@crystal kite Has your question been resolved?

[devout snow]

@crystal kite Has your question been resolved?

[pulsar ermine]

Draw the two graphs

Or another approach is to use trig angle formulae

[crystal kite]

i did that already and got the answer

but the question is how from all 4 solutions that i got to write the set notation

[devout snow]

@crystal kite Has your question been resolved?

[devout snow]

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• Show your work, and if possible, explain where you are stuck.
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[restive river]

What is Range of a function?

[obsidian elbow]

The set of all outputs of a functions is called Range..

[restive river]

for example what is the range of this function f(x)=(x^2-2x-8)/x-2

how do I find that?

[tender lotus]

find the domain first

[restive river]

domain is all numbers that are not 2

[lyric hornet]

Are there any horizontal asymptotes?

[hidden dragon]

This is quadratic/linear

[restive river]

sorry I do not know what horizontal asymptotes mean

[hidden dragon]

Alternative method: Just assume it equal to y and form a quadratic in x by cross multiplying and solve Discriminant greater than or equal to 0. Them you will get range of y but before you dictate it's the actual answer, check for the coefficient of the highest degree variable of quadratic in x which you formed,equate that coefficient to 0, you will get a value of y. Put that value of y in original equation...if you get any value of x then it means your original answer is right. However, if you don't get any value of x then remove that value of y which you got from equating that coefficient of x^2 to 0, from the original answer. That will be your final answer.

[tender lotus]

or draw table of variation

but u need to find the derivative first

[restive river]

I see but the answer says that the range of function is all real numbers?

I maybe failed in explaining what I meant

sorry I am bad while talking about math in english

[tender lotus]

yes but u need to prove it

[tender lotus]

french?

[restive river]

no

I do not think I need to prove it cuz the answer just states that it is all the real numbers. not sure tbh.

[lyric hornet]

I don't think he knows what a derivative is if he's doing domain and range of rational functions 😅 but hey not one to assume

[restive river]

I know what derivative is but I do not know what it has to do with the range xD

[tender lotus]

derivative is strictly positive, so the function is increasing from -inifnity to +infinity therefore, the range is all real numbers

[lyric hornet]

For some rational function $\frac{f(x)}{g(x)}$ where both $f(x)$ and $g(x)$ are polynomials there are three cases:\
\begin{enumerate}
\item Case 1: $f(x)$ has greater highest degree than $g(x)$. Result: No HA
\item Case 2: $f(x)$ and $g(x)$ have the same highest degree. Result: HA is the top coefficient of the highest degree divided by the bottom.
\item Case 3: $g(x)$ has greater highest degree than $f(x)$. Result: HA is at $y=0$
\end{enumerate}

[restive river]

wait I think I get it, the range is the number sthat the function pass through?

[tender lotus]

u'll clearly see it if u draw table of variation

[woven radish]

XxMrFancyu2xX

[lyric hornet]

(hope i did that right )

[restive river]

what is HA

[tender lotus]

Horizontal Asymptote

[restive river]

so all those cases are right for f(x)/g(x)

[lyric hornet]

yes those are the only three cases

in your equation above: $\frac{x^2-2x-8}{x-2}$

[woven radish]

XxMrFancyu2xX

[lyric hornet]

what is the highest degree of the top polynomial?

[restive river]

2

[lyric hornet]

and the bottom?

[restive river]

1

so case 1?

no HA

meaning Horizontal Asymptote

[lyric hornet]

and therefore there is not case that the line breaks going up and down

therefore the function is defined over the entire range

so then what is the range?

[restive river]

wdym

breaks?

[lyric hornet]

uhhh

gimmie a min

while i make a beautfil artwork

describing whati. am saying

the dotted line the horizontal asymptote

see how it cuts through the line

[restive river]

yes