help-0

[tough hatch]

why are u getting all the numbers with t together

that is counterproductive to the goal of finding t

[acoustic abyss]

one sec

[tough hatch]

u want the equality t = .....

[acoustic abyss]

ill try doing it once

just give me a min

[tough hatch]

sure

[alpine sable]

can somebody help me?

[acoustic abyss]

hey i got it

[tough hatch]

?

[acoustic abyss]

v = u +at
u + at = v
u = v - at

v = u+at
u +at = v
at = v-u
t = v-u/a

t = 30-10/2.5

t = 8

[upper pebble]

[acoustic abyss]

correct?

[tough hatch]

ok, but the first set of equations had no point at all.

[acoustic abyss]

yea lol

[tough hatch]

,calc 20/2.5

[ocean seal]

Result:

8

[acoustic abyss]

so is it correct?

[tough hatch]

yes

[acoustic abyss]

alr tysm anyway

[alpine sable]

?

[ionic jewel]

JUST ASK

[acoustic abyss]

ask ur quetion

[alpine sable]

oh

[ionic jewel]

It says it in the emote

[tough hatch]

............................

[upper pebble]

[alpine sable]

sorry i cant read it well

[ionic jewel]

the future really is now

[tough hatch]

..............................................................................................................................

[alpine sable]

uh so i am having trouble understanding how to do the chain rule of the derivative
i know that its like one term and the other is not derivated but which one

[acoustic abyss]

_ _

[ionic jewel]

derivative of f(g(x)) = f'(g(x))g'(x)

[alpine sable]

huh

[ionic jewel]

is that not the chain rule

do you mean the other chain rule

like you want to take the derivative of something like log(2x+1) right?

[alpine sable]

no i was just saying huh because i didnt know what the ' meant but i know now

[ionic jewel]

ah

yeah it meant derivative lol

it's pronounced "prime"

[alpine sable]

puh-ri-m

like this right

[jagged imp]

prime

rhymes with lime

or time

[upper pebble]

rhymes with rhyme

[jagged imp]

like crime but with a p sound

[acoustic abyss]

um?

[gray isle]

assuming the goal is to isolate y
what have you tried?

[alpine sable]

Can anyone correct my homework?

[upper pebble]

maybe

[alpine sable]

Can you see this?

[harsh swallow]

@upper pebble Ty sorry for not reacting i was getting my first vaccine

[upper pebble]

oh cool np

but umbreon >

[red ledge]

I have a question

[upper pebble]

[red ledge]

What does it mean for a limit not to exist

For a limit to exist, the right side limit must equal the left side limit otherwise the limit doesn't exist

But I don't understand what does it mean for the limit not to exist

[rigid smelt]

the function doesnt approach the same value when x approaches some value

also known as a discontinuity

oh oops, abstract, if you still have some confusion or questions, please move to another channel

[red ledge]

What!

Why another channel I typed here first

[rigid smelt]

not really

[glass lichen]

you didnt

[rigid smelt]

please just move

[glass lichen]

move to another channel

[red ledge]

Fine

Bye

[glass lichen]

what have you tried..?

ok.... do you have working to show you've tried the question

you know.. since it asks for a diagram of the vectors

[stray hearth]

Shouldn't there be a distance or something

[glass lichen]

not needed.

[stray hearth]

Oh wait. I see

[glass lichen]

the 7 wont be orthogonal to the 1.5 if the boat goes off at an angle

the 1.5 will always be orthogonal to the width of the river, which ends up being the resultant vector.

yes.. so find the angle.

[stray hearth]

Double it maybe

Wait. The question just wants to to work out the angle with a protractor from what it looks like.

[glass lichen]

???

you're given the units on the vectors if that's what you mean..

that's not fully necessary but ok

[golden tartan]

What are some good resources to use during the time until I go to college so I don't forget stuff because I still have 2 more months to wait

[upper pebble]

Khan Academy

[golden tartan]

Ok I'll have a look at that

[upper pebble]

it's completely free

although i'm not sure how effective it is for college since i haven't started college yet

i've seen people say it was helpful for them in college though

[ocean seal]

Callaway

Callaway

Callaway

[teal epoch]

wait wut?

ugh it's getting spammy i'll do it on another channel

[deft creek]

How do you get the cube root of a number? I'm having trouble understanding it

[harsh girder]

if a*a*a=b, then a is the cube root of b

[deft creek]

yes i understand but how do you get a

[jaunty plover]

calculator

[undone dock]

There isn't really an easy way to find the cube root of a number

[harsh girder]

Do you want to know the numerical calculation method? you can search for bisection method, Newton's method

[deft creek]

I understand now no need for that, thank you

I'll stick to using the calculator

[hallow finch]

Big general math question, when it comes to learning a new "Area" of Mathematics, did you or do you have a "Process" that you go through to memorize or recognize certain patterns for future use?

[wooden crag]

memorising specific patterns is ultimately pointless, you need to build up your belt of problem solving tools for that specific area

which usually comes down to solving different practice problems, and learning the fundamental intuitions

[alpine sable]

i get to top part, but where does the /17 come from??

also i understand that the intergrals cancel eachother out

[lethal stump]

cuz you have the integral on the LHS

so they add together

16+1 = 17

[alpine sable]

thats what i have done so far

from the bottom half haha

top half was my first go

[lethal stump]

ah i c nws

yo where's that 2 coming from

shouldn't it be 17?

[alpine sable]

i got the two because i added the intergral on the end to the other side

[lethal stump]

ya but you have 16 of the integral on RHS

[alpine sable]

since they were the same intergral, which gives you two of the same intergral

am i supposed to do something with that as well?

so i do the same to the rhs of the intergral as well so its then 16 + 2e^-xsin(4x) which would be 17, and then divide everything by 17?

[lethal stump]

wait i think ur confusing urself

the 16 on the RHS

thats supposed to be 16I right?

[alpine sable]

ah i see jesus

so its 16 of the intergrals, you add it it makes it 17

then you divide

i think the light bulb went off 😛

[alpine sable]

is that the right way to think of it? sorry for the ping. i just wanna understand the concept 🙂

[noble sinew]

try to figure out how many solutions there were if no contraints on x1 and x2

[lethal stump]

yaya das right

[merry hamlet]

@noble sinew 14.950 is true

[noble sinew]

?

[alpine sable]

pls bal

[still kraken]

<@&286206848099549185> can anyone give me the steps to solve this?

[wooden crag]

draw it

[harsh girder]

you can write the vertex in the fourth quadrant as $(x,-3\sqrt{1-\frac{x^2}{4}})$

[ocean seal]

秋水

[brisk ferry]

I don't understand how you can evaluate this trig equation like this somebody pls help

[ocean seal]

Muzan Jackson

[stark trail]

@brisk ferry

[brisk ferry]

oh that makes sense thanks

[rich haven]

is the answer 100?

[ancient creek]

yes

[flat tundra]

Is it because of similar triangles ? I lack the knowledge in this area

[still kraken]

what is the answer of this

[crisp grail]

It is 100

Because BCA=BDA

And than idk in english but you use the in a circle inscribed quadrilateral

@rich haven

[ancient creek]

look into inscribed angle theorem

[wooden crag]

you can figure out the whole thing with inscribed angle theorem and corresponding angles

[flat tundra]

Thanks

[plain dawn]

In a triangle with sides 5,12,13 what is the distance from the center of inscribed circle to the closest vertex of the triangle?

[flat tundra]

Is it because bdc=bac ? So in the triangle abc we have 50+30 degrees and we miss 100 that is the angle abc ?

[unkempt nexus]

\sqrt{1-cos^2x}

[stark trail]

Wut

[stark trail]

Try drawing a diagram

[unkempt nexus]

i thought its the answer for the problem of TeXit... Sry if I contact u directly

[plain dawn]

i did, still dont know how

[tired estuary]

what does region stand for?

[lost cairn]

There are 90 000 five-digit positive integers. However, only some of these five-digit integers satisfy the following conditions: • the middle digit is 0, • the ten thousands digit and the tens digit are equal, • the thousands digit and the ones (units) digit are equal, and • the number has exactly 5 prime factors. All of these prime factors are odd and none are repeated. Determine all five-digit positive integers that satisfy the given conditions.

[stark trail]

@plain dawn

[lost cairn]

@stark trail can you answer it PLEASE

[alpine sable]

[stark trail]

Let’s say AB=5
BC=12
AC=13
r=radius of the circle
5,12,13 is a right triangle so m$\angle{ABC}$ is equal to $90^\circ$
The circle is tangent at E,F, and G
A,B,and C are the vertices of the triangle
The centre point of the circle is D
First of all,try to determine the radius of the circle
The area of ADB,BDC,ADC makes the area of the triangle
$A_{ADB}+A_{BDC}+A_{ADC}=A_{ABC}\
\frac{5r}{2}+\frac{12r}{2}+\frac{13r}{2}=\frac{5\cdot 12}{2}\
\
15r=30\
r=2\
\text{ }$Then solve for AD,BD,CD because those are the distance between the centre of the triangle and each vertex. After that, determine which is the smallest distance and that’s going to be your answer. You can use phytagorean theorem to solve it @plain dawn

[ocean seal]

Muzan Jackson

[sly mantle]

@lost cairn don’t spam your question and don’t ghost ping me

[versed burrow]

Hi! Can anyone explain how the domain came to be? I'm confused

[gusty ravine]

welp the function is defined everywhere except for those hole at x = -5 and x = 5

so the domain R\{-5, 5}

what they wrote is an elaborate but equivalent way to write R\{-5, 5}

[alpine sable]

秋水#5244 but who else willing to help math

@harsh girder

Oh ok sorry then @harsh girder

[versed burrow]

oh so the part in between the middle where there's 5,5 is the combined one?

[gusty ravine]

no, the entire domain is the union of three of those sets.

u union all three of these sets together and u got ur domain

basically they're skipping over -5 and 5 cuz they're not in the domain

@versed burrow does this make sense ?

[versed burrow]

yesss, tysm!

[gusty ravine]

noice

[neat merlin]

Which of these are true and why?

[alpine sable]

I need help

My mathematics tutor has proved to me in every possible way so far that everything is triangles

I need proof otherwise

(not limited to geometry)

[tough hatch]

and could you tell us exactly the entire 'proof'?

[alpine sable]

uhh basically anything you can think of he will think of a way that it is technically a triangle

a circle is infinite triangles rotated infinitely to make a circle

[tough hatch]

and other examples?

[alpine sable]

uhh basically everything is a triangle even the arrangement of quarks and whatever else (the names arent coming to me rn) makes up atomic structured are arranged in a triangle

[tough hatch]

it's only a proof if it works all the same for 'everything'

[alpine sable]

hmm

[tough hatch]

they didn't prove anything

sure, triangles, or triples, are common in nature

but that doesn't mean everything is made up of triangles

[alpine sable]

I am trying to remember if it applies to literally everything

I suppose everything physical and mathematical

such as the vocal cords that go into producing those sounds

hey

i had a quick question

would you mind answering to it?

[tough hatch]

u can post on an unbusy channel

[alpine sable]

oh sure sorry for the disturbance caused

[lavish depot]

The most basic polygon is a triangle so I mean any object can be modelled by it (subdivided by triangles)

That's probably what the tutor meant

[alpine sable]

mmm most likely

in which case I would still require proof otherwise

a triangle where the other 2 sides are = to 0

no they just are triangles where 2 of the sides are equal to 0

uhhh

a straight line is a triangle where the base is equal to 0

and therefore a singular point would be one where 2 of the sides (length) would be equal to 0

[tough hatch]

is this a question for some assignment?

[alpine sable]

not particularly no

I just wanted to disprove it

as i refuse to accept that its all triangles

[tough hatch]

how about taking nothing

how is that "made up" of triangles?

[alpine sable]

its the absence of a triangle technically in a triangular shape

its essentially an anti triangle

[tough hatch]

just because your teacher demonstrated many ways that everything is made up of triangles doesn't actually prove it

[alpine sable]

ok

but until i find something which goes against this

I cant really disprove it

proved or not

[strong furnace]

But what is the point of this ? I don't get it

[alpine sable]

there isn't really one

[tough hatch]

but ur question was about whether anything can be decomposed into triangles

[alpine sable]

yes

Im looking for something that cannot be decomposed into triangles

[tough hatch]

u can't decompose nothing into something

[strong furnace]

You cannot decompose smooth curves into finite triangles

[alpine sable]

not finite no

but infinite

[tough hatch]

your so-called 'anti-triangle' is the absence of triangle
nothing cannot be formed from having no triangles if triangles are the most fundamental "building block" of everything

[alpine sable]

yes but the existence around it makes the shape of a triangle

and that existence is made out of more triangles

[strong furnace]

It's like saying points make up everything and since a point is a triangle and absence of point is anti triangle

[tough hatch]

only existent things make up the triangle

[alpine sable]

pretty much

[tough hatch]

not the empty space inside it

[alpine sable]

wait

no

my head hurts

[ionic jewel]

I'm losing brain cells reading this

anything that has nonzero area can be modeled by some number of triangles, notable this doesn't include lines, points, or nothing

it also extends to 3d pretty well, which is literally how video game graphics work

it's all triangles

always has been

[alpine sable]

yep

time to go cry

[tough hatch]

in general triangles don't include the area enclosed by the sides

[tough hatch]

so ur argument falls apart

[ionic jewel]

^

[tough hatch]

sure, u CAN take existent things that do form the shape of a triangle, or decomposable into triangles, that together enclose this empty space

but u CANNOT include the enclosed empty space in ur triangle

the abundance of triangles in real life doesn't imply everything is decomposable into triangles

just like the abundance of subatomic particles doesn't imply everything is decomposable into subatomic particles

because nothing, is part of 'everything'

i cringe using everything in casual sentences

reminds me of the set paradox

[dense carbon]

Class 10, ncert, polynomials

Every question I did was easy until my teacher dropped this practise worksheet

[rigid smelt]

What have you tried

[dense carbon]

I erased everything but let me send the method I used

The teacher gave us the answer at the back but still hasn't told us how to solve it

4√3 x2+ 5x -2√3

From calculating the product I have figured out c = -2 and a = 4

[jagged trout]

$\frac{-8 + \sqrt{6}}{4*\sqrt{2}}=\frac{-b}{c}$

[ocean seal]

Moriarty

[upper ember]

there is a very simple thing you can do here
if u didnt know, a quadratic equation can be written as
a(x^2-Sx+P)
where S is the sum of the roots, and P is the product

[regal flare]

or just (x-a)(x-b) where a and b are the zeroes

same thing

[upper ember]

^

exactly

these are the "tricks" that u can use

[dense carbon]

The thing is my teacher has only taught me this so the methods and tricks you are giving to me seem very foreign

Thank you for responding btw

[regal flare]

might seem new but if u've been working with quadratics this is nothing new

working backwards to the zero product rule

[dense carbon]

o wait

[regal flare]

you know that if (x-a)(x-b) equals zero, then either x equals a or x equals b

so obviously if x equals a or x equals b, then (x-a)(x-b) equals zero

[dense carbon]

I think there is a barrier between the way we learn because Im from a different country, I have never learnt (x-a) (x-b) = 0

India btw

[regal flare]

how do you solve quadratics

[dense carbon]

I solve it cutting middle term and the prove it by using the -b/a and c/a

[regal flare]

how would you solve $x^2-3x+2$

[ocean seal]

mjjA

[regal flare]

oh

so yeah using the middle term

rewrite this as $x^2 - 2x -1x + 2$

[ocean seal]

mjjA

[regal flare]

now factor factor the first two and last two terms

$x(x-2) -1(x-2)$

[ocean seal]

mjjA

[regal flare]

you with me so far?

[dense carbon]

Yup

[regal flare]

now factor out $(x-2)$

[ocean seal]

mjjA

[dense carbon]

That's what I do

[regal flare]

$(x-1)(x-2)$

[ocean seal]

mjjA

[regal flare]

set it equal to zero

[dense carbon]

equal to zero??

[regal flare]

yeah

[dense carbon]

I don't know what that means ;-;

how do you set it equal to zero

[regal flare]

see the word "zeroes" in the question?

[dense carbon]

yes

[regal flare]

that means you're looking for values that make the polynomial equal to zero

[dense carbon]

yes

But i cant solve it

[regal flare]

so when you solve $x^2-3x+2$, you're finding what value of x makes the expression equal to zero, which means solve for x in $x^2-3x+2=0$

yes you can

[ocean seal]

mjjA

[regal flare]

so we turned $x^2 - 3x +2 = 0$ into $(x-1)(x-2) = 0$ by factoring right?

[ocean seal]

mjjA

[alpine sable]

<@&286206848099549185>

Can someone please help

😭

[regal flare]

set x = 5

[dense carbon]

yes

[acoustic shadow]

What do you not understand and also ping helpers after 15 min

[regal flare]

okay so we have two numbers that are being multiplied, and the result is zero

[alpine sable]

Huh

[dense carbon]

I understand that

[regal flare]

this can only happen if one of the numbers is equal to zero

[alpine sable]

This is my first time taking algebra

[dense carbon]

Can you explain this question step by step?

[regal flare]

so either (x-2) = 0 or (x-3) = 0

[dense carbon]

Find a quadratic polynomial whose zeroes are -2/√3 and (√3)/4.

[acoustic shadow]

Don’t ping everytime

[dense carbon]

By using -b/a and c/a?

[regal flare]

yeah to do that u need to understand the zero product first

[acoustic shadow]

How old are you and what do you not understand

[regal flare]

i don't know how to do it like that, but to me the zero product is much simpler

and better than blindly plugging into formulas

[alpine sable]

Everything I’m 15

[acoustic shadow]

Pls stop pinging

[dense carbon]

Okay wait let me reread it

[acoustic shadow]

Read the rules first on how to use the server and you’ve to explain where you’re getting stuck

[alpine sable]

Bruh I only pinged you one time????

[acoustic shadow]

Ffs when you reply to me if pings ,type normally

[dense carbon]

what is the formula of your method?

[alpine sable]

Meh

[acoustic shadow]

Pls go read the rules first and how to use discord. I’m not being rude rn but you should atleast know how to use it

[regal flare]

if a and b are the zeroes of a quadratic, then the quadratic is (x-a)(x-b)

that's all

[dense carbon]

so I have to do (x-(-2/root3)) (x- (root3/4)??

[regal flare]

so your zeroes are $\frac{-2}{\sqrt{3}}$ and $\frac{\sqrt{3}}{4}$

[ocean seal]

mjjA

[regal flare]

yes

so your quadratic is $(x-\frac{-2}{\sqrt{3}})(x-\frac{\sqrt{3}}{4})$

[ocean seal]

mjjA

[regal flare]

,w expand (x-\frac{-2}{\sqrt{3}})(x-\frac{\sqrt{3}}{4})

[ocean seal]

Results provided by WolframAlpha

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

Requested by mjjA#2284

[regal flare]

that's your polynomial

[dense carbon]

sorry I don't understand how to calculate

Also is wolframalpha a good website for doubts?

[regal flare]

no

it's just a calculator on steroids

u need to pay up if u want step by step explanations

2nd line does not equal third line

[ionic jewel]

it's good for checking answers, not good for doing math and showing steps

[regal flare]

make it easier by substituting a and b for the zeroes

a = -2/sqrt(3) and b = sqrt(3)/4

so u have (x-a)(x-b)

= x(x-b) -a(x-b)

= x^2 -bx -ax + ab

= x^2 -(a+b)x + ab

now substitute a and b back in

[dense carbon]

are we splitting the middle term in this?

[regal flare]

no we are not

[dense carbon]

kk

Also I want to thank you for being so nice even though I am asking so many questions

[regal flare]

we are using the fact that (x-root)(x-root2) for any quadratic

and working backwards by expanding

[regal flare]

thanks to u too for the compliment

[dense carbon]

Im going to sleep for now

It's midnight here

[regal flare]

good night

[dense carbon]

ignore the request

just sent it to keep a reminder

[regal flare]

ok

[dense carbon]

Goodbye :)

[limber narwhal]

how would you solve for the sides?

[fresh lake]

shorter leg is half the hypotenuse

and longer leg is the shorter leg times √3

[limber narwhal]

yea i got that

[gray isle]

trigonometric ratios and/or special triangles

[limber narwhal]

ohhhh

[limber narwhal]

aight thats what i was forgetting

ty

[fresh lake]

btw longer leg is opposite the 60° angle

[limber narwhal]

yea

i got that down

so n is 2 sqr 2 and m is 2 sqr 6

[fresh lake]

oh then just do ,w 30-60-90 triangle in #bots if you forget again

[fresh lake]

np

[fresh lake]

yep

[limber narwhal]

ty

[fresh lake]

np

[plain dawn]

nvm

wait but doesnt the altitude have to be 90 degrees?

how do you know r is 90 degrees

[plain dawn]

i got answer, though but i still dont know how center to those tangent points is 90 degrees

[vagrant rover]

Determine the probability of landing on tails at most 33 times if you flip a fair coin 80 times. Round your answer to the nearest tenth.

How do I find this? I know that I need to use choose here or something related to permutations, but I don't know what numbers to actually input to get the result the question wants.

Would appreciate some help.

[plain dawn]

what is the probability of it zero

once

twice

maybe hockey stick or the pascal's triangle thing will help

[fresh lake]

at least 67 must be heads

so chance of getting 67 heads

1/2^67

[vagrant rover]

but it wants tails?

[fresh lake]

at most

not at least

at most means there can be 0 tails

it's a roundabout way to ask what the probability of getting 67 heads is

and even if it's asking probability of getting 67 tails it's the same thing

[vagrant rover]

But 67 heads isn

't a probability

I think it's looking for a fraction or a percentage\

[fresh lake]

i didn't say that 67 heads is the answer

[plain dawn]

how did you find that the incenter to the tangent points was 90 degrees for it to be an altitude

[fresh lake]

i said the probability of getting 67 heads is the answer

which would be $\left(\frac12\right)^{67}$

[ocean seal]

Bored Videos

[vagrant rover]

I don't understand

[plain dawn]

the coin flip 80 times

remeber

not 100 btw

[vagrant rover]

^

[fresh lake]

oh

doesn't matter

[plain dawn]

do u mean 47 maybe

[fresh lake]

oh right

it does

so yeah 1/2^47

[vagrant rover]

What is that

What is 1/2^47

I'm sorry I just don't understand

[fresh lake]

the reciprocal of the product of 47 2's

or

,,\left(\frac12\right)^{47}

[ocean seal]

Bored Videos

[still kraken]

Can i turn this into a continuous function?

[ionic jewel]

which part?

a function cant have two outputs for the same input, so no if you mean all of it

also its not continuous

yeah idk what ur asking

[alpine sable]

I'm weak on transforming sums like that. Since n is not used in the actual sum we can just convert it...
Can anyone explain the intermediary steps?

[arctic mango]

What is this?

If the index was from j = 1 to j = n, the sum would surely by n/3.
Since this is basically the same case, with i = j + 1, the sum has to be n/3.

[ionic jewel]

yeah this is wrong, should be n/3

[still kraken]

yeah i was so dumb with that

[vagrant rover]

100, 95, 55, 85, 75, 100

For this population, how many scores are within one standard deviation of the mean?```

Is this 5? I calculated the standard deviation to be 17.6, so that means 100, 95, 85, 75, and 100 are all within one standard deviation, right? and 55 is the only one that is not within one standard deviation?

Did I calculate the standard deviation correctly?

When I did it by hand i got 17.6, but when I use a calculater I'm getting 16.07. Did I do something wrong or is the calculator getting messed up???

[wary stream]

,w std 100, 95, 55, 85, 75, 100

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[wary stream]

Probably inputted into calculator wrong

[vagrant rover]

That's weird. Fair enough.

And did I do the other stuff correctly?

Would appreciate some help if you have the time.

are 100, 95, 85, 75, and 100 the only ones that are within one standard deviation? @wary stream

[orchid kayak]

Anyone there to help?

So, I had a test question a few weeks ago, and I still don't know how to do it
Which is this one

[austere sinew]

Try adding the fractions then crossmultiply

[orchid kayak]

Mk

But how

[austere sinew]

Lcm

Or make the denominators the same

[orchid kayak]

Alright I will try rq

[austere sinew]

Good luck

[orchid kayak]

I can't find a way to make them the same

[fresh lake]

first of all

[orchid kayak]

[elfin snow]

I can help

[fresh lake]

factor x^2-1

using the difference of squares formula

[elfin snow]

^

[orchid kayak]

Alr

[fresh lake]

tell me what you get

[orchid kayak]

Mkay

(x-1)(x+1)

[fresh lake]

yep

so what's the lcm of (x+1) and (x-1)(x+1)

[elfin snow]

or you could just multiply the first term by (x-1)/(x-1) since that would make the denoms the same and wouldnt change the value

[fresh lake]

uh

[orchid kayak]

(x-1)(x+1)?

[fresh lake]

yes

[orchid kayak]

o

[elfin snow]

if that makes sense

[fresh lake]

but like

i'm trying to explain why that works

and why (x-1) specifically

but yeah

[elfin snow]

oh ok

[fresh lake]

,,\frac{x-2}{x+1}=\frac{x-2}{x+1}\times1=\frac{x-2}{x+1}\times\frac{x-1}{x-1}=\frac{(x-2)(x-1)}{(x-1)(x+1)}

[ocean seal]

Bored Videos

[fresh lake]

i'll just tell you at this point $\(x+1)\times(x-1)=(x-1)(x+1)\(x-1)(x+1)\times1=(x-1)(x+1)$

[ocean seal]

Bored Videos

[fresh lake]

so you can turn (x+1) into (x-1)(x+1) by multiplying

and you can turn (x-1)(x+1) into (x-1)(x+1) by multiplying

so (x-1)(x+1) is the lcm of them both

makes sense?

[orchid kayak]

I think yes

But there's some part that I am still confused

Hold up lemme analyze for a bit

[fresh lake]

ok

yeah algebra can be hard to figure out at times

[orchid kayak]

indeed

[plain dawn]

Find the smallest possible value of x+y so that x^2−y^2 is divisible by 74, where x,y are positive integers.

the is difference of squares so (x+y)(x-y) = 0 mod 74

but idk what to do after dat

[elfin snow]

dude don't introduce mod arith into this

[fresh lake]

😩 why not

[plain dawn]

oh but what do i do after (x+y)(x-y) is divisble by 74

what do i test and stuff

[orchid kayak]

Where/How did this *1 appeared?

[elfin snow]

oh wait it was a new question

@plain dawn please ask your q somewhere else

[plain dawn]

oh oops i thoguht channel was open sry

[elfin snow]

no worries

[fresh lake]

$(x-1)(x+1)\mathbf{\times 1}$?

[plain dawn]

i asked in channel 2

[ocean seal]

Bored Videos

[orchid kayak]

Mhm

[fresh lake]

well

that's what you multiply by (x-1)(x+1) to get (x-1)(x+1)

we are turning (x-1)(x+1) into the lcm

and since it is the lcm

we just multiply by 1

[elfin snow]

(remember multiplying by 1 doesn't change the value)

[fresh lake]

ye

[elfin snow]

and @orchid kayak you understand what the lcm is right?

[orchid kayak]

Oh, so the lcm of this is 1, and then you multiply the result with the lcm?

Yea

[elfin snow]

ok good

[fresh lake]

1 isn't the lcm

but it's what you multiply by to get it

[orchid kayak]

Mhm

so if it was (2-2x)(2+2x)
would be (2-2x)(2+2x)*2 right?

[fresh lake]

(2-2x)(2+2x)*2 is 2(2-2x)(2+2x)

not (2-2x)(2+2x)

so we again multiply by 1

[orchid kayak]

O
Now I got it, I was thinking that it worked different

[fresh lake]

,,(2-2x)(2+2x)\times\mathbf1=(2-2x)(2+2x)

[ocean seal]

Bored Videos

[fresh lake]

still the same

[fresh lake]

oh ok

anyways

[static valve]

anyone here know linear algebra?

[vagrant rover]

Is Y= a + bX and y= ax+b the same thing?

[fresh lake]

might be a good idea to ask in #linear-algebra

[static valve]

ok

asked

[orchid kayak]

In the start, algebra seemed to be easy in the start
But everytime you learn more stuff from algebra, it gets more confused

Anyways, how do we continue?

[fresh lake]

then you move on to algebra ii and want to go back immediately

[orchid kayak]

Yea

[fresh lake]

gonna repost the question

first

we gotta convert (x-2)/(x+1) into a fraction over x^2-1

so what do you multiply by (x+1) to make it x^2-1

[vagrant rover]

bump

[fresh lake]

h

[orchid kayak]

You make (x+1)²

[fresh lake]

what

[orchid kayak]

wait

[fresh lake]

in y=a+bx, a is the y-int and b is the slope
in y=b+ax, b is the slope and a is the y-int

so it's just switching the variables

and the same values

but idk

[orchid kayak]

I forgot how the y-int and slope works

[orchid kayak]

(x-1) then?

Sorry I think my brain is scrambling around on this calculation

[upper pebble]

(x + 1)(x - 1) = x^2 - 1

so you should be right

so after that i think you can multiply (1)/(x - 1) on the RHS by (x + 1)/(x + 1) to make its denominator x^2 - 1, and then go from there

[fresh lake]

yee

do ,w (x-2)/(x+1)+(3)/(x^2-1)=(1)/(x-1)+(x)/(x^2-1) to check your answer when done

ping me if you still don't know what to do

[torn epoch]

how do I solve this? Suppose P(C) = .048, P(M ∩ C) = .044, and P(M ∪ C) = .524. Find the indicated probability.
P(M)

[random talon]

P(M ∪ C) = P(M) + P(C) - P(M ∩ C)

You have everything you need to compute the probability

[torn epoch]

ok thank you. I got it. In my head I'm visualizing venn diagrams and I cant comprehend what the problem means.

[fresh lake]

so uh

[distant epoch]

hello, may i ask what this means?

what does it mean to multiply a coordinate?

[ionic jewel]

(200t,200t)

[distant epoch]

what does that mean?

and why does it make this? @ionic jewel

is there a term for this so i can study it on my own

[clever folio]

Scalar multiply in this case

[distant epoch]

is there a more general topic?

[ionic jewel]

yeah it's called a line

[distant epoch]

line arithmetic?

[ionic jewel]

scalar multiple is the correct term for this

if you want to look it up

[clever folio]

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

[distant epoch]

thanks a lot for the sources

what is t specifically?

is it just a variable letter or does t imply something

[strong furnace]

parametric equation/ parametric form of line would explain why this is a line and this is a parameter from that POV
but as bunny said scalar multiplication t is just a variable scalar in this case

[distant epoch]

thanks again

[junior cedar]

I have found an interesting number. Well more like numbers. It is an equation that alternates between two numbers. With both numbers getting more precise. How should I solve this?

[glass lichen]

solve what?

you described an equation with no actual concrete statements

[junior cedar]

Well an infinite series. It’s simple but kind of complicated. I send part of it.

1 + 1/1 - 1/2 + 2/3 - 3/5 + 5/8… so I was messing with primes and this arose.

[glass lichen]

8 isnt prime

[jagged trout]

1 too

[junior cedar]

Sorry I meant the fibb. Sequence

I was as well working with primes too though.

[lunar relic]

For matrices, what does the word echelon mean in row echelon form? I understand what row echelon form is, but I'm wondering specifically about why it's called that

[jagged trout]

Because it looks like a stair

[thin star]

if a hat is 3 dollars, but I can buy 3 for 5 dollars, what % am I saving on that deal?

[junior cedar]

But you are losing money though?

[thin star]

no of course not

I just need to know the % I am saving

[junior cedar]

Wait I read it wrong sorry!

[thin star]

haha no worries

do you know the answer

[junior cedar]

Trying to solve it rn

[jagged trout]

5/9

[thin star]

but in a %?

[jagged trout]

,w 5/9*100

[ocean seal]

Results provided by WolframAlpha

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

Requested by Moriarty#2262

[thin star]

is that so?

is it really saving 55%

if you're buying 3 hats for 5 dollars rather than 1 hat for 3

what if I buy 10 hats for 10 dollars

[jagged trout]

Then every hat will cost 1 dollar

[thin star]

yes

so whats the % I save

[jagged trout]

33,33%

[lunar relic]

That honestly makes a lot of sense, thanks!

[thin star]

thank you

[junior cedar]

I think it is 500% each hat with the discount is . 60 divide that by 3 then you get 5 = 500%

[thin star]

ah I mean like the whole total

[junior cedar]

What do you mean?

Oh I think I know what you mean.

[charred flint]

10 to 20

shift that down 9

[alpine sable]

Hi, I'm geo and I would like to know if someone could help me with my math homework, I'm using a translator because I'm Peruvian, I speak Spanish and I don't speak English very well but please help me with my homework, please, my mother is ashamed of me.

[sleek elbow]

https://dontasktoask.com

[alpine sable]

alguien que hable español porfavor?

@here

https://asktoask.com

??

[dense pine]

Hello guys, is it possible to create a formula for turning speed from these stats ?

(deg/sec)

[versed burrow]

When i graph according to c, d, e, f it will be like only one graph? or will i make different graphs per letters?

[gray isle]

you want one graph satisfying every single property listed

[versed burrow]

• how do u graph the c one ?

im confused with the e sign

[gray isle]

in

element of

just means when x is in that interval,
i.e when x is between -inf and -6 exclusive

[willow anvil]

can someone please explain function notation to me

I get that 4f(p) = 16
p = 4

but it is unclear to me what I do with p = 4

why do we plug it into the original equation

[jagged trout]

4 * f(p) = 16 | :4
f(p) = 4

---

f(p) = 6 - p
4 = 6 - p | +p -4
p = 6 - 4
p = 2

|f(4*p)| = |6 - (4 * p)|
|f(4 * 2)| = |6 - (4 * 2)|
|f(8)| = |6 - 8|
|f(8)| = |-2|
|f(8)| = 2

[gritty gull]

Students randomly receive 1 of 4 versions (A, B, C, D) of a math test. What is the probability that at least 3 of the 5 students tested will get version A of the test? Express your answer as a percent, and round to the nearest tenth.

anyone have an idea

for the formula

[charred flint]

@gritty gull you'll have to split it up into cases of exactly 3, 4 and 5

[gritty gull]

?

like

3/5 4/5 5/5

[daring rapids]

Are you guys done

Can someone help me?

[thorn kindle]

no lmao

[daring rapids]

Oof

[pearl fern]

i kinda need help solving this without l’hopital rule 😦

[pliant cape]

With area between 2 graphs, do I scrap the negative on the 32 (because the area is absolute??)

Or did I do it wrong

[gray isle]

in that interval you subtracted the higher curve from the lower curve resulting in a negative value

if you do the subtraction the other way around you'd get the correct value
alternatively, you could apply abs value around the integral

[pliant cape]

i see thank you :)

[alpine sable]

hi all why is this wrong

i already got it wrong so i was wondering if anyone may know what is correct and why

[ionic jewel]

,w max 3/x, x>0

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

yeah i didn't think so

hmph

oh curvature not max

,w derivative 3/x

,w max -3/x^2, x > 0

[alpine sable]

wait

im so confused

it will show u the max automatically?

,w max -3/x^2, x > 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by xoxo#7837

[alpine sable]

hmm

[alpine sable]

im not sure thats right @ionic jewel

[split sandal]

Can someone help me wuth this

[jagged imp]

do you have the product to sum identities?

if so you can just use that

[split sandal]

Ok ill try that

[alpine sable]

how do i use the wolfram alpha tool?

[jagged imp]

,w 2+2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Sneaky#0928

[ionic jewel]

yeah i think it might be max of 2nd derivative

nvm idk what I'm talking about apparently

[alpine sable]

i did that and

its like

giving me large numbers

[jagged imp]

curvature is something entirely different bunny

https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/differentiating-vector-valued-functions/a/curvature

[alpine sable]

i know its based on the derivative

in fact the equation for curvature is

[ionic jewel]

oh yeah i remember doing that stuff

literally haven't used it since calc 1 or 2 or whatever i learned it

[alpine sable]

second derivative / 1+ first derivative^2 ^ 3/2

i just dont know how to find hte max

the*

from a logical perspective 1 and 3 makes sense

[jagged imp]

ig you'll have to parameterise the function somehow and do all that that's in the Khan article. I'm sure there's some shortcut you could use in this case that you're given the cartesian equation here, but I'm not educated enough to know it and not motivated enough to figure it out

[alpine sable]

to find the max?

hmm ok ill see since i dont see anything about max

[keen crane]

how do you get direction?

i understand u get r , but not the theta

[alpine sable]

if anyone knows this can u pls ping me

[sturdy fog]

someone help ? 🙂 ty

[gray isle]

apply the trig formula for area of a triangle

[sturdy fog]

yp i just finished

thank u

[keen crane]

where 180 from

ahh

i c

[fallen patio]

While finding the range of y = (x^2-2)/(2x-3), I am unable to express x as function of y.

How do I express x in terms of y?

ANYONE?

[upper pebble]

i wish i could help but idk either

[gray isle]

you could rid yourself of fractions,
and apply the quadratic formula

[fallen patio]

That's what I wasnt able to do

[vale wigeon]

it didn't occur to you to multiply both sides by (2x-3)?

[strong citrus]

How to attempt this question calculators are not allowed

[radiant pasture]

i mean

you have log base 2

what's $log_22$

[ocean seal]

Subdivisions X-1

[strong citrus]

1

[radiant pasture]

yes

and is log an increasing or decreasing function

[strong citrus]

Increasing

[radiant pasture]

thus

what value is it definitely above

[strong citrus]

1

[radiant pasture]

and what's the next easy value you can get from log base 2

[strong citrus]

Log2 4

[radiant pasture]

which is

[strong citrus]

2

So it's btw 1 and 2?

[radiant pasture]

yes, but as you can see you don't have that as an answer

[strong citrus]

But the MCQ have 3 options

[radiant pasture]

exactly

[strong citrus]

Yes

[strong citrus]

???

[radiant pasture]

you don't have

between 1 and 2

as an answer

you have different ranges encompassed in (1,2)

[strong citrus]

Ik but what to do now?

[radiant pasture]

honestly idk, the question itself seems a little weird

what grade are you in?

oh

i know

$you have log_22, you have log_24 and you know log_2 is an increasing function. thus what is true about log2_3?$

[ocean seal]

Subdivisions X-1

[radiant pasture]

oh shit

fuck

ok so

what is the relation

between $log_22$ and $log_23$

[ocean seal]

Subdivisions X-1

[radiant pasture]

here's a hint

you know that

$log_22 < log_23 < log_24$

[ocean seal]

Subdivisions X-1

[radiant pasture]

so

how can you manipulate this

to get some numbers similar to the answers out of it?

though come to think of it my idea may not be that great

[vale wigeon]

$\log_2(2)$

[ocean seal]

Ann

[strong citrus]

It's 1

[vale wigeon]

yes, but i was not asking you for that

i was only showing @radiant pasture the proper formatting

[strong citrus]

How to solve it?

[strong citrus]

This

[vale wigeon]

i was going to make a suggestion just now

what i had in mind is that you could multiply everything by 6

and thus compare $\log_2(3^6)$ to $8, 9, 10, 12$ and $18$

[ocean seal]

Ann

[vale wigeon]

find which two of these numbers it lies between

,calc 3^6

[ocean seal]

Result:

729

[vale wigeon]

729 lies between 512 and 1024

[manic pike]

hi, anyone has any idea on this question? I’ve no idea how to begin..

[vale wigeon]

$m = \frac{k}{p^3}$, where $k$ is a constant

[ocean seal]

Ann

[manic pike]

so from there I substitute in the m = 9?

[stiff pawn]

yes, and the particular value of p, you can say like p'

[manic pike]

so it becomes something like 9 = k/p^3?

[stiff pawn]

yes

[manic pike]

how do I find the value of m when p is tripled from there then

sorry Im not good at maths

[stiff pawn]

that p is the particular value, and the question is asking for m value when that p is tripled

so what's the expression?

[manic pike]

9 = k/p^3?

lmao Im confused

[vale wigeon]

m = k/p^3

express k/(3p)^3 in terms of m

[manic pike]

in other words m = k/(3p)^3?

[alpine sable]

Is this channel taken?

I'll suppose not.

[dark granite]

This channel is taken.

[alpine sable]

Oh, my bad.

[stiff pawn]

no, m = k/pˆ3. the question is asking for k/(3p)ˆ3, what's that in terms of m

[dark granite]

@alpine sable I think question 2 channel is open tho

[manic pike]

9 = k/(3p)ˆ3?

[stiff pawn]

no

[manic pike]

or is it m = k/(3p)^3

[upper pebble]

no, m = k/p^3

[stiff pawn]

m = k/pˆ3, and the question wants you to tell what's k/(3p)ˆ3

in terms of m

then you substitute m by 9 in the end

[burnt pond]

Is anybody good with variational calculus?

I'm trying to create a variational calculus problem

I would like to find the optimal function of a soccer free kick between two specific points

Kinda looks like this:

As you can see, the only constraint would be that f(9) = 1.8

Because in free kicks there is a wall

And it needs to go over it

But idk how to pose this as a variational calculus problem

[fallen patio]

I did multiply both the sides with 2x-3 but I still wasnt able to express it that way.

[harsh girder]

@fallen patio $$$$

$$\begin{aligned}
&y=\frac{x^2-2}{2x-3}\
\Rightarrow &(2x-3)y=x^2-2\
\Rightarrow & x^2-2yx+(3y-2)=0\
\Rightarrow &\Delta=4y^2-4(3y-2) \geq0 \
\Rightarrow &y \leq1 \text{ or } y\geq 2

\end{aligned}$$

[ocean seal]

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

[fallen patio]

Ohhhhhhhh
Now I get it, thanks!
Idk why I wasnt able to solve this

[vagrant rover]

Determine the probability of landing on tails at most 33 times if you flip a fair coin 80 times.

Can someone please help me with this

I don't understand it

What am I supposed to do to find the answer?

[vale wigeon]

do you want the exact answer or will a good approximation be good enough

[vagrant rover]

The closer the better, but I just want to know how to do it. Like what method

[vale wigeon]

i mean, ok, are you familiar with these things called distributions

specifically the binomial distribution or the gaussian distribution

[vagrant rover]

Yeah, kind of. I know a bit

Binomial I've heard of before

I don't know exactly wht it is but I've heard of it

Is that what I need to look into?

[vale wigeon]

yes

[vagrant rover]

Awesome, give me one minute and I'll send you my answer and you can check it if you have time

[vale wigeon]

uh

[vagrant rover]

If you don't that's fine

you want the probability of being beyond 1.65 standard deviations from the mean in only one direction. So .0495 ?

[vale wigeon]

let me see

[vagrant rover]

ok ty ❤️

[vale wigeon]

,calc sqrt(80 * 1/2 * 1/2)

[ocean seal]

Result:

4.4721359549996

[vale wigeon]

,calc 7/4.4721

[ocean seal]

Result:

1.5652601686009

[vale wigeon]

1.56 not 1.65

[vagrant rover]

Oh

@vale wigeon Is this correct?

[vale wigeon]

wrong input

[vagrant rover]

how?

[vale wigeon]

you want P(X ≤ 33), thus to comply with what this online calculator is telling you to input you'll need to calculate P(X < 34)

[vagrant rover]

Do you mean this? @vale wigeon

[vale wigeon]

oh, so it actually calculates that for you too, but you chose to conceal it from me.

[vagrant rover]

xd, yeah I didn't put the entire thing in the picture xd, therei s more too :C

[vale wigeon]

your problem asks for the probability of at most 33 tails

[vagrant rover]

Yeah? Is this not at most?

😢

[vale wigeon]

P(X ≤ 33) is.

[vagrant rover]

Ah ok, so then it's 0.0728?

[vale wigeon]

...yes

[vagrant rover]

Cheers, why does the question ask me to round to the nearest tenth then?

That would change the answer

" Round your answer to the nearest tenth."

[vale wigeon]

i don't know

rounding a probability to the nearest 0.1 sounds too crude

but if they insist, then i guess you can answer with 0.1

[vagrant rover]

Yeah, I don't understand it.

Do you have time for one more? @vale wigeon

You are taking a true/false test that has 60 questions If you guess on each question, and have the same chance of guessing the correct answer on each question, what is the probability you get at least 65% of the questions correct?
Do I need binomial distribution for this as well?

[vale wigeon]

yes

[winter onyx]

Hello, may I get help?

Just practicing since I will have exam on wednesday,

There's no answer key in the book,

May I know if my processes is right

[hollow beacon]

im pretty sure when y = 0, x = 0 not 1?

[vagrant rover]

@vale wigeon Are my inputs correct? And would it be P(X=x) this time?

[alpine sable]

Hi

[vale wigeon]

you want "at least 65%"

[alpine sable]

Is channel free

[hollow beacon]

no

[alpine sable]

K

[vale wigeon]

no, not at the moment.

,calc 60 * 0.65

[ocean seal]

Result:

39

[vagrant rover]

Oh so P(x < or = x) again?

[vale wigeon]

no

at least, not at most

[vagrant rover]

> or equal?

Uh

[hollow beacon]

are you supposed to have that many dp

[alpine sable]

Hi

[vagrant rover]

this one @vale wigeon ?

[winter onyx]

Help

[vale wigeon]

yes @vagrant rover

[vagrant rover]

ty ❤️

You're amazing

[vale wigeon]

also jeez why does everyone, EVERYONE pile up into #help-0

fuck

[hollow beacon]

what about it

[alpine sable]

,rccw

[dull onyx]

hi is this channel still being used

[vale wigeon]

if you have to ask then yes it's still being used

don't use #help-0

[dull onyx]

okay

[dense carbon]

In elimination method of linear equations in two variables, how do we know when to add and when to subtract?

[wild burrow]

How can I find the range of K in this problem

[alpine sable]

with practice you'll eventually notice, but essentially, if you have a +y in the first equation and +y in the second equation, if you add them both, you'll end up with +2y, while if you substract both, you will cancel them both as y-y=0.

similar idea with the adding, if you have on the first eqn -x and on the second one a +x, if you substract both, you'll end up with -2x, while if you add both they will cancel.

[upper pebble]

oops

[upper pebble]

use arctan
tan(theta) = 18.3/34.4
theta = tan^-1(18.3/34.4)
theta = ~28 degrees

180 + 28 = 208 degrees

my earlier explanation was mistaken, sorry about that. i somehow performed the incorrect calculations and still managed to get ~28 degrees when i checked at the time. weird

[proud sentinel]

I am getting some problem with markov's and chebyshev inequality
Can I get help here?

[alpine sable]

A stone is thrown vertically upward. On its way up it passes point A with speed v, and point B, 3.00 m higher than A, with speed v/2. Calculate (a) the speed v and (b) the maximum height reached by the stone above point B.

Is part (b) impossible to solve?

The max height is y'(0)^2/(2g), but we cannot figure out what y'(0) is.

[vague coral]

in general to calculate maximum height, you need to consider that at this point, the velocity is equal to 0

[alpine sable]

Right, I found that the max height is y'(0)^2/(2g)

[alpine sable]

But I can't find y'(0)

let's pause and try to find v first before heading onto the max height.

do you have any ideas?

@alpine sable

[alpine sable]

I found v = 8.85 m/s

I just can't find the max height

okay, wait let me check this before moving to max height.

Okay

[idle bloom]

1
1 2 1
1 2 1 3 1 2 1
1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
Here actually the nth line gives (2^n -1 ) numbers
How did they come up with this solution? My figuring out manually?

[alpine sable]

@idle bloom please read #❓how-to-get-help , this channel is occupied.

[alpine sable]

alright this is good.

so starting off assuming you already have a drawing in your notebook, if not please do.

Yes

what's everything we know about the ball from the point B onwards?

as in what information we have now about the ball from B onwards?

I don't know

well, look at what we just found, what piece of information do we know about the ball on it's journey from B onwards?

Its velocity at B is 8.85/2, and it will eventually decrease to 0 when it reaches the max height then go back to 8.85/2 when it comes back to B on its way down

great.

it's velocity at B is 8.85/2 which is 4.43 approximately.

now, if you notice, we can think of the journey from B onwards as a whole new vertically thrown ball with an initial velocity of 4.43

Oh wait, can we use y'(t)^2 = y'(0)^2 + 2 y''(0) * y(t)

With y'(0)^2 = 4.43^2