help-39

[jolly parrot]

Martin

[frank goblet]

now that is a nicer to solve integral

i personally like this video: https://www.youtube.com/watch?v=Pb6ViPlKcS0

when you get to integration by parts, he also made a cool video

[deep girder]

oh cool

thanks man! that was super helpful!

[frank goblet]

👍

[pearl pond]

@deep girder Has your question been resolved?

[pearl pond]

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[drowsy leaf]

How is this wrong

<@&286206848099549185>

[cedar ember]

I have more than 5000 pings

AHHHHHHHHHHHHHHHHHHHHHH

[drowsy leaf]

help me

<@&286206848099549185>

[cedar ember]

didnt they give su = lr and tu = ln?

wtf u struggling with?

[drowsy leaf]

idk how to order it

[cedar ember]

Proof: SU = LN(Given)
SU = ST + TU AND LR = LN + NR.
SO,
ST + TU = LN + NR[TU = TR, GIVEN]
ST = LN

[drowsy leaf]

Yeah now you have to describe it

[cedar ember]

i messed up the naming

of the ln and nr lol

[cedar ember]

what exactly do you mean describe it? 2 line segments are given to be equal

and each is decomposed into a + b = c

[drowsy leaf]

I have to make a proof

[cedar ember]

and we have a part, b from each to be equal

[drowsy leaf]

its all simple but you have to describe it

[cedar ember]

so if were to get rid of the common the remains would be equal

since b is common in each

we can subtract it from each

and thus get the same

thats the theory part for you

nothing else

[cedar ember]

cool?

[drowsy leaf]

ok so

what is the answer

theres 8

[cedar ember]

wdym?

"2 line segments are given to be equal and they are each formed of another 2 line segments a + b = c, [you write both the linesegment in this format it basically means the lin + blah = blah form}
Since TU = LN, we can take it as common from both the segments and so we get NR =ST

@drowsy leaf

[drowsy leaf]

its writing a proof not answering it

[cedar ember]

bro formulate a proofo based on the information i gave

i gave you what to write

you cant be that reliant on others

💀

🤦‍♂️

[drowsy leaf]

welll

I got it right

.close

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[thin nymph]

find the coordinates of A so that A paritions the segemnt BC in the ratio 5 to 2 if B(-4,-8) AND C(8, 10)

[thin nymph]

i just want to know if I can solve normally, or if I have to take the ratio to account

[versed ledge]

How can you solve normally?

2 Points given , 3rd point is in between those 2 points somewhere

How can you find the point

[thin nymph]

3rd point would be the midpoint right? so x1+x2/2, y1 + y2/2

[versed ledge]

Who said that?

[thin nymph]

my teacher

[versed ledge]

[thin nymph]

well not for this eq

[versed ledge]

Well question doesn't say that A is mid point of BC

[versed ledge]

we are talking about this equation

[thin nymph]

just assumed most of these were the same

[versed ledge]

If the ratio given was 2:2 then you could have assumed it's mid point

[thin nymph]

ok

not really sure how to solve now

[versed ledge]

There's a formula to find such point . If the point is between (x1,y1) and (x2,y2) in the ratio of m:n then
Cordinate= (mx2+nx1)/(m+n) and (my2+ny1)/(m+n)

[thin nymph]

oh ok thank you

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[keen marlin]

Could someone who is familiar with optimization assist me with formulating a linear program?

[tall flint]

!da2a

[pearl pond]

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

@keen marlin Has your question been resolved?

[pearl pond]

@keen marlin Has your question been resolved?

[keen marlin]

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[glossy mango]

what do i do to solve a problem like this?

[plush bramble]

Not enough information

Do you know anything about g

[glossy mango]

i dont think so

btw it says this on the top

[plush bramble]

Well that's absolutely crucial to the question

[glossy mango]

what do i need to know about g? @plush bramble

[plush bramble]

It's a quadratic

Describe a quadratic function

[glossy mango]

It has a y value and an X value

[plush bramble]

No

That's like all functions

Write the general formula for a quadratic

[glossy mango]

F(x)=Ax^2+bx+c

[plush bramble]

Yes

Plug that function into your two pieces of information

(F(0)-F(-3))/(0-(-3)) = ...

You'll get equations in A, b, c

[glossy mango]

Should I put not enough information?

[plush bramble]

What no

[plush bramble]

I started what you should calculate here

[plush bramble]

Do this

[glossy mango]

O ya ok

Thx

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[lunar helm]

Could somebody help me explain this? Idk the shape name and the formula

[next dove]

!original

[pearl pond]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[lunar helm]

Alright

Just number 4

An arbitrary quadrilateral has side dimensions as shown in the following image.

Determine the perimeter of the quadrilateral

[next dove]

your work seems alright

[lunar helm]

But whats the formula tho? I just use the regular square formula

Side²

[next dove]

but it is not a regular shape

[lunar helm]

Wdym by that

[next dove]

the shape given have indefinite proportions

so you can't determine its perimeter by simple formula

[lunar helm]

Ohh

Do i need to use

Fractions?

[next dove]

wait are you talking about the area?

[lunar helm]

Find the keliling

Around

Oh perimeter

[next dove]

well that's what you have successfully found here

[lunar helm]

Oh

So the answer i put is the area

[next dove]

no area is a different thing

[lunar helm]

Oh

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[pastel widget]

can anyone help me out pls

[pastel widget]

i started by rearranging inside the brackets

to get y^5 in the denominator

[pearl pond]

@pastel widget Has your question been resolved?

[pearl pond]

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[versed ledge]

What have you done till now ?

[grave parcel]

@versed ledge

[midnight haven]

The present age of a father is three years more than three times the age of the son. Three years hence, father's age will be 10 years more than twice the age of the son. Determine their present ages.Can anyone help me doing this?

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[versed ledge]

Second one , change into a quadratic equation maybe

Or not , let it be

[grave parcel]

Hmm

[versed ledge]

@grave parcel (c) now

[runic ginkgo]

have you tried logx base y = logx/logy

[grave parcel]

Please this is my ticket stay out

[versed ledge]

No need let it be

[grave parcel]

Wdym

[versed ledge]

Let's come to c first

[grave parcel]

Ok

[versed ledge]

Don't simplify b

[grave parcel]

Yep

Ok let’s do c

[runic ginkgo]

oh sorry for the problem

[versed ledge]

In your b multiply 2 both side first

½ * x * (x+2) = 4
Multiply 2 both side

[versed ledge]

No, there was a ½ . Where did it go?

[grave parcel]

I multiplied it by 2

Cause 0.5 x 2 is 1

[versed ledge]

Then why did you make inside brackets as (2x+4)?

It will remain (x+2)

[grave parcel]

Cause 1/2 x 2 is 1
2 x X is 2x
And 2 x 2 is 4

Right?

[versed ledge]

That 2 is gone while doing 0.5 x 2

[grave parcel]

Ohhh

So what is it then

[versed ledge]

Multiply 2 both side
2 * ½ * x * (x+2) = 4 * 2```

x * (x+2) = 8

[grave parcel]

What is * sorry I’m little confused to this servers symbols

[versed ledge]

Multiplication

[grave parcel]

Ok

So what next

[versed ledge]

I am already using x as a variable, can't use x as multiplication

[grave parcel]

Makes sense

[versed ledge]

x²+2x= 8

[grave parcel]

Make it 0 to the right

Next?

[versed ledge]

Now question is saying make one side as 0

[versed ledge]

Yes

How can you do that?

[grave parcel]

Move the 8 to the left

[versed ledge]

Perfect, do it

[grave parcel]

X = 2 or x = -4

[versed ledge]

Well c is only asking for the equation

d is asking for solution

[grave parcel]

I done d as well

[versed ledge]

Ok as x is base, it can't be negative so we will ignore -4

[grave parcel]

How bout question 7

Is it the same

Basically

[versed ledge]

Yep same

[grave parcel]

Thank you buddy,

🙂

[versed ledge]

No problem

[grave parcel]

Enjoy the rest of your day 🙂

[versed ledge]

You too

[grave parcel]

.close

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[grave parcel]

@versed ledge sorry to ask but can I get help with 8c

Please

[versed ledge]

Sure

[grave parcel]

I did part a and b

Are they right?

[versed ledge]

Let me see

Well you have already solved c also @grave parcel

😅

[grave parcel]

Have I

[versed ledge]

X and X+1 are 2 consecutive numbers

[grave parcel]

lol

Can I get help questions 10 11 12 and 13 please?

[versed ledge]

Sure

Do .reopen

[grave parcel]

.reopen

[versed ledge]

Else this channel will be closed

[pearl pond]

✅

[grave parcel]

Is the length 10+x?

And the width x?

[versed ledge]

For 10 , there are 2 figures .
First one is 10x10 square

[versed ledge]

Correct

[grave parcel]

x(10+x) = 375?

[versed ledge]

Yes should be like that, because out of 475 . 100 belongs to that 10x10 square

So the rectangle part should be 375

[grave parcel]

Ok easy

Let’s do question 11 please

I can do 10 in my own time 🙂

[versed ledge]

There are 2 squares

[grave parcel]

5 * x =24?

[versed ledge]

One with side tm ,other with side 5+x

[versed ledge]

No

[grave parcel]

Yes I see

[versed ledge]

The bigger square area - inner square area = 24

[grave parcel]

Yes

[versed ledge]

So
(5+x)(5+x) - 5x5 = 24

[grave parcel]

Can u explain that please

[versed ledge]

Veranda is

[versed ledge]

This color region

How do you find the area of that color region?
You find total square area then you subtract area of that inner square whose side is 5m

Ohhhh one small mistake I did @grave parcel

Bigger square side will be 5+x+x

[grave parcel]

Isn’t inner square 25

[versed ledge]

Yes area = 25 for inner square

[grave parcel]

Wouldn’t the area of the whole thing be 25 + 24?

[versed ledge]

Correct ,but you need to find x

How can you find that?

[grave parcel]

5 +x+x

[versed ledge]

This red length is (5+x+x)m

[versed ledge]

Correct

[grave parcel]

I’m not sure

[versed ledge]

Find the area of bigger square = (5+x+x)(5+x+x) = 25+24

[grave parcel]

Ye that makes sense

[versed ledge]

Solve that and find x value

It will be a quadratic equation

[grave parcel]

Do I use null factor?

[versed ledge]

Means = 0?

[grave parcel]

Ye

[versed ledge]

You always need to make it = 0 to solve

[grave parcel]

Yep

[versed ledge]

Is this question clear?

[grave parcel]

Idk how to solve it

[versed ledge]

(5+2x)(5+2x) = 49
Do you know (a+b)² formula?

[grave parcel]

Idk that formula

[versed ledge]

(a+b)² = a²+2ab+b²```

[grave parcel]

Oh is it the completing the square formula?

[versed ledge]

(5+2x)(5+2x) is (5+2x)²

[grave parcel]

Yes I know that

[versed ledge]

Then solve this
(5+2x)² = 49

Expand the square, then take 49 to left side

Or, you don't even need to do that @grave parcel

[grave parcel]

Can I do complete the square method

Where I square the 49

[versed ledge]

(5+2x) = √49```
You can proceed like this as well

[versed ledge]

You find a number whose square is 49 actually

[versed ledge]

Yep

[grave parcel]

2x = 7-5

2x = 2

x =2

[versed ledge]

1

Not 2

[grave parcel]

Oops

Or x = -6

[versed ledge]

Nope

[grave parcel]

Why not

[versed ledge]

Remember you need to consider the positive value of x and discard negative value because x is length and length can not be negative

[grave parcel]

Ahhh

[versed ledge]

X is the width of veranda, have you ever heard -5m veranda

[grave parcel]

No lol

So this guys width is 1m?

[versed ledge]

Yep

[grave parcel]

Can we try 12

[versed ledge]

Which one of 12? First is easy just put t = 1.5

Second put h = 3

Try them and let me know which one you are facing difficulty

[grave parcel]

Alr

H = 3.75 at 1.5 sec?

[versed ledge]

I don't have a pen paper but I trust your calculation

[jolly parrot]

Result:

3.75

[versed ledge]

Yeah

[grave parcel]

How do I do b?

[versed ledge]

Put h = 3, it will be a quadratic equation

[grave parcel]

Is b just 1?

[versed ledge]

3 = t(4-t)

[versed ledge]

1 and 3 both I think

[grave parcel]

Yep

Ok how about d

[versed ledge]

When ball is at ground h will become 0

[grave parcel]

T(4-t) = 0?

[versed ledge]

Yep

[grave parcel]

How do I solve it

4t - t^2 = 0

[versed ledge]

T(4-T) = 0 means either T = 0 or (4-T) =0

4-T = 0 , what will be T?

[grave parcel]

T = 4

Cause -t = -4

[versed ledge]

So after 4 sec ball will hit ground

[grave parcel]

Yep

Let’s do question 13 please

[versed ledge]

Same bro , you just need to put the values in equation and solve it

[grave parcel]

Thank you

For all the help!

I have a test on quadratics and probability tomorrow

So I may need some help on probability

But I think I’ll be fine

Tyyy

[versed ledge]

Your welcome

Good luck

[grave parcel]

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[winter leaf]

Good day guys

[winter leaf]

how can I rank faster?

.

[next dove]

erm rank faster in what?

[rough forge]

matrix rank

[pearl pond]

@winter leaf Has your question been resolved?

[cursive wraith]

you can find the kernel instead

and then do dim(E) - dim(ker)

but RREF is a pretty good way too

[pearl pond]

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[tulip steeple]

Can someone tell me how to start solving this question?

[light helm]

start with using conjugates

[tulip steeple]

Thnx

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[knotty geode]

I know the solution is very easy to test and find out, but is there an even more direct way?

[pearl pond]

@knotty geode Has your question been resolved?

[knotty geode]

<@&286206848099549185>

[iron stream]

IG am gm inequality can help

But still,( 22/n)^n , we will have to maximise this

[drifting ivy]

The Max value of (22a-a^2) is 121. It's a parabola whose max value occurs at the highest point. The value of highest point is
-D / 4A where D is discriminant.

[knotty geode]

but it could be made up of even more smaller integers

i found out that the answer is 3^7

by brute forcing of course, but this is a olympiad problem, so there should be a smart solve or smth

[drifting ivy]

3^ 7 is a very big number

[knotty geode]

yeah

[drifting ivy]

Is it right ?

[knotty geode]

for some reason it isn't...

the right answer is 2916

i just looked at it

[drifting ivy]

Maybe

The number of integers is not written, I have taken it as 2.

[knotty geode]

yeah looks like there can be any number of integers

as long as their sum is 22

[drifting ivy]

It's a tricky question. From number theory. At first I didn't seen that number of integers is not specified. I took 2 integers. That's why I got the answer so easily. 😅

[pearl pond]

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[mild tartan]

im on (a)

to find this average rate of change cant i just use slope formula?

no calculus is needed correct?

i get 10 for (a)

ok now (b)

i got the points (20, 300) and (60, 700)

and inputted them to get 10

for (a)

ok anyways

(b)

what interval would give me 0

can it just be one point

i know x = 40 would be 0

oh so multiple

interval

(10, 400) & (50, 400)

ez

now (c)

[40, 60] is the larger rate of change

now (d)

so (d) i got -6.667

but it wants me to explain what the value represents geometrically

do i explain the rate of change?

can i say

the value -6.667 represents the rate of change on the interval [10, 40]

the value $-6.667$ represents the average rate of change on the interval [10, 40]

how to add spaces

there

is that valid for (d)

[jolly parrot]

Devil Wears Prada

[mild tartan]

there

[merry carbon]

I’d think so, or “the gradient of the secant line between [the relevant points]”

[mild tartan]

can i say "the slope of the secant line on the interval [10, 40] is -6.667"

my teacher didnt teach us the word gradient yet so it would be out of place

[merry carbon]

Sure (I just don’t like the word slope personally )

[mild tartan]

all good

thanks for the help

.close

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[fleet orchid]

Hey

[fleet orchid]

I am trying to do a math project where I try to optimize the surface area to volume ratio of a snowman

if I am trying to assume that the top snowball's volume is 5000cm^3,

i find the radius of that snowball and then find the SA and hence the SA:V ratio

what can i do next to find the middle snowball

i was thinking maybe volume of revolution

but im not sure if that would help

[pearl pond]

@fleet orchid Has your question been resolved?

[pearl pond]

@fleet orchid Has your question been resolved?

[pearl pond]

@fleet orchid Has your question been resolved?

[pearl pond]

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[fossil drum]

Ok so for this question I thought the rank was 2 at first but now I think its 1

[fossil drum]

because

ok

so we can see that c1 is a multiple of c2

c3 is a linear combination of c1 and c4

[jade mortar]

do you know that row rank = column rank

[plucky python]

when u say c1, u do mean column 1 right?

how exactly is column 1 a multiple of column 2?

[pearl pond]

@fossil drum Has your question been resolved?

[pearl pond]

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[midnight haven]

hey i am back

[midnight haven]

Q = theta

no

EDA is 100 deg

[cedar bough]

OH

tf

i missed that

[cunning veldt]

What q do they want you to find exactly?

do they mean theta?

ohh mb

didnt read rest of the message sorry

anyways so in that case i think you solve it using the property the sum of any triangles angles is 180
so for the triangle in the middle the third angle EDA has to be 100
so that means the angle ADC is 180 - 100 (since ADC and EDA add up to a 180 line) which is 80

so that means the angle at the very top of the triangle to the right is 180 - 80 -80 = 20

wait i actually havent realy thought about where i should go from here tbh

well we also know that the angle AEB = 180 - 50 = 130

[next dove]

from there angle EAC and angle AEC are equal so AC=EC

also ADC = 80 degrees
so AC=AD too

[midnight haven]

i think theta is 50 deg

[next dove]

no it can't be

[midnight haven]

yes then BAE has to be zero

Ig

[next dove]

yeah

[next dove]

from these you can conclude that BD=AC too

[midnight haven]

AC = AD = BD now it's done

ABD is iso scales

so angle B = 40 deg

amicorrect?

yes

.close

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[native salmon]

Hello

[native salmon]

i needed help

in some questions

[uneven smelt]

but not anymore?

[native salmon]

what

no i need it rn

😭😭

[uneven smelt]

u could let the breadth be x

what would the length be?

[native salmon]

can u solve n show on a paper

[uneven smelt]

no

:(

[native salmon]

☠️

ok

just

tell me

the

final answer please

[uneven smelt]

answer?

no

[uneven smelt]

.

[native salmon]

then

after that

tell me what will be the value of breadth and lenght

??

[uneven smelt]

u let the breadth be x

what would the length be?

[native salmon]

BRO

IF I KNEW IT

WILL I ASK U

TELL ME THAT

[pearl pond]

@native salmon Has your question been resolved?

[pearl pond]

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[summer sky]

hii have i done this correctly?

[plush bramble]

you can plug in your t to the very beginning to check

[summer sky]

oh ye thats true i will have to be sure that i solve it correctly haha

thanks

.close

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[copper stratus]

what even tf is this. never done anything like this

nor been explained it

but its on my homework

[pearl pond]

@copper stratus Has your question been resolved?

[copper stratus]

<@&286206848099549185> can i get some help, i hate to ping but its been a while

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[languid plinth]

i need help with number 4 plz bro

[undone moss]

Note that option a is showing that the slope of MN is equal to the slope of DE. Parallel lines are defined by having equal slopes.

[copper stratus]

i already winged it and got it wrong

i was gonna have a stroke

[languid plinth]

yall both seem smart wanna help me out rq

[languid plinth]

.

please bro

[copper stratus]

what kinda question is that bruh

[languid plinth]

combination or premutation or smth

[copper stratus]

what math class is this for

[languid plinth]

the course is data management if that helps

grade 12 university level idk

[charred lynx]

I dont got you bro 🙏

[copper stratus]

how many soups are there

[languid plinth]

2

[copper stratus]

im ngl

i think its like a big ass number

idk if my way of solving it is right

[languid plinth]

its gonna be massive

cause 18! is really big or 20! depending on how u do it

[plucky meadow]

How many ways can the soups be beside each other?

[copper stratus]

should be 19! right

[languid plinth]

how many total ways can u line up everything if the 2 soups arent allowed to be next to each other

2 rows of 10

18 things that arent soup

[copper stratus]

ok this is the answer i got but it may be wrong

so take this with a grain of salt

[plucky meadow]

Yeah i think you have to count the complement and subtract from the total

[copper stratus]

2,189,611,807,358,976,000

boom

no clue if this is right

[languid plinth]

lemme check if ive gotten that as well at one point

how did u come to that conclusion

[hot stone]

This problem gives me anxiety xD

Looking forward to the solution

[languid plinth]

math avengers pulled up to answer this

all 3 of u

[copper stratus]

combine the 2 soups so now its 19! super block.
19! x 2!
20! - (19!x2!)
Calculate
20!
19!
2!
20! - (19!x2) = 2,432,902,008,176,640,000 -(121,645,100,408,832,000×2) = 2,432,902,008,176,640,000 - 243,290,200,817,664,000 = 2,189,611,807,358,976,000

[charred lynx]

That's what I got too.

[languid plinth]

wdym combine the soups

what does super block mean

[copper stratus]

make a super block

[languid plinth]

a block of soup

[plucky meadow]

Wait but is there 19!x2 ways? there are more than 19 ways to place the block

[languid plinth]

19! ways to place it, x2 because the same thing in reverse order

i think

[copper stratus]

somethin like that, im not that good with factorials tbh

[plucky meadow]

but you could place it vertically for 10 possibilities, horizontally for another 18 ways?

[copper stratus]

@languid plinth is it like something you can submit and see if its right?

[languid plinth]

no

[copper stratus]

hmmm

[plucky meadow]

I got 20!-28x2x18!

[languid plinth]

wanna explain ur thinking

[plucky meadow]

We are trying to complementary count the number of possibilities

So we take the total number and subtract the number where the soup is together

So we count the number where the soup is together

[languid plinth]

i can only see 24 ways the soup can be together

wait no

theres 40

[plucky meadow]

How many ways can the soup be together?

[languid plinth]

40 ways

cause 2 rows of 10

20 ways vertically/horizontially

x2

cause u can flip it

[plucky meadow]

I got 10 ways vertically

and 18 ways horizontally

[languid plinth]

wait i got

10 ways vertically x2

so 20

and then 5 ways horizontally on both rows

which makes 10

x2 cause u can flip it

so 40 ways

[hot stone]

Maybe think of all the ways the 2 soups can't be arranged

[plucky meadow]

There aren't 5 ways horizontally on both rows

there are 9

[languid plinth]

18! i think

[plucky meadow]

the cases can overlap

[languid plinth]

?

no they cant

they have to be beside each other they cant be on top

[hot stone]

Think of the soups as 2 adjacent pieces and then imagine how they would fit as a 2 x 1 block in the buffet

Those possibilities would be the complement of the desired probability

[plucky meadow]

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

1,2 is a block

2,3 is a block

3,4 is a block

and so on

[hot stone]

Yea exactly

There's only so many blocks

From there every other spot would have the same number of possibilities

Identify all 2x1 blocks then sum all those

You'd get the complement of your answer

[languid plinth]

i see 38 possibilities

is the answer 18!x38 u think?

[hot stone]

Then also each block

Actually has a clone

[plucky meadow]

i don't see 38 possibilities

[hot stone]

Where the 2 soups exchange location

[languid plinth]

how many do u see

[plucky meadow]

I see 28*2=56

[hot stone]

18 per row

2 per column

[languid plinth]

i see 56 too

i re counted

[plucky meadow]

so 56*18! right

[hot stone]

No other restrictions on the other dishes?

[languid plinth]

that would be my guess but ima let zedzilla finish cause he seems smart

[languid plinth]

no

none

[hot stone]

I think it makes sense then

Just a permutation from there

[plucky meadow]

Then you would do 20!-56*18!

and you should be done

[hot stone]

Yea!!

[languid plinth]

alr bet thanks guys

appreciate ur existence

.close

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[flat dirge]

How could I draw the second free body diagram (the one that is in the air)? My biggest problems are two, I dont know what to do with the static friction and what happens with the tension at body 2.

[pearl pond]

@flat dirge Has your question been resolved?

[pearl pond]

@flat dirge Has your question been resolved?

[eager pasture]

h

[pearl pond]

@flat dirge Has your question been resolved?

[flat dirge]

.close

[pearl pond]

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[tranquil badger]

alright.......

[tranquil badger]

so

i have a uhm

some new questions to ask

well the same but a diff angle

From my understanding, because of the way that 2 was a multiplicative operation at step 1 that only affected (x+3) and never did anything else, I view it as only an "operation" rather than a number.

Given this understanding, I do not understand how (2+(x+3)) would then convert into (x+5) because if 2 was a multiplicative operation ONLY that cannot be changed no matter what you do then how did it become an addition operation? Factoring shouldnt be able to change that.```

the only way this would all finally make sense

is if 2 in itself i s a number somehow

which doesnt really work because then in situations like

2(x+3) youd have to also add 2

[teal hornet]

is this the answer key or your work?

[tranquil badger]

This is a video I was sent by astro to help me understand how quadratic factoring works.

[teal hornet]

not that it matters but from what I see its legal, since you can treat it as one big parenthesis, and since the (x+3) is a common factor you can just pull it out

and yes the 2 is treated as a number

but a number being multiplied

which was how they were able to pull out the x+3 from the (x+3)^2 and 2(x+3)

once you pull it out it becomes an addition problem

[tranquil badger]

wait...... so because 2 is technically a positive number the refactoring allowed it to become positive 2?

was the ONLY reason it was multiplication because it was next to the (x+3)

[teal hornet]

yea

[tranquil badger]

uhm......

[teal hornet]

() means times

[tranquil badger]

you do realise

how long

it took me to figure that out...

right?

[teal hornet]

wait

what are you saying?

2 is negative?

[tranquil badger]

like weve been at this for like 3 days and im the type of guy to just wake up in the morning eat and then just do math all day

and that was uhm

[feral leaf]

I do not understand how (2+(x+3)) would then convert into (x+5)
You can apply math properties to get that, like commutative and associative property

[tranquil badger]

the SINGULAR point of confusion

that broke everything

[teal hornet]

^

[tranquil badger]

well atleast its over now sob:

hopefully the damn metacognition stops this type of error

ratchet

[teal hornet]

the two could be 100,000 and as long as you pull out (x+3) itll still give you an answer of the same form

[tranquil badger]

i doubt understanding that will be as hard as it was understanding the last part

[tranquil badger]

alr so continuing off of that

so say you had like

2(x+3) as usual

uhm

no no wait

[teal hornet]

IN THIS CASE

you would distribute the 2

[tranquil badger]

2(x+3) = 10

[teal hornet]

oh

then divide by 2

x+3 = 5

and subtract 3

x= 2

or

2x + 6 = 10

[tranquil badger]

pro~1

[teal hornet]

10-6 = 4

2x=4, x =2

you can work it however you want to

which is the beauty of math

[tranquil badger]

Calculations

[tranquil badger]

POV: Techno literally all day

[tranquil badger]

meanwhile brain all day be like:

metaflow

https://tenor.com/view/ohio-made-in-ohio-ohio-final-boss-final-boss-made-in-uwu-gif-27178319

[teal hornet]

im a third year in college if i cant do this I wont surive lol

[tranquil badger]

bro exactly lol

im not in college but i want to do WGU CS coarse

discrete math

and

i did like

terrible

in school when i was young

cuz mentally i was not like

locked in ykwim

[teal hornet]

same

[tranquil badger]

BRO REAL

realism

[teal hornet]

I was a D child in elementary school

now Im keeping a 3.6 GPA as an engineering major

[tranquil badger]

i do online

[teal hornet]

ah

[tranquil badger]

to be fair it doesnt matter like

im still learning it

i just have to catch up

[teal hornet]

true

[tranquil badger]

its just like that costs money so

real

you heard of

WGU?

[teal hornet]

There are a lot of useful properties you should learn about like that guy said earlier

[tranquil badger]

i will look into them

[teal hornet]

have not

[tranquil badger]

i hate how

like

so many times

i just thought like

[teal hornet]

you want to see my homework lol

[tranquil badger]

no literally the first thing

i thought when i got stuck

was

this would all make sense IF

2 could be added

[teal hornet]

go with your gut

[tranquil badger]

like just if i were wrong about how it worked that would be the case

[tranquil badger]

but the problem is

i dont pay enough attention

and bro

some of the HARDEST PROBLEMS

problems MILLIONS OF PEOPLE

had issues solving

i thought of the solution

but just didnt

keep going

like on roblox (i dont play that anymore dont nuke me)

there was this game where

well it was called uhm

your last thoughts at the end of time

and there was a badge called meaning

and like

a 1million+ ppl

and 5 ppl got it

and i was thinking one day

they said "where did i tell you this?" in reference t o something they said

and i was like oh

the map?

and i couldnt find the map

so i gave up on that idea

but it turned out

you literallyy had to type in the chat the map name to get the badge lol

like the game that was referenced off of

that was wild

sorry ik thats off topic

https://media.discordapp.net/attachments/1015759484708208792/1045835008012714017/a_3a6633f55a6525e045c618e50b97782a12.gif

memories tho

well anyways

i vibe

tysm man

[tranquil badger]

by this i mean like alot of the time you have that feeling you just cant... materialize it you dont like its just on the edge of your mind so you dont see it.

shrug

oh well

.close

[pearl pond]

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[teal hornet]

do a lot of practice!

[tranquil badger]

https://media.discordapp.net/attachments/1015759484708208792/1045835008012714017/a_3a6633f55a6525e045c618e50b97782a12.gif

i will

https://tenor.com/view/death-note-near-rage-anime-think-gif-22182706

[pearl pond]

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[ionic lantern]

I need help finishing the first problem and 2nd, not sure what to do next or how to graph it and how to identify the solution

[pearl pond]

@ionic lantern Has your question been resolved?

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[knotty geode]

what rigorous method can be used here, instead of guessing until you get the answer?

[lime river]

Hmm can't think of a rigorous method but the guessing process can be made more efficient with the help of fermats two square theorem

[knotty geode]

can you demonstrate?

[lime river]

Wdym demonstrate?

[knotty geode]

i mean like show the fermats two square theorem

[lime river]

https://artofproblemsolving.com/wiki/index.php/Fermat's_Two_Squares_Theorem

[knotty geode]

thanks

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[cerulean smelt]

The cosine and sine law method for calculating the sum of displacement vectors can only be used for two vectors at a time

is this true or false

[cerulean smelt]

my guess is true

[pearl pond]

@cerulean smelt Has your question been resolved?

[cerulean smelt]

<@&286206848099549185>

[midnight haven]

?

wht happen

[cerulean smelt]

.

[midnight haven]

true

cuz only a and b r there no in formula

[cerulean smelt]

thank you

.close

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[thick wagon]

why you cant use the disk method of integration for surface area but you can for volume of sphere?

[tight copper]

I assume it doesn't work since you can't approximate segments of a function that aren't horizontal with other horizontal segments, so the disk method can't compute the surface area. You could just use the surface area integral if you want to calculate surface area.

[thick wagon]

I am not sure if i understand this: you can't approximate segments of a function that aren't horizontal with other horizontal segments. And what is surface area integral

[pearl pond]

@thick wagon Has your question been resolved?

[pearl pond]

@thick wagon Has your question been resolved?

[pearl pond]

@thick wagon Has your question been resolved?

[pearl pond]

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[dusk otter]

I would like some opinions on the structure of my answers for some discrete math questions.

[dusk otter]

There are like proofs but I was confused on how to structure them, because they are more like checking if * fufills, not actually proving some specifically

[plucky python]

i'm assuming ur at uni? anyway if so i think you don't have to write stuff out fully when it's obvious

like it's really obvious here that a * b is a real number

so i would just say closure is obvious

similarly, you've done quite a few steps to show that g * h = (g+h)^3

at uni like it's fine to just say "notice that g * h = (g+h)^3"

obviosly when ur attempting the question u'd want to do those steps to realise that g * h = (g + h)^3

but what u do in ur working and what u eventually write up in a proof are different

[plucky python]

yeah actually like when you check associativity is a good example

i would do all the steps u've done there to work out "is * gonna be associative or not"

once i've realised * is not associative, i'd find my counterxample

g=h=2, i=0 and just go

"observe that $(2*2)*0 = 64^3 \neq 1000 = 2 * (2 * 0)$"

[jolly parrot]

LY

[plucky python]

so like the full thing i write would b

b). Observe that $(2*2)0 = 64^3 \neq 1000 = 2 * (2 * 0)$ so $$ is not associative.

[jolly parrot]

LY

[dusk otter]

Yes I am at uni.

[dusk otter]

Somaybe I should elimintate the part when I am actually explaining about what closure is?

because that is obvious to us

[plucky python]

yes

so like just a). Closure is immediate

[dusk otter]

Okay this makes sense

[plucky python]

yeah that's fine

[dusk otter]

great thank you! I think perhaps for c), d) and e) they are okay as well

My prof usually likes a tad more detail than normal

[plucky python]

ah fair

[plucky python]

i didn't read those, i only read a and b but i hope that gave some indication of what's expected

[dusk otter]

Yes it did, thank you!

[plucky python]

yeah looks fine

[dusk otter]

Great thanks! Also Idk if you have any experience with permutations and cyclic notation but did I isolate this correctly?

[pearl pond]

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[plucky python]

what is the original q?

[pearl pond]

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[dusk otter]

Oh right! Will send it

[pearl pond]

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[fluid axle]

the end result is correct, your working is a bit weird tho

on one side it seems like your multiplying by st on the left (to cancel (st)^-1)

but on the other side you multiply on the right

maybe it's just your way of writing & you're fine w/ it

it's a bit confusing for an outsider nonetheless

@dusk otter

you can still simplify a bit tho

focusing on the (w p^-1)^-1 part

[plucky python]

be careful with ur working

S8 is not an abelian group

[pearl pond]

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[plucky python]

so multiplying on the left vs right matters a lot

[plucky python]

also ^

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[brittle onyx]

Is b right?

[pearl pond]

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[brittle onyx]

<@&286206848099549185>

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[terse tide]

i didnt understand how you did it, but its correct

however, its 0.325m above the board

they asked for the max height reached, that makes it 5.325 m

[terse tide]

and c) is also correct, nice

[terse tide]

side note.. the angle at which she enters the water is not the same as the initial/diving angle

dont label them both theta!

its because theyre not at the same height/level, initial is at y=5 and final is at y=0

for fun, compute the y-velocity of when the diver is again at level y=5 (after reaching the max height / on the way down)

and deduce that the angle at that instant is equal to the initial angle!

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[brittle onyx]

Ok thx I understand

.close

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[void gulch]

does |||x-7|-5|-2|>=2 include 2 and 12?

[void gulch]

I was graphing it and it looks like this

however when i use the bulit in inequalities it looks like this

does that mean that 2 and 12 are not solutions or am i missing something

[light helm]

probably some error with how its coded.

[woven garnet]

I think so too

2 and 12 are solutions

[void gulch]

great!

you know what

im stupid i can just plug it back in

yeah so 2>=2

ok problem solved

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[void gulch]

.close

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[rapid bough]

How do I know if a product of finitely generated abelian groups is cyclic by looking at the order of the groups?

[rapid bough]

Is it simply when the orders of the groups are coprime?

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[cinder flower]

is the finitely generated abelian hypothesis is even needed here? i think in general, a product of (2, and thus of finitely many) groups is cyclic iff both are cyclic and have relatively prime orders

or even countably many

[rapid bough]

Oh alright, I thought so I just wanted to make sure. I included that because that was context needed for the problem at large rather than just this portion, but thank you

[cinder flower]

makes sense

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[stuck widget]

not a math question but rather need help understanding a question

[stuck widget]

what does it mean saying the dipole moment is all orientated in the direction of the electric field

??

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[brisk lichen]

Is the factor form of y=3cos²x-cos x-6

[brisk lichen]

not $y=(cosx-\frac{-(1+\sqrt73)}{6})(cosx-\frac{(1+\sqrt73)}{6})$?

[jolly parrot]

jj

[brisk lichen]

I redid my quadratic formula multiple times and couldnt spot what i did wrong. I even graphed it on desmos to compare both the original and simplified equation(all in radian), they matched except for the factored form... Someone please help me, idk what am I missing here or, am not supposed to do that like a normal quadratic equation?

[signal atlas]

Quadratic equation gives the roots but you still need the correct scaling to get it to match

[brisk lichen]

like this?

[signal atlas]

If u expand that you will get 36cos^2x but that is the general idea yes

[brisk lichen]

still doesnt match tho

[signal atlas]

I was saying you know this is incorrect BECAUSE you get 36 in front of cos^2x instead of 3. You should see a 3cos^2x upon expanding. Originally you only got cos^2x (coefficient of 1)

Also remember a polynomial can be expressed in this form:

p(x)=a(x-b)(x-c)(x-d)…

A quadratic specifically would be q(x)=a(x-b)(x-c)