help-19

[marble vale]

let me think

we have to add a -2 somewhere in the identity matrix, like in the first or second row but i dont know where

you said Row2 - 2*Row1, so it's

$\begin{bmatrix}
1 & 0 & 0 & 0 \
-2 & 1 & 0 & 0 \
0 & 0 & 1 & 0 \
0 & 0 & 0 & 1 \
\end{bmatrix}$

@low locust

[clever fjord]

lilisworld

[low locust]

yes

[marble vale]

ok thanks

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[stray blaze]

Hi there

[stray blaze]

20 a) answer is 0 while b) answer is 1 correct?

[upbeat drum]

ye

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[rapid kestrel]

Is either one of these more correct?

[low locust]

no. same thing

[rapid kestrel]

Thanks

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[storm ruin]

It's a related rates problem, I do chain rule and get 1/2(2x+1)^-1/2 * 2, I don't know if this is correct. Please help

[storm ruin]

I know the answer to a is 1, I don't know how to get there tho

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[winged abyss]

i have system of equations:
2x + 3y - z = -2
3x + 2y + 4z = £

i have to indicate whether it will have exactly one solution, no solution or it will be homogeneous depending on the £ parameter

[winged abyss]

no clue how to do it

i did matrix in the reduced form already

[odd edge]

Show your work, and if possible, explain where you are stuck.

[winged abyss]

in the end i have the solutions depended on the z

and £

is there such an £ that there will be only and exactly 1 solution for this equations?

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[frosty gorge]

Hi

[frosty gorge]

For part b I get a different answer. Here’s my working and the textbook answer:

Can anyone see where I’ve gone wrong? I don’t understand where they got the t basic solution

X5 is a leading 1 but it’s x5 = 0 so surely if anything it would be t * 0 vector

[void yew]

Well

At the very beginning

On the third line 4th column

5th

U wrote a 1 instead of a 3

[frosty gorge]

Oh 😔

Thanks

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@thick jay Has your question been resolved?

[thick jay]

<@&286206848099549185>

[cold viper]

Hi. First off your penmanship is amazing

I’m not a helper but I can help with this question. Is that ok?

[thick jay]

Thank you! Any help is appreciated very much!

[cold viper]

A and b are good

C is just asking for the equation of any house to the cell tower. So what variables do you need to know in order to find the slope of the line you just drew?

Because the line is linear your equation mx + b

What does m represent?
What does x represent
What does B represent

[small dew]

Why are you asking for a slope?

[thick jay]

Wouldn’t I need to use the distance formula?

[small dew]

Yes I think so

[cold viper]

Oh crap I see now

Yea the slope is constant

I’m so sorry

[thick jay]

No problem!

How should I go about solving?

[cold viper]

Thank u so much I just wanted to help so thank u for forgiving me

[small dew]

Say something similar to question 2. e=distance east of the cell phone tower and n=distance north of the cell phone tower. e^2+n^2=(distance)^2, then sqrt(e^2+n^2)=distance

[cold viper]

I’ll try to be more careful from now on

[small dew]

Please ping me if you have response

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[pine sorrel]

find the smallest positive value of x for which y=0, y=3+6sin(3x)

[pine sorrel]

ans say x=70 deg

how

?

[halcyon hill]

put y = 0 and try and solve it but i assumes you did that already

it becomes 3 + 6sin(3x) = 0

[pine sorrel]

yes

sin 3x = 1/2

then basic angle is 30

[mystic saffron]

3x = the basic angle

you will still have to solve for the x

i think

[lean vortex]

sin 3x = -1/2

[pine sorrel]

yes

i do know how to get that

but how do i get to the answer

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@pine sorrel Has your question been resolved?

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@pine sorrel Has your question been resolved?

[drifting valley]

3+6sin(3x) = 0
sin(3x) = -1/2
and you're looking for the smallest x > 0 such that it's true
you have to be in third quadrant, and by knowing your trig angles well, you know it's then 3x = 210 degrees

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[pure yoke]

How to do this

[viscid flint]

what's the equation for P(x), the profit associated with making and selling x units?

[pure yoke]

is that the demand function? so -1.5x+250

Actually nevermind profit is Revenue-Cost so it should be -1.5x^2+25x-(.03x^3-4.5x^2+224x+250) I think

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[fringe trout]

So I'm at the part where I have to prove that n=k+1 is true

[robust pollen]

show ur steps

[fringe trout]

sure

[fringe trout]

step one is just showing n=1 is true and step 2 is assume n=k

[robust pollen]

Next time write a line, 'a belongs to positive integers'

[fringe trout]

right ok

[robust pollen]

and ur def not going to do that

what interesting about divisibility, is that u need to change the subject in ur assumption

most likely

[fringe trout]

oh

what do you mean by that?

[robust pollen]

so ur assumption is: k^3 + 2k = 3M, where M belongs to positive integers

what u want to do and need to do, is to change the subject

[fringe trout]

right

[robust pollen]

k^3 = 3M - 2k

[fringe trout]

OHHHH

righttt

I forgot about that

[robust pollen]

lol

[fringe trout]

thank you

[robust pollen]

np

[fringe trout]

no

[robust pollen]

umm...

[fringe trout]

it's proof by induction

[robust pollen]

Let me ask u someth'in

Do u know how to do a simple induction

1 + 2 + 3 + .... + n = n(n+1)/2

U know u need LHS and RHS to prove right, jonnyboy

[fringe trout]

yes

I know how to do that

[robust pollen]

Use LHS and RHS to do

doin't do like this

[fringe trout]

hahaha ok

[robust pollen]

Do u know what format does LHS need to be?

[fringe trout]

(n+1)(n+2)/2

is that what you mean

[lime root]

bro what the hell i read the question this is so simple with induction

[robust pollen]

???

ys and idk why he need to struggle that long

[fringe trout]

lol

[robust pollen]

I mean ref to ur question

do u know what u need get from LHS

the format

I need to ensure that u didn't miss any basic concept

[lime root]

$k^3 + 3k^2 + 3k + 1 + 2k + 2 = (k^3+2k) + 3k^2 + 3k + 3$

[clever fjord]

nalin

[lime root]

use your inductive step for k^3 + 2k

done

2 lines

lmfao

[robust pollen]

Bruh

why u saying the answer

u should lead him and not telling him the correct answer immediately

[fringe trout]

yeah I use n=k

[fringe trout]

I already got it

[robust pollen]

and I think u still didn't get the main concept...

whatever

[fringe trout]

sorry I don't get what you mean by the question

[robust pollen]

Like this question

[fringe trout]

by the format

yeah

like the concluding statement?

[robust pollen]

U know you need to have a format of 3Q, where Q belongs to positive integers, right?

[fringe trout]

yes

[robust pollen]

gd

[fringe trout]

I got 3(a+k+k^2+1)

I substituted 3a-2k for k^3

[robust pollen]

yup

[fringe trout]

right ok

[fringe trout]

thank u once again

[robust pollen]

np

[fringe trout]

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[spark monolith]

Hi! I need a video, or simply a name / formula / vague direction that would help me to solve a problem. I am looking for a formula of a surface area after revolution around an axis, but "curved". Ie. I do not want it to simply rotate around an axis (and therefore follow a shape of a circle while doing so), but follow a shape of a slinky. (A visualization below). I want it to calculate the minimum area of a catenoid, but on the shape of a slinky. Pictures below

[mystic saffron]

MFW there is no picture below:

[spark monolith]

I hope it is more clear now. I just wanted to find a better picture of soap film, but this one represents it best

[spark monolith]

Any ideas? 🙂

[mystic saffron]

I was just reporting that there wasn't any picture for the sake of other helpers

I don't know nearly enough calculus to calculate the surface area of this shape

[spark monolith]

<@&286206848099549185>

[weak stag]

What bruh

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[undone prawn]

I need help solving and understanding the steps to solve these. I'm supposed to use the substitution method and figure out X and Y

[undone prawn]

I've been trying to watch videos but they just speedrun it and get the answers in an instant and when i see the same question but different numbers my brain just melt, please explain it as simply as possible

on the first image, I think it's adding 2x on -2x so y = 5

but that's all i know

[chilly moss]

well

-2x+y = 5

x+2y = 5

there are 3 ways to solve this (usually)

[tight crescent]

Do you know what solving by substitution means?

[undone prawn]

I'm just roughly translating it from swedish

[chilly moss]

ok

[undone prawn]

But it's through subtracting and dividing

[chilly moss]

is that means we are using something like y = 2x + 5?

can you write down the swedish here

[ocean orbit]

Hi, so since 2 equations are given we can use one to find a temporary value for x or y thats your choice. then we can input the temporary value into the second equation to find the answer

do you need more step by step help?

[tight crescent]

That's solving by substitution^

[undone prawn]

yes please

like i'm genuinely dumb at math so please explain like i'm newborn 💀

[ocean orbit]

Alright so we've got

1. -2x + y = 5
2. x + 2y = 5

Solving using substitution would be,

lets consider the 1st eq.

-2x + y = 5
y = 5 + 2x (1)

Now that we have the value of y we can put this into the second equation to give us:

x + 2(5 + 2x) =5

x + 10 + 4x = 5

5x = 5 - 10

x = -1

now that we have the value of x we can return to (1) to find y

y = 5 + 2(-1)

y=3

replicate this proceedure for the 2nd question

[undone prawn]

i'm a little confused at this part:

y = 5 + 2(-1)

y=3

i know that the 2 is negative but what about the (-1)?

[ocean orbit]

2(-1) = -2

5 + (-2)

5 - 2 = 3

[undone prawn]

oh, sorry

[ocean orbit]

no worries

[undone prawn]

x = 3y - 2
x + y = 6

Am i supposed to make it

y = 3x - 2
x + y = 6?

or is it y = x + 6

[odd edge]

@undone prawn Has your question been resolved?

[undone prawn]

@ocean orbit is there a specific way i'm supposed to solve show what Y equals to?

refering to the question above

[ocean orbit]

theres no "specific" way, i guess that would be how your teacher did it in class. what grade are you in btw

[ocean orbit]

x + y = 6

y = 6 - x

[undone prawn]

i'm on my last year of high school

[undone prawn]

wait what

[ocean orbit]

look at it this way
let x be 2 and y be 4

2 + 4 = 6

2 = 6 - 4

[mystic saffron]

well in subsitution method u try to bring only one variable on the left hand side and try to get the other variables on right hand side

and make sure the variable on left hand side has coefficient

as

1

after u do this step

substitute that equation in the another equation

like lets say u have ur equations as
x-y=6
x+3y=2

so now u can start with any equation ill choose x-y=6

so ill try to get in terms of x

so ill get
x-y=6
x=6+y

now i got the value of x in terms of y

ill substitute this value in the other equation which is
x+3y=2
after substitution ill get
6+y+3y=2

4y=-4

y=-1

i got my y value

now i can get x value

substitute y value in any equation

ill choose

x-y=6

so
x-(-1)=6

x+1=6

x=5

this is how u use substituion

and solve

[undone prawn]

so it really doesn't matter what equation you start and end with?

[ocean orbit]

no it doesnt, just use the first one for convenience

[mystic saffron]

yep

u can start with any

[undone prawn]

oh my god so i was overthinking that this entire time

[mystic saffron]

ill tell u a trick always go for the equation that u think looks easier

[undone prawn]

which in this case is x + y = 6

[mystic saffron]

ya

it was easy for me here to represent one variable in terms of other

[undone prawn]

thank you so much!

[mystic saffron]

no probs

this was tbh secondary highschool maths

and its an important basic u need to know

just to get a good hold over this

practice as much as u can

u got the steps

just be calm n solve slowly

[undone prawn]

i'll make sure to practice this

thank you guys again

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[merry harness]

I am unsure how the memo came to the conclusion that dy/dx = 4 or why they use y-1 = 4(x-2)

[merry harness]

I understand everything up until the blue line

[long tinsel]

they found the derivative at the required point

that's where dy/dx = 4 comes in

The line after that is simply the point slope form of a line

[merry harness]

Oooh my soul thank you

[clever fjord]

NEON

[merry harness]

I see now

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[unborn osprey]

Anyone got any idea how to do this question?

[unborn osprey]

Pls ping if you have any ideas

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[feral adder]

https://i.imgur.com/E7CzXkX.png

[feral adder]

https://i.imgur.com/l9rqqhK.png

for ∂h/∂x = a(t)

if i plug a(t) in for ∂h/∂x

do i need to take into account the square

as in would the derivative be different since i would have to apply the chain rule

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!close

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[civic wren]

Is the answer for 7a 0?

[plain lagoon]

!show

[odd edge]

Show your work, and if possible, explain where you are stuck.

[plain lagoon]

I don't think it's 0 tho.

[civic wren]

Where did i get it wrong?

[plain lagoon]

why is
1 - a(-1) = 1 ?

and what is lim x -> 1+ x ?

[civic wren]

Can you show me how to solve it?

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[mystic saffron]

Hey, I am solving exercises from my calculus I book and this question is from rolle theorem part:
need help with the following:
$y=x^{3}+3x^{2}+16$
show that there is exactly one real root value of x

[clever fjord]

someonee

[snow marten]

find y'

and find the critical points

[mystic saffron]

0,16 & -2,20

from there i realise that between (-inf,-2) the function is increasing between -2,0 decreasing and 0,inf increasing

but how does that prove there is one root?

[snow marten]

try sketching y

then youre gona see

[mystic saffron]

i cant though

can you help

[snow marten]

ok

[mystic saffron]

so from the tings i explained

things*

the derrivative of the function is 0 at x=-2,0

and +,-,+ respectively between

that means it comes to critical points on 0 and -2 but increase and decrease in between.How to prove from that?

[mystic saffron]

oh lol

my brain froze i guess

you need to evalute y and connect

ty

.reopen

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[summer hazel]

Is this correct?

[long tinsel]

change the limits

[summer hazel]

I plan to put t back to its og form

Thats works too right?

[long tinsel]

I mean sure but its just faster to do it this way

Whatever suits you

$\int_0^1 \frac{1 - x}{1 + x} \cdot \frac{\dd{x}}{\sqrt{x^3 + x^2 + x^}}$

[clever fjord]

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

[summer hazel]

oh i se

[long tinsel]

Good luck doing that for something like this

[summer hazel]

yea

tbh id just change the limits

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[junior ether]

$f'(x)=(4-x)x^{-3}$

[clever fjord]

Jash

[junior ether]

im trying to find if x=0 is a relative minimum or relative maximum or neither
but if i use second derivative test f''(0) is undefined

(the domain of f is all real numbers)

[wooden python]

are you sure the domain of f is R

[junior ether]

its given in the problem

[wooden python]

it sure does not look that way

!original

[odd edge]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[junior ether]

BRUH IT SAYS X>0

[wooden python]

exactly.

[junior ether]

ty

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[night tree]

for the graph on the left, I don't think I've made the adjacency matrix on the right properly. Could I get some help?

[night tree]

or it could be correct, I'm not too sure

I think it's correct, actually

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[night tree]

.reopen

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✅

[night tree]

and I don't quite understand what it means by determining the number of paths of length 3 from v1 to v4

[wooden python]

yes it is asking you to multiply 3 copies of A together

[wooden python]

which part of "determine the number of paths of length 3 from v1 to v4" is unclear to you?

[night tree]

To be honest, the whole thing. but specifically I don't know what the length of a path is, but I am assuming the paths are the edges connecting the vertices?

[wooden python]

a path is a sequence of vertices in which there is an edge from each vertex to the next (except for the last)

the length of a path is the number of edges in it

[night tree]

ah ok, so for example would the answer for the number of paths of length 3 from v1 to v4 be 2? One that I am thinking of is v1 to v1, then v1 to v2, then v2 to v4

[wooden python]

why 2?

v1-v1-v2-v4 is one such path yes

what's the other one?

and how do you know there are no others?

[night tree]

Another I was thinking of was v1 to v4, v4 to v2, then v2 back to v4

[wooden python]

and do you know for sure no others exist?

you need to count them after all.

[night tree]

I dont think so because v1 only has 3 edges out from it, 2 of them can have length 3 when reaching v4 (the 2 that I mentioned) and if it takes the edge v1 - v2, it will not be able to reach v4 by being length 3

thats my thought process for it, I dont know if its correct

[wooden python]

i think it is futile to try and count them this way

there's a reason why they have you calculate A^3, you know?

the count that you want will be the entry at position (1, 4) in A^3.

[night tree]

ah ok, I did not know that 😂 the textbooks explanations have not really been too clear to me, so I've been trying to understand it the best I can

so to count the number of paths of length 3 from v2 to v3, I would find it at (2,3) of A^3?

[wooden python]

yes

[night tree]

alright, thanks!

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[wary berry]

can anyone help with this

do I get it to be x^2/20 = y? then what?

[reef sandal]

Couple ways

If you have a quadratic equation, f(x) + ax^2 + bx + c, then the vertex, (h,k) is simply (h, k) = (-b/2a, f(h))

In your case, y = f(x) = 1/20 x^2 + 0x + 0

[wary berry]

Ohhh

not really sure how to do that honestly

x coord makes sense, idk what f(h) is

[reef sandal]

Just plug whatever you got into h into f(x)

[wary berry]

0 I believe?

so okay that makes sense I guess

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[feral adder]

https://i.imgur.com/rR7TQgc.png

[feral adder]

is it legal to rewrite the first integral to the integrals below

[royal herald]

Is that d[a(t)]

Also what’d u even do to go from step 1 to 2

[feral adder]

yes

[feral adder]

solving it by separation of variables

so i put the - with the dt

[royal herald]

$\frac {da}{dt} = \frac {-2a^3}{1+a^2}$

[clever fjord]

Stephen

[royal herald]

$\int da(1 + a^2) = \int dt(-2a^3)$

[clever fjord]

Stephen

[royal herald]

Is this what u were looking for

[feral adder]

was just wondering if ur allowed to rewrite this integral to this

(ignore - sign)

[royal herald]

Right but tell me how u separated those variables

And where did the x come from

[feral adder]

oh typo

x=a

[royal herald]

Ok

I think I see what u did

But it’s incorrect

Fractions can only be split like that in the numerator

[feral adder]

https://i.imgur.com/AveVbNg.png

[royal herald]

$\frac {-2a^3}{(1+a^2)} \neq \frac 1{2x} - \frac 1 {2x^3}$

[clever fjord]

Stephen

[feral adder]

ye but this is the same isnt it?

[royal herald]

Notice how the 1+x^2 is in the numerator

$\frac {a+b}{c} = \frac ac + \frac bc$

[clever fjord]

Stephen

[feral adder]

oh oops

lol

messed up basic math

[royal herald]

$\frac {a+b}{c} \neq \frac ca + \frac cb$

[clever fjord]

Stephen

[feral adder]

.close

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[feral adder]

.reopen

[odd edge]

✅

[feral adder]

nvm i made a mess and meant something else

my original integral is (1+a^2)/(2a^3)

[odd edge]

@feral adder Has your question been resolved?

[feral adder]

.close

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[eternal cove]

Where did 49.22 come from

[tepid yacht]

Plug in 3 for t

[eternal cove]

Like this?

[tepid yacht]

Yes

[eternal cove]

Okay thanks

Tys.

Tysm

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[weary pelican]

!status

[odd edge]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[weary pelican]

simplify the square roots first

notably sqrt(18) and sqrt(50)

[olive meadow]

would (2√2 * 5)/2 = 10√2 be correct

[weary pelican]

for which part? the final result?

[olive meadow]

yes

[weary pelican]

uh

[weary pelican]

a is not 10 here

unless you were talking about 2sqrt(50) maybe?

[olive meadow]

yes

[olive meadow]

a being 2sqrt(50)

[weary pelican]

2sqrt(50) = 10sqrt(2) ok yes

what about 12/sqrt(18)

[olive meadow]

(26√2 - 2√2 + √2)/2 = 25√2/2 = 12.5√2 is this correct now?

[weary pelican]

why is everything divided by 2?

what did you find for 12/sqrt(18)?

[odd edge]

@olive meadow Has your question been resolved?

[odd edge]

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[balmy isle]

4cos^2 (2x+1) sin (x/3) = 0, how do I get started on this question and how do I solve this?

[balmy isle]

question number 2 on this page

trying to do 2-12

dont really understand

[dreamy yacht]

The product becomes 0 when one of the factors becomes 0

[balmy isle]

huh

oh

okay

[balmy isle]

i dont understand the steps to get to the answer

in general

i was absent during class

and im already behind on alot of work

my teacher a bully she dont wanna help

can you walk me through it?

if possible

[dreamy yacht]

Do you understand what I meant with my first hint?

[balmy isle]

not really no

😭

life is hard

[dreamy yacht]

Let's say we have ab = 0. For real numbers a and b this means that either a or b have to be 0

Ok?

[balmy isle]

yes

that makes sense yeah

[dreamy yacht]

So here if the whole product becomes 0 then either cos(2x+1) = 0 or sin (x/3) = 0

Ok?

[balmy isle]

okay

yeah

[dreamy yacht]

So when is sin (x/3) = 0?

[balmy isle]

uh

when x is 0

sin (x/3) = 0

so

x = 0??

[dreamy yacht]

Yes, but that is not the only solution

[balmy isle]

how do i get the other solutions

am i just slow

😭

[dreamy yacht]

Because sin is periodic

[balmy isle]

ye

wouldnt that mean theres an infinite number of answers?

[dreamy yacht]

It takes some time to get use to "how the sin function looks" but sin x is 0, when x = k*pi for k in Z

[dreamy yacht]

Yes

So x/3 = k*pi

What's x then?

[balmy isle]

3kπ

when x=3npi,nez

but isn't cos(2x+1) = cosx =-1/2

[dreamy yacht]

Yes 🙂

[balmy isle]

no i mean it'd be cos2x + cosx = cos^2x-sin^2x+cosx😭

i dont get this

😭

[dreamy yacht]

What? Where is this from?

[balmy isle]

the full thing right

wait im tripping

dont mind that

[balmy isle]

what happens after?

answer key that doesnt provide steps says the answer is : .0285, 1.86, 3.43 and 5.00..

i dont know how to get there 😭

[dreamy yacht]

You should have mentioned 0 < x < 2pi

[balmy isle]

oh

shit

i sent the image late

my bad

[dreamy yacht]

We only did take a look at the second term providing us with a solution. Now we have to repeat the same with the first one

[balmy isle]

okay

so

what would that look like

i learn really good with visuals

so

im trying hard rn

😭

[dreamy yacht]

When is cos a = 0 for a in [0,2pi]?

[balmy isle]

pi/2 , 3pi/2

i think

[dreamy yacht]

There's something odd with the answers from the answer key. 0 should be an answer, too.

[balmy isle]

0 is a given

tho

it says it there

and we already solved that opart

so

i didnt turn it in

i mean

send it

[dreamy yacht]

And I don't think 5 is an valid answer

[balmy isle]

okay

[dreamy yacht]

,calc 4*cos(10+1)cos(10+1) sin (5/3)

[clever fjord]

Result:

7.7987437024063e-5

[dreamy yacht]

Ah, apparently it is close enough to an valid answer and they just rounded it

Anyways, let's continue

[dreamy yacht]

Yes, very good !

So basically pi/2 + k*pi

So how would you proceed from here?

[balmy isle]

uh

i dont

know

😭

[dreamy yacht]

Just do as we did before; We know if cos a = 0 then a = pi/2 + k*pi

[balmy isle]

you do cos inverse pi/2 plus k*pi

or is it cast determine it'll be quad 1 and 4

[dreamy yacht]

No

[balmy isle]

😭

neither

?

😭

[dreamy yacht]

We want to do 2x+1 = pi/2 + k*pi

What's x then?

[balmy isle]

so x=pi/4-1+k*pi?

[dreamy yacht]

k/2*pi I think

So now we just need to plug in the values

[balmy isle]

huh

[balmy isle]

wait

what

how

if its possible could you write it on paper

[dreamy yacht]

x=pi/4-1+k/2*pi?

[balmy isle]

its hard to explain

😭

or understand

without visual

[dreamy yacht]

Because you need to devide everything on the right side

[balmy isle]

could you

write it on paper

possibly

please

[dreamy yacht]

,calc pi/4-1+1/2*pi?

[clever fjord]

The following error occured while calculating:
Error: Unexpected end of expression (char 15)

[balmy isle]

wha

[dreamy yacht]

There is some mistake

[balmy isle]

,calc pi/4-1+1/2*pi

[clever fjord]

Result:

1.3561944901923

[balmy isle]

you added tehq uestion mark

do you think you could do this on paper

jus asking again

[dreamy yacht]

Ah, okay. There was another mistake

So 2x+1 = pi/2 + kpi

2x = pi/2 + k*pi -1

Now we have to devide everything by 2

x = pi/4 + k/2*pi -1/2

Now we should be able to plug in different values for k

;calc pi/2 + 1*pi -1

,calc pi/2 + 1*pi -1

[clever fjord]

Result:

3.7123889803847

[dreamy yacht]

Wrong formula, lol

[balmy isle]

wha

[dreamy yacht]

,calc pi/4 + 1/2*pi -1/2

[clever fjord]

Result:

1.8561944901923

[dreamy yacht]

Finally

So for k = 1 we get our first solution. Okay?

[dreamy yacht]

.

[balmy isle]

okay

[dreamy yacht]

So now we can plug in k=2. Can you do this?

And k = 3

[balmy isle]

yes

thats it

really

,calc pi/4 + 2/2*pi -1/2

[clever fjord]

Result:

3.4269908169872

[dreamy yacht]

Yes 🙂

And k = 3?

[balmy isle]

,calc pi/4 + 3/2*pi -1/2

[clever fjord]

Result:

4.9977871437821

[dreamy yacht]

And that's another two solutuions !

[balmy isle]

and if i plug in k = 4 the solution is > 2pi

right

which isnt allowed

[dreamy yacht]

So now we are still missing one solution ! Do you know what still needs to be done?

[dreamy yacht]

Exactly !

[balmy isle]

no

what

isnt that it

what other solution

am i trippin

what do i do

[dreamy yacht]

We forget that k = 0 is also a possibility 🙂

[balmy isle]

,calc pi/4 + 0/2*pi -1/2

[clever fjord]

Result:

0.28539816339745

[balmy isle]

pff

im dumb

[dreamy yacht]

xd

[balmy isle]

thank you

alot

[dreamy yacht]

You're welcome

[dreamy yacht]

Maybe if I sum up what we did will help you:

1. We figured out that if the whole product is 0 then either cos(2x+1) = 0 or sin(x/3)
2. We looked when cos a = 0 => a = pi/2 + k*pi
3. Then we set 2x+1 = pi/2 + k*pi and solved for x
4. We plugged in values for k to get our solutions
5. We basically did the same for sin(x/3)

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[mystic saffron]

need some help with stats

[mystic saffron]

also i want to know how u can figure out if this is a left or right tail test. i get how to figure that out when it's a single mean but when it's two population means how do you know which one is right or left

[mystic saffron]

also having trouble interpreting the multiple choice question

this website says u1 and u2 for determining left and right tail but how do u know which mean is u1 and which is u2

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

<@&286206848099549185>

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

i really need help pls <@&286206848099549185> :((

been stuck on it for a week now and my professor wont explain it

[odd edge]

@mystic saffron Has your question been resolved?

[odd edge]

@mystic saffron Has your question been resolved?

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[acoustic quest]

is there anyone who can help me with mathlab?

[main creek]

matlab or mathlab?

[acoustic quest]

matlab

[main creek]

post your question

[acoustic quest]

an=n-sqrt n^2-4n

and i cant use any form of toolbox

[odd edge]

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[verbal schooner]

isnt d/dx(x^2+1) just 2x

[twilit smelt]

it is

[verbal schooner]

then howd they get that

[twilit smelt]

2x * blablabla

[signal oar]

Commutativity of multiplication

[verbal schooner]

ok thx

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[candid ledge]

Let f : Mat2×3 → Mat2×3 be a map between the set of 2 × 3 matrices. Suppose that f satisfy
f(A + B) = f(A) + f(B), f(λA) = diag(λ, λ)A
and for any 3 × 3 matrix B, we have f(AB) = f(A)B. (1) Does there necessarily exist a 2 × 2 matrix C such
that f(A) = CA? (2) If (1) is true, is such C unique

[candid ledge]

how should i solve this problem

@twilit smelt can you help me this

[odd edge]

@candid ledge Has your question been resolved?

[odd edge]

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[candid ledge]

reopen

[candid ledge]

@verbal schooner

@main creek

@acoustic quest

[verbal schooner]

stop pinging ppl

[candid ledge]

i just want some help,sorry

[nimble blaze]

noone will be able to help if you don't state what you need help with

[candid ledge]

Let f : Mat2×3 → Mat2×3 be a map between the set of 2 × 3 matrices. Suppose that f satisfy
f(A + B) = f(A) + f(B), f(λA) = diag(λ, λ)A
and for any 3 × 3 matrix B, we have f(AB) = f(A)B. (1) Does there necessarily exist a 2 × 2 matrix C such
that f(A) = CA? (2) If (1) is true, is such C unique

that's it

please! ! ! ! !

@nimble blaze hello???can you help me with it?

[weary pelican]

did you mean f(λA) = diag(λ, λ)f(A)

[candid ledge]

yeah

actually,i can hardly understand it,because my teacher only taught us how to do elementary row operation

but this is the homework he left for us, he hoped we could learn it by ourselves.

@weary pelican please 😦 i need your help badly:(

[odd edge]

@candid ledge Has your question been resolved?

[candid ledge]

anyone can help?

[odd edge]

@candid ledge Has your question been resolved?

[odd edge]

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[timber notch]

How to make a 120° angle using compass

[raw gale]

https://youtu.be/iTtK9e1mmvg?t=31

this should help you

its time stamper

[timber notch]

o

ty

I'll check

[raw gale]

np

[timber notch]

It's always an Indian when it comes to math (the video is made by an Indian) they fr so good

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[solid sand]

yo i am back :D with my trig stuff , so i did learn a bit from last time about trig functions and how they convert to other functions and ratios and stuff like that , but i still dont have any idea when they ask something like

the sum of the possible values of the expression sin(x) * cos(x) given that csc(x) - sec(x) = 2.

[lethal sundial]

Can you explain what you mean by "the som of the possible values"

[solid sand]

tbh i am not even sure what does it mean , that is how its written ,_,

i think i foudnd a answer but i still dont understand anything of it

kokler toplami = sum of the roots

[lethal sundial]

If you start from this initial equation

You want to rewrite it such that you get a result for cos*sin

Because there is specific values only for which the equation holds

[solid sand]

and they are asking for the sum of those values i suppose

[lethal sundial]

The possible values are possible x's

Then I guess what they are asking afterwards is to sum sin(value) * cos(value)??

Yeah it's quite blurry

[solid sand]

the nice thing is that i understnad what is done in the photo , i just dont have any idea why , like i can understand thta upper part but like why square it ?

meh forget it i'll ask the teacher its so annoying when questions are vague and there is not really a lot of recources where you can learn what is happening nor even check your answer

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[solid sand]

.reopen

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✅

[solid sand]

actually okay forget the question , how would you go from

csc(x) - sec(x) = 2

to what value is sin * cos

like how would you go about converting the first equation to the second

i know the basic stuff and my algebra is not that bad but like i have no idea how would you go from this to this

[lethal sundial]

So exactly what was show in the image basically

[lethal sundial]

Here

When you get to this polynomial equation of degree 4

I don't get what you did after that

[solid sand]

thing is , its not mine i found the photo on internet

[lethal sundial]

Ow okay so I just have to explain what's written basically

[solid sand]

i was thinknig someone could explain what or why he did it

[lethal sundial]

Can you vc by any chance?

[solid sand]

yeah 1 min

[lethal sundial]

Thank u

[solid sand]

private ?

[lethal sundial]

Yup

[solid sand]

ok

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[unkempt pollen]

i have a physics problem. a stone is thrown from 2 meters above ground with a speed of 13.5 m/s. At 11.3 meters it reaches its top point before starting to fall downwards. the question asks to find the total time the stone is in the air. i am supposed to use the equations with constant acceleration to solve this problem but i cant get the right answer

[silent flax]

the constant acceleration is 10 m/s

[unkempt pollen]

well i am supposed to use 9.8m/s^2

[silent flax]

ok

does your stone have to fall back to ground?

[unkempt pollen]

yes

[silent flax]

ok

so

the distance it travelled when going upward is 11.3-2=9.3m

[unkempt pollen]

yes

[silent flax]

the constant acceleration is 9.8 m/s

or -9.8 when going up

[unkempt pollen]

yes

[silent flax]

then you can use your acceleration and distance formula

i forgot what the formula says tho

but you definitely can use it

[unkempt pollen]

yes, i have the solution here. i am supposed to use s = v0t + 1/2a*t^2

but what i dont understand is that s = -2

[silent flax]

what does s stand for?

[unkempt pollen]

when i use s = -2 i get the right answer, 2.89 seconds

i am from norway so it means distance

[silent flax]

oh ok

[unkempt pollen]

but why does s = -2

[silent flax]

wait are you sure

[unkempt pollen]

eys

yes

but i guess at its final distance it is -2 meters

[silent flax]

yes

[unkempt pollen]

thats what i dont understand

[silent flax]

so i can only think of one answer

if what you said is true

which is the problem is not written correctly

because -2 meter is the distance that you actually travelled

actual meaning the displacement

[unkempt pollen]

yes, at the ground you traveled 2 meters away from your starting point

since the starting point was 2 meters above ground

[silent flax]

yes

but if you actually plug the number in

it shouldn't give you this amount of time

[unkempt pollen]

i get 2.89 seconds

[silent flax]

so

can you show me how you plugged your number in?

and don't use letters please

[unkempt pollen]

at line 5

[silent flax]

can you write me the acceleration and distance formula again with no letters, only full words pleas?

[unkempt pollen]

distance = startspeed * time + 1/2 * acceleration * time^2

[silent flax]

ok

so startspeed is 0

so startspeed*time well also be 0

[unkempt pollen]

no startspeed is 13.5

[silent flax]

sorry

can you solve for time

[unkempt pollen]

yes

[silent flax]

typo

didn't mean that

[unkempt pollen]

i did in my screenshot at line 5

[silent flax]

we can separate this problem into 2 part

when the stone is going up

[unkempt pollen]

yes, thats what i also thought

[silent flax]

and when it's going down

now

[unkempt pollen]

yes

[silent flax]

after a certain amount of time

the stone travelled 9.3 meters

and has a velocity of 0

so then you solve for the time

[unkempt pollen]

yes at 9.3 velocity is 0, start velocity is 9.3

no sorry 13.5

[silent flax]

so now you plug the numbers in to the equation

and solve for t

wheich is

a stone is thrown from 2 meters above ground with a speed of 13.5 m/s. At 11.3 meters it reaches its top point before starting to fall downwards.

this is just for reference

distance = startspeed * time + 1/2 * acceleration * time^2

ok

so

when you plug it in

[unkempt pollen]

well the only thing that changes is distance

[silent flax]

9.3=13.5t+1/2-9.8*t^2

[unkempt pollen]

its not solveable

[silent flax]

i mean 1/2*-9.8*t^2

typo

-4.9t^2=13.5t-9.3=0

that's the amount of ttime it takes to reach the top

but it still has to go down

so 11.3=0t=1/29.8*t^2

[unkempt pollen]

why -4.9?

[silent flax]

because

--4.9=-9.8/2

and -9.8 is the acceleration speed

[unkempt pollen]

why divide by 2

[silent flax]

since it's going up

oh

that

because in the equation

there's a 1/2accelerationtime^2

[unkempt pollen]

oh

right

[silent flax]

that's why

ok

now

when going down

the distance is 11.3 meters

since it's at the top

[unkempt pollen]

but isnt it -11.3 meters

[silent flax]

and has to go all the way to bottom

right

yea

i just do it simpler

it won't be a big issue tho

so -11.3=0t+1/2-9.8*t^2

4.9t^2-11.3=0

and then you solve the equation

add the 2 t together

you should get the answer

[unkempt pollen]

in the first equation i get -0.5

seconds

[silent flax]

oops

must have messed up the sign

you should flip the sign then

[unkempt pollen]

which one

[silent flax]

the - in -0.5

it should be 0.5

[unkempt pollen]

but you cant just do that

[silent flax]

cause time can't be neg

why

well

if you are thinking that flipping the signwill not show the work

[unkempt pollen]

you cant just get a negative number and just say that it shouldnt be negative then flip it. There has to be something wrong with the numbers we plugged in the equation

[silent flax]

yea

so the reason is

[unkempt pollen]

but for the stone going down is 1.5 seconds

[silent flax]

if you look at the acceleration

i put -9.8

[unkempt pollen]

yes because its de-accelerating

[silent flax]

and for the distance i put a positive value

but for the the downward half

i also put positive for d

and that's not right

because they are the opposite

and the displacemnt is -2

so if you add the 2 d

they dont give you -2

and that's wrong

[unkempt pollen]

well they do, 9.3 meters in positive direction then when stone falls down it travels 11.3 in negative direction

[silent flax]

yea

but

[unkempt pollen]

9.3 - 11.3 meters = -2

[silent flax]

but

you are changing view point

we always look at it from the starting direction

but

if you draw it

it's actually not right

they overlap if you draw them