help-17

[shell laurel]

Did I make a mistake? how do you solve for the other constants?

[vocal sleet]

@shell laurel Has your question been resolved?

[hard atlas]

linear system of equations

eg by gaussian elimination

[shell laurel]

i dont know how to do gaussian elimination

however, in the coefficients part I think I made a mistake cause x^2; 0=A+B+D but also -2=A+B+D

I just dont know where I made a mistake

[shell laurel]

<@&286206848099549185>

[neat wave]

did you mean to write 3Cx?

i see 2Cx + Cx in the right expansion, and then you do A + 2C + 2D after

[shell laurel]

SHIT

THANK YOU SO MUCH LMAO

[neat wave]

np lmao

[shell laurel]

tytyty

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[vast shale]

I am clueless as to how to find the domain and range here

anyone know

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

<@&286206848099549185>

Ur range is (-inf,2] U (4,inf)

[halcyon wing]

,rccw

[vast shale]

steps if possible?

No steps really, Note that the domain of your left segment is (-inf,6], center (-6,2], right (4, inf), Take the union of these and you have the domain

Ah alright thank you

Much appreciated

Ur range is {5} U (-inf, -7)

thank you very much

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[vast shale]

good morning, i need some help here

[vast shale]

in this question he is asking the angle of the arch

[ebon rapids]

!status

[vocal sleet]

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

[vast shale]

5

[vast shale]

so the answer is 150

but it's from the up part

and the down part

how would i know if it's asking the down// up part of the arch

sorry, i get it now xD

he is asking the little arch

not the big one

my bad

[proven garden]

conventionally we consider the smaller arc

[ebon rapids]

^

Typically if we want the major arc we would say all the points the arc hits

like arc ADC

[vast shale]

hummm, i see, thanks

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[odd cloak]

im so confused on how im supposed to do this using b^2 - 4 ac because that was in the answer sheet

i typed out only the last question at the bottom of the picture the rest above i just copied the answers

[proven garden]

show that 7x^2-4x+2 have no real solutions using b^2-4ac

[odd cloak]

oh then (2x-1) is the only one real root?

why did i not think of that

tysm

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[vocal sleet]

@winter briar Has your question been resolved?

[sacred swift]

someone can give me a hand

i don't know how to open a channel

[round plover]

!help

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To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[sacred swift]

si ma non ci ho capito un cazzo

oh no

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[long flame]

i am trying to find intersections of circles, and i get these stupid fraction coordinates that end up in an utter mess

[long flame]

i removed much of my calculations because i needed more space on my page but

does it seem to you that there is an obvious simplification to this?

or are the answers meant to be this complex?

my methodology is, for lines c and d:

get intersection line of c and d, call it cd

plug cd in one of the circles

solve for y

(which means quadratic equation)

then plug y values into cd and get x values

to me the equations given seem stupidly and unecessarily complex, taking away from the learning factor of actually finding intersections

but rather making a million calculations and making sure they are correct

[summer spoke]

If those answers are correct, you probably won’t get much simpler than that aside from combining fractions

[long flame]

in this instance they were not correct but i suspect the answer is off by just one calculation mistake or two

this was correct for a previous problem with lines c and d at the top

but that's so stupid, i am not learning about circle intersections like this, i am forced to be a human calculator

and i keep running out of space so i cannot even retrace my errors

because i need to remove previous calculations

[round plover]

from graphing them, the circles appear to be tangent

[long flame]

yeah the answer should be only a single point

[round plover]

and the point of intersection seems to have a nice form

[long flame]

but from my methodology i dont see how i can end up getting only a single line

i have an intersection line cd, i plug it into c, and i get a quadratic equation

[round plover]

I'm not entirely sure what you've done to be honest

[long flame]

to get the intersection line cd, i was taught to expand circle equations of both c and d

then to multiply (-1) with c or d, then equate them

this typically cancels x^2 and y^2 and some other terms

and should give me the intersection line cd

then i solve cd for x, and plug cd into either of the original circle equations

this gives me a quadratic equation

which again gives two solutions

[round plover]

\begin{align*}
(x+8)^2+\left(y+\frac{397}{5}\right)^2-(x+5)^2-\left(y+\frac{322}{5}\right)^2&=5850-3744\
% \left(x+8+x+5\right)\left(x+8-x-5\right)+\left(y+\frac{397}{5}+y+\frac{322}{5}\right)\left(y+\frac{397}{5}-y-\frac{322}{5}\right)&=2106\
\left(2x+13\right)\left(3\right)+\left(2y+\frac{719}{5}\right)\left(\frac{75}{5}\right)&=2106\
6x+39+30y+2157&=2106\
6x+30y&=-90\
x+5y&=-15\
\end{align*}

[twin meteor]

Desync

[round plover]

doing your method should give this

and x + 5y = -15 should be the tangent line to the intersection point

[long flame]

okay so i was off by a bit on the k value of cd

hold on let me plug this again and see what happens

still no

i take cd, solve for x to be x = -5y - 15

then plug cd into c, so:

$(-5y-15+5)^2 + (y+\frac{322}{5})^2=3744$

[twin meteor]

marty

[long flame]

and get $26y^2 + \frac{1144}{5}y + \frac{10084}{25} = 0$

[twin meteor]

marty

[round plover]

I think your constant is off

I get 12584/25

[long flame]

exactly that would give D = 0

[round plover]

,w 3744 - (322/5)^2 - 100

[twin meteor]

Results provided by WolframAlpha

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

Requested by .desync

[round plover]

plugging it into the quadratic formula yields y = -4.4

and that's the y-coordinate of the intersection point

[long flame]

not sure exactly what i'm looking at here

is this a trick to find the constant easily?

[round plover]

when you expand a binomial (ay+b)^2

the constant is just b^2

your binomials are (-5y-10)^2 and (y+322/5)^2

so your constant overall (on the right side) is 3744 - (-10)^2 - (322/5)^2

it doesn't matter, it just gives the constant

so we have $y^2+\frac{1144}{5}y=-\frac{12584}{25}$

[twin meteor]

Desync

[long flame]

aaah okay

i see

and yeah i realized my mistake

i somehow forgot to do 10*10 for the first binomial expansion

this gives D = 0

thus -1144/260 which gives -4.4 as you correctly stated

and then i'd plug that into cd to get x values

[round plover]

yep

or into one of the circles

whichever is easier

[long flame]

typically cd i find

still it is unecessarily complex right

[round plover]

uhh, I get x=7

[long flame]

to work with circle intersections

[round plover]

well, it's not that much work

for the initial subtraction step

you can use difference of two squares to speed it up

the next step is solving a linear equation in one variable

then finally solving a quadratic

[long flame]

yeah

[round plover]

it's not that bad

[long flame]

but when the given equations are v large numbers and fracitons

it makes it unecessarily complex imo

[round plover]

I'd try leaving everything as fractions and not combining stuff until you need to evaluate it at the end

[long flame]

i know how to work with them but it takes up about twice as much calculation size

[long flame]

yes i also get this

[long flame]

i will try this now

thank you

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[pale isle]

Any idea how to solve thisp

[wraith parrot]

Use the definiton of logs

[paper depot]

!status @pale isle

[vocal sleet]

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

[pale isle]

1

I know the log rules

[paper depot]

do you know the definition of log

i.e. $\log_a(b) = x \iff a^x = b$

[twin meteor]

Ann

[pale isle]

Yes

Oh

Thx

I got it

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[still anvil]

I'm confused about how to approach this problem using u substitution

ik i can substitute cos^2theta to 1-sin^2theta but like that doesnt rlly do me any good and i thought i could make u=costheta but that didnt work either rlly

[sage wind]

why dont you try to split it into 2 fractions instead of u sub

[still anvil]

o true that might work

[still anvil]

ok i did the sin/cos^2 one but im having trouble with the integral 1/cos^2theta

nvm u j change it to | sec^2x which is = tanx

ty

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[sage wind]

sorry i was late

np you did everything

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[knotty jasper]

I have a math question

[knotty jasper]

1/0 is usually undefined

because it goes towards both infinities

BUT

couldnt that mean

that 1/0

would be ±∞ (plus or minus infinity)

because in algebra, we have plus or minus

so wouldnt it make sense to be plus or minus infinity

or am I just being stupid rn

[loud pivot]

No

[knotty jasper]

No what

[loud pivot]

You can prove this by contradiction

Let's assume that your statement is correct: $\frac{1}{0} = ∞$

[twin meteor]

USS-Enterprise

[loud pivot]

This means that $0 * ∞ = 1$

[twin meteor]

USS-Enterprise

[loud pivot]

Anything times 0 is always 0, never 1

So 1 over 0 can not be infinity

[knotty jasper]

Ohhh

Okay

[loud pivot]

1 over 0 is undefined but certainly not infinity

[errant briar]

Infinity is a concept not an actual number, so defining 1/0 as ±inf is not correct

[knotty jasper]

Aren't imaginary numbers a concept too?

[errant briar]

No, the term "imaginary" is misleading

[knotty jasper]

oh okay

[loud pivot]

I mean, yeah it's very tricky. Don't consider what I said as definitive math because it isn't, because infinity is something very abstract and you pretty much can't "math" it as you can other things

But yeah, what you said isn't correct. You simply can not divide by 0, and you can't divide 1 by 0 and get infinity

Imagine you have 5 apples

You can't share them to zero people

You can't have "no" share of 5 apples

This doesn't mean you have an infinite amount of apples though.

[knotty jasper]

oh okay

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[rapid ravine]

can someone help me

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[lilac plaza]

Can someone tell me why I am wrong?

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[abstract palm]

how am i supposed to deal with inequality here?

[abstract palm]

where p is parameter

from real numbers

[cursive turret]

what is your question?

[abstract palm]

i need to find the solution of this inequality but i know how to solve it if it is equal

but i am stuggling with that ineqal sign

what am i supposed to do

find discriminant and what?

[cursive turret]

i am not sure. you have 2 unknowns. p and x. what solution do you want to find? the solution for p so the inequality holds for all x? or the solution for x of the inequality in terms of p?

[vocal sleet]

@abstract palm Has your question been resolved?

[abstract palm]

i am trying to find sets of valoues of p for which solution of x is the same

if i explained it right probably not

here is solution maybe it helps

[cursive turret]

so youre searching for solutions for x expressed in terms of. replace > with =. solve the equation. think about when the graph is > 0 (outside the zeros or between the zeros).

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@abstract palm Has your question been resolved?

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[slate crypt]

Sooo, I came across this site and was wondering if I need to memorize all the rules to do anything useful with math irl... https://algebrarules.com/

I get that this is question is pretty vague... but gotta start somewhere 🤷‍♂️

Thanks

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[patent pasture]

How do I set up the double integral?

[vocal sleet]

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[patent pasture]

<@&286206848099549185>

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.close

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[winter kestrel]

Hi if I were to apply a limit so t>0 and I applied that to sin(1/t) that would make the limit undefined right

[sly sierra]

limit as t->0 from the positive side?

[livid tapir]

side shouldn't matter

[sly sierra]

well they said t>0

[visual oracle]

Undefined either way

[winter kestrel]

from both sides

[peak axle]

1/0 is indeterminate

[livid tapir]

oh ye

[sly sierra]

just want to make sure i understand the question

[peak axle]

So it would be undefined regardless of if you approached from +, -, or put it in a tangent instead

[livid tapir]

that's the wrong reason for it actually. You could for instance have a function f(x) = c for some constant c

[sly sierra]

the intuition for why it's undefined is that sin(1/t) = +1 and -1 for infinitely many values of t in any neighborhood of t=0

[livid tapir]

Then make g(x) = f(1/x)

Limit would exist and equal c even if "undeterminate" at 0

[winter kestrel]

ok doks so if I did something like cos(t) * sin(2/ t) as t approaches 0 that would make the equation undefined

[livid tapir]

If you make it sin(t)*sin(2/t) the limit would actually exist and equal 0

But not your version

[sly sierra]

technical point: it's an expression, not an equation
it's perfectly well defined for any nonzero t
but it's not defined at t=0, and it has no limit as t approaches 0

[winter kestrel]

ok thanks guys

.close

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[hollow karma]

Hello

[pale perch]

greetings

[hollow karma]

im confused where the 2^3 came from here

[sly sierra]

recall that if you multiply any row of a matrix by a scalar c, then the determinant gets multiplied by c

here, all three rows are multiplied by 2

more generally, if A is n x n, then det(cA) = c^n det(A)

[hollow karma]

so in c^n the number of rows is n?

[sly sierra]

yes

[hollow karma]

got it, tysm

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[rapid ravine]

is this correct?

[vocal sleet]

@rapid ravine Has your question been resolved?

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@rapid ravine Has your question been resolved?

[rapid ravine]

<@&286206848099549185>

[halcyon wing]

look at corresponding angles

[rapid ravine]

are geb and dhf corresponding angles?

[halcyon wing]

no

[rapid ravine]

so they are supplementary then

[halcyon wing]

exterior supplementary, yes

[rapid ravine]

can yu help me with this one too

[rapid ravine]

.close

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[cerulean sentinel]

I don't understand how to find KLM

I so far did 66-54= 12

[royal kestrel]

KLM is KLN + NLM

why

[cerulean sentinel]

but that was incorrect

[royal kestrel]

KLM is equal to the two smaller angles

[cerulean sentinel]

so 66 + 54?

[royal kestrel]

sorry im on my phone so its a bit whack

but notice how the two smaller yellow angles

add up to the red angle

so yes you add them together

[cerulean sentinel]

I got it

[royal kestrel]

👍🏻

[cerulean sentinel]

.close

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[cerulean sentinel]

.reopen

[vocal sleet]

✅

[royal kestrel]

i believe you use the protractor to measure the angles

[cerulean sentinel]

Yes

[royal kestrel]

which is kinda obvious but im not sure how to use the site

[cerulean sentinel]

I don't know how to use it

[royal kestrel]

how u rotate it i have no idea

[cerulean sentinel]

I can move it around but unsure on where it put it

[royal kestrel]

but the small circle hole

on the bottom of the protractor

should be where the yellow circle is (Point O)

[cerulean sentinel]

It's there

[royal kestrel]

can i see

[royal kestrel]

are you able

to rotate the protractor

[cerulean sentinel]

yes

[royal kestrel]

what angle are you measuring

[cerulean sentinel]

NOP = 180

[royal kestrel]

NOQ or POQ

mhm

[cerulean sentinel]

I guess both

[royal kestrel]

ah

well its supplementary angles

so measure one

[cerulean sentinel]

the question

Where do I put the proracter to measure NOQ ?

[karmic imp]

Rotate the proracter 180 degrees

[cerulean sentinel]

it is

[karmic imp]

What does it look like

[karmic imp]

You can find the measure of NOQ

[cerulean sentinel]

67 I believe

[karmic imp]

Yep looks about right

[cerulean sentinel]

I got

it

[karmic imp]

Because the angles are supplementary angles, you can find POQ

[cerulean sentinel]

Thank you

I know I need 2 pairs so 4 numbers

but what numbers repersent T to Y

x,1,2,3 ?

[karmic imp]

What are you asking

[cerulean sentinel]

what numbers represent T to Y

[karmic imp]

You don't need numbers to represent T to Y

[cerulean sentinel]

oh.

What do I need to do then ?

[karmic imp]

Do you know what a linear pair is?

[cerulean sentinel]

2 pairs that = to 180

for example 90 +90

[karmic imp]

Can you mark angle TYW?

[cerulean sentinel]

Yes

it is a right angle

[karmic imp]

No it's not

[karmic imp]

But I'm asking for you to draw on this image, where <TYW is

[cerulean sentinel]

how do I draw

[karmic imp]

Wdym?

[cerulean sentinel]

I can't draw on my problem

[karmic imp]

You just trace over where <TYW is

You took a picutre of it, you can edit that picture

[cerulean sentinel]

oh okay one momment

[karmic imp]

As you mentioned a linear pair is two angles that add to 180, you just marked one angle, what is the other angle combined with TYW that makes it a linear pair?

[cerulean sentinel]

TYV?

[karmic imp]

Yes but is there a number there that you can reference?

[karmic imp]

.

[cerulean sentinel]

90?

[karmic imp]

Is that angle labeled with a number?

No

[cerulean sentinel]

6?

[karmic imp]

No

Is there a number associated with TYV?

[cerulean sentinel]

how do I know which number goes to which line

[karmic imp]

It gives you all the info you need

[cerulean sentinel]

5

5 goes to w and v

I believe 5 isn't right

[karmic imp]

You just said TYV is a linear pair, why did you just say 5?

[cerulean sentinel]

becuase 5 goes to w and v

6 also does but they are both wrong

oh

TYV

[cerulean sentinel]

TYW & TVY are linear pairs

[karmic imp]

And no TWY is not one

[cerulean sentinel]

TYW ****

[karmic imp]

You are correct that TYV is a linear pair with the angle it asked about, TYW but is there a number that you can reference the angle TYV?

Do you see how there are the numbers 1 - 6?

Those are to reference the angles, like 1 references angle TXS

So for TYV is there a number that you can reference?

[cerulean sentinel]

Angle X because we had to find it ?

I am so unsure I don’t understand how to tell number goes with what angle

[karmic imp]

.

Do you see where TXS is?

[cerulean sentinel]

Yes I see it

[karmic imp]

Do you see how there is a 1 there?

[cerulean sentinel]

Then it would be Y

[karmic imp]

No that Y is a label for that point

[karmic imp]

The question is asking for the angle number

Is there a number that represents angle TYV?

[cerulean sentinel]

3

[karmic imp]

No

[cerulean sentinel]

that is the only number in the bracket that v & r are in

[karmic imp]

Do you understand how to read that image?

[cerulean sentinel]

I do not

[karmic imp]

I just marked two examples for you. That 1 is the angle number for the orange angle I traced, TXS. The 6 is for the green one, UYV

So you marked TYV as a linear pair with TYW, is there a number next to TYV that you can reference?

[cerulean sentinel]

number 4

[karmic imp]

No

That does not got with TYV

[cerulean sentinel]

TYV = number 3

[karmic imp]

No

Do you see the examples I presented?

[cerulean sentinel]

YXR = 3 ?

[karmic imp]

Yes

[karmic imp]

.

[cerulean sentinel]

The only number on that side is 3 , Y & R

If it not 3 Y or R then I don't know

[karmic imp]

But is there a number associated with TYV that you can use?

Is there a number that labels TYV?

[cerulean sentinel]

then it has to be 4 or 5

It can't be 5 because 5 = TYW

[karmic imp]

Do you see how 4 labels this angle here?

[karmic imp]

No

5 does not label TYW

[cerulean sentinel]

I need to go watch videos on this

I don't understand

.close

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[vast shale]

Hey. Is anyone here experienced with the TInspire? Matrix help needed please

[vast shale]

X = 351.75
Y = 261.08

[thin vale]

questions about how to use calculators are not the point of this help channel. But if you have a math problem then someone can help you with that

[vast shale]

I have no idea how to get these values

[vast shale]

Sorry, I just attached the problem.

Does anyone have any idea?

[round plover]

you haven't really asked a question, just sent a picture of a matrix and the values of two variables

but I'm assuming that that's supposed to be an augmented matrix representing a linear system in X and Y

[vast shale]

im trying to figure out how i can properly plug the matrix into my calculator to get those x and y variables

[round plover]

don't know how to do it for your specific calculator, but you could row reduce the matrix to isolate the value of Y

https://www.youtube.com/watch?v=BqKvwv4EOjw

maybe this will help

[vast shale]

it was able to solve it, but i didnt get those specific values

this is what i keep getting

[round plover]

that's not what an augmented matrix represents

oh wait you're inverting it smh

are you using degrees

make sure it's not in radians

or grads

[vast shale]

it is in radians

[round plover]

50 and 30 look like they should be degrees

[vast shale]

i forgot it was in radians

let me try again

OMG IT WORKED

i am so slow

thank you

bro. ive spent the last HOUR doing this

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[south scroll]

first order derivative?

ohh

remainder theorem

use that

[round plover]

I don't think that factorises

[south scroll]

yea it doesnt

its impossible

[round plover]

remainder theorem is that if a polynomial p(x) is divided by a linear factor (x-a), then the remainder is p(a)

a corollary of this is the factor theorem, which basically when the remainder is zero in the factor theorem (so (x-a) is a factor of p(x) if and only if p(a)=0)

yeah

and specifically, if you get zero

then (x-6) is a factor

so you can do the polynomial division, and try factor the lower degree result

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[vast shale]

The definite integral between 3 and 1 of that curve will give me the non shaded area right

Under the x axis

[gritty spade]

Yeah, you can test points to find out if it works, I tested (3,0) and (1,0)

0 = (3-2)^2 -1
Which gets me 0 = 0

0 = (1-2)^2 -1
That also gets me 0 = 0

So both points should be in the shaded area which it is

[vast shale]

?

What

What are you testing for I’m confused

[vocal sleet]

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[dusty phoenix]

PLS HELPP I don’t understand how they come up with these graphs

[vocal sleet]

@dusty phoenix Has your question been resolved?

[dusty phoenix]

Plss

.close

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[naive snow]

need help finding the 50th term of the sequence in question f)

[paper depot]

,rccw

[naive snow]

is the only way to do this by manually writing out every term until the 50th?

[vast shale]

You have the formula for f, so just plug in 50?

[paper depot]

i mean i'd probably write out a few terms to see if anything interesting pops up

[paper depot]

it's a recursive formula.

[naive snow]

yea i'll send a pic of what i got

[vast shale]

Ah okay

[naive snow]

I’ve tried using algebra but it seems to be impossible to solve by finding a new ewuation

what I’ve determined is that the numerator is 3x the denominator of the previous term

[paper depot]

oh ugly

[vocal sleet]

@naive snow Has your question been resolved?

[naive snow]

any other mathematicians wanna give this a shot?

[vocal sleet]

@naive snow Has your question been resolved?

[naive snow]

i decided to brute force it by using excel, but i'm wondering if there's any other way to do it

would using cauchy’s sequence definition work here?

[vocal sleet]

@naive snow Has your question been resolved?

[regal bane]

@naive snow
You could check for fixed points. That is, any solution to:
x = 3 / (2x + 1)

[vocal sleet]

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[fleet salmon]

for 6a

hiw do i graph

n get points

[vast shale]

what do you know about graphing a fx

[fleet salmon]

like

should i plot

the points

then graph

or how do i do this

yk how there og poiints

for parent functions

do i use those

and transform them

into

the ones

needed

for this function

[grizzled halo]

do you know how to sketch hyperbolas

[fleet salmon]

cant i use

x/k +d

for z

x

and ay+ c

and transform the points

of parent function

to

it

[vast shale]

man... just type it all in one line lmao

[fleet salmon]

acc nvm

i think i got it

mb 😭👍

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[mighty stone]

1,3,7,15,31

how can i write a recursive sequence using function notation

[civic otter]

Notice what happens if you double a term of the sequence...

[mighty stone]

the second change multiplies by 2

i get how the sequence works

im just having a hard time writing an equation

[civic otter]

So each term is 2·previous + 1, right?

[mighty stone]

ye

+1?

1,3,7,15,31

2 4 8 16

this is the change

the change mutliplies by 2

@civic otter would 2^n-1 work?

[civic otter]

Do you want a recurrence relation or the general formula?

[civic otter]

Yes

[mighty stone]

Recurrence

[civic otter]

$$a_n = 2^{n-1}$$ is correct, but it's not a recurrence relation

[twin meteor]

Alberto Z.

[mighty stone]

So how do i make one?

[civic otter]

Using this observation @mighty stone

[mighty stone]

Multiploes by 2

[civic otter]

The recurrence relation is $$a_n = 2 \cdot a_{n-1} + 1$$, or equivalently $$a_{n+1} = 2 \cdot a_{n} + 1$$

[twin meteor]

Alberto Z.

[mighty stone]

How does the an-1 work

[mighty stone]

how does the a_n-1 work?

[vocal sleet]

@mighty stone Has your question been resolved?

[civic otter]

Wdym?

[vocal sleet]

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[sonic wigeon]

Hello. I am confused how this expansion of this bracket of fun cos functions has lead to this result with these mystery sin functions appearing. I am confused how they have expanded the brackets, signs have flipped and now the 2 sin terms appearing in the numerator. Could someone explain to me what they did here as I don’t know what they did here. Apologies if it’s an easy question to answer, my brain is just puzzled at this step. I’ve marked it in green pen to make it clear what step I am referring to

[sonic wigeon]

Oh wait

Nvm

I am blind

I see what it is they have done… ffff

.close

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[sonic wigeon]

.reopen

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✅

[sonic wigeon]

Ok new issue here

I thought in these prove questions you can’t use the eqn you are trying to prove to prove itself as I thought you had to end up with the eqn you are wanting to prove to successfully complete a proof in this sense. I’m just perplexed to why we are now using the very thing we want to prove in our proof if you get what I mean, I’ve circled it in red to the line that made me raise an eyebrow

Apologies if this seems like a dumb question. I am just confused as I thought you were not allowed to do this since you are trying to make the eqn in the end and at no point should the eqn you want to prove should be used in the proof itself part way through it

Like the only time you should write the eqn you want to prove is at the end of your proof writing your final line.

(I’m not a pure mathematician btw as I study physics so I’m looking at this from the physics perspective of approaching maths if people are wondering why I’m blathering on about proofs so much and how I don’t understand it.)

[grizzled halo]

is your problem the $\frac{\sin^2A}{\sin^2a}$ at the front?

[twin meteor]

chlamydia

[sonic wigeon]

Yea

As I’m like that’s using the formula we want to prove

[grizzled halo]

well we're not referencing what we're trying to prove

it's just creating a starting point so we can move from sinA/sina to sinB/sinb or c

[sonic wigeon]

Oh

[grizzled halo]

if the proof suddenly threw in that the LHS=sin^2B/sin^2b then that'd be wrong, but the proof is working its way from one side to the other to show that its true

[sonic wigeon]

So it’s not we are using the thing we want to prove explicitly but setting up a scenario where it can fall into the thing we want to prove?

Apologies btw if I seem dumb with this, I’ve never approached a proof like this before in this way.

[grizzled halo]

for proving $\frac{\sin^2A}{\sin^2a}=\frac{\sin^2B}{\sin^2b}$,

[twin meteor]

chlamydia

[grizzled halo]

colloquially, i'll call them A and B

like in real life, to get from A to B, we need a vehicle to move between them

in this case, the vehicle is everything else we know about trig, like sin^2+cos^2=1

maybe not a good metaphor

[sonic wigeon]

no i actually like that way of putting it

good metaphor

[grizzled halo]

so within the metaphor, we're not picking up place A and physically moving it to place B, we're moving between them ig

now that's a stretch

[sonic wigeon]

i think i get you, we are basically trying to show that the stuff we have can work interchangablly i.e if we can get it to fall in to our sin^2A/sin^2a then it should fall into the other cases as well

the way ive put that sounds like proof by induction i.e assuming if case 1 works then case n+1 should also work

[grizzled halo]

yeah in a way

[grizzled halo]

but yeah essentially, showing that it generally works

[sonic wigeon]

ok. btw just for future references are proofs at this kind of level always like this? usually well from the physics way of doing things we would say perform derivatives to get the thing we want to come out of the function to say yes we have proved it as we have did this and this then rearranged and we have thing or from the more mathematical way of doing it using proof by contradiction/counterexample or induciton (my knowledge on proofs is dog btw if you havent noticed😅 )

[grizzled halo]

you know plenty

this is more of a direct proof, rather than trying to prove impossibility or anything

i'd say trig proofs mostly look like this

there's a lot of different identities and variables to work with

[sonic wigeon]

tell me bout it, the amount of trig identities ive seen i have no idea how we are expected to memorise em all

[grizzled halo]

modern education system moment right there, because the internet doesn't exist

[sonic wigeon]

thank you though for your help. you have helped me at least open my eyes to this way of approaching a proof (just hoping i can spot em in the future and not overcomplicate)

[grizzled halo]

it gets better with experience

[sonic wigeon]

yea, something i envy about maths students, they do this more often than we do. well problably that might change now at this level but yea

thank you

[grizzled halo]

np man

[sonic wigeon]

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[dusty phoenix]

Can someone please help with quesidon 7

How would I find the equation

[karmic imp]

It gives you the parent function, y = 3/x, and it states that the other curves are produced by translating the parent function. Do you know your transformation rules?

[dusty phoenix]

Yes

[karmic imp]

So given the parent function, how would you produce curve A?

[dusty phoenix]

We’ll Ik that if I’m translating up or down, I add it to the y intercept

And if it’s to right I subtract from x

And left I add form x

That’s all Ik but idk how ro use ir in that question

[karmic imp]

Take a easy point in the parent function, let's say (1, 3)

[dusty phoenix]

I took 1,1 and got it wrong

[karmic imp]

If you translate that point to curve A, what direction did you go in and how many units?

[dusty phoenix]

U go up but idk by how many unit

[karmic imp]

Do you see how the green curve is the parent function?

You're comparing it with curve A, the blue one

[dusty phoenix]

Will it be -2

[karmic imp]

-2 meaning what exactly?

[dusty phoenix]

As in y=k/x -2

It translates 2 down

[karmic imp]

Yes from the parent function to curve A, it translated down 2 units

But you are given the parent function of y = 3/x

[dusty phoenix]

Righttt

I got ittt

[karmic imp]

So what is the equation for curve A?

[dusty phoenix]

Y= 3/x -2

[karmic imp]

I'm assuming you're using U to represent curve A?

[dusty phoenix]

I meant y

And yes

[karmic imp]

Yes that's the equation that represents curve A, that was produced by translating the parent function

Just apply that process to the rest of the curves

[dusty phoenix]

Alrr tyy

.close

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[jovial gulch]

can someone help me from 2 to 5 ?

[halcyon wing]

multiply it out

move everything to one side

and solve

[jovial gulch]

transform each of the ff equations in the form ax2 + bx + c=0

help

[halcyon wing]

did you try that?

[jovial gulch]

yee

Pls correct if wrong

[proven garden]

2x?

where'd x come from

[jovial gulch]

that’s what the teacher put when she showed us an example

here the example

@proven garden

[proven garden]

bruh

5 times x is 5x

you don't get x when using s as variable

[jovial gulch]

OHH

i just realized 😭

[jovial gulch]

its 2s ? 😭 im confused

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@jovial gulch Has your question been resolved?

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[wide marsh]

Quelqu'un peut m'aider ?

[wide marsh]

Or can someone help me?

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[vast shale]

42. Aldona thought of sewing a skirt based on a paper cutout. She learned
    that the cutout is made as follows: two semicircles are drawn from the same
    center. The radius of the larger semicircle is equal to the radius of the
    smaller semicircle and the length of the skirt combined (+) I !Then two lines are
    drawn in the drawing at an angle of 30° and the rest parts to be cut off
    .The length of the smaller bow of the remaining cutout should be equal
    to half the circumference of Aldona's torso.
    a) Calculate the lengths of the radius of both semicircles to the nearest
    1 cm if Aldona's waist is 64 cm and the length of her skirt is 50 cm.
    b) When cutting a skirt according to a cutout, the fabric is folded in half
    and the cutout is placed at the fold line as shown in the drawing. What
    is the minimum length and width of a piece of fabric needed to sew
    a skirt? (To the calculated length and width, add 2 cm each for seams.)

[vast shale]

any help will be helpful

[vast shale]

😦

no help

im hopeleeeeeeeeeess

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

oke

i solved

a by myself

im proud of myself

can somebody help me b? <@&286206848099549185>

theres translation

[vast shale]

^

i solved a and i got 60 and 10 for the answers , but im stuck on b tho

you got any idea how to solve or start atleast ?

its supposted to be hard

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

<@&286206848099549185>

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

<@&286206848099549185>

[vast shale]

<@&286206848099549185>

[solar saffron]

Hello there.

I honestly don't understand this image

[vast shale]

Me either

[solar saffron]

I am guessing a) is asking us to find the radius..?

[vast shale]

I've solved a

I'm stuck on b

[solar saffron]

Oh ok, what did you get for a)

[vast shale]

10 and 60

[vast shale]

Smaller 10 bigger 60

[solar saffron]

I haven't seen this type of question before

[vast shale]

I don't remember how I solved it but it was like r1 - smaller radius r2 - bigger radius
r2 = r1 + 50
r1 * pi = 64/2
r1 = 10
r2 = 60

[vast shale]

It is supposted to be hard

[vast shale]

It says fabric fold line

From lithuanian to english

[solar saffron]

I'm never going to be a skirt designer so

[vast shale]

Yeh

That's not the point

[vast shale]

Skirt is like arc

Idk how it's called in english

[solar saffron]

Yes but I don't understand how they worded the second image

[vast shale]

Yeh me either

[solar saffron]

Languageeee

[vast shale]

?

Lithuanian

[solar saffron]

I would ask your teacher for help if you can.

[vast shale]

Well

Mayne i will tmrw

For now I quit

.quit

.vlose

.close

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[proper dawn]

Hi guys, here for a questionning. I'm French btw

i want to make an equation of this text

International standards define the danger threshold as : 85 dB for 8 hours. This threshold increases by 3dB each time the exposure time is divided by 2.

[proper dawn]

It means u can resist 8hours hearing a 85dB sound without ur ears getting hurt.

it s like 85+n3 = ...

<@&286206848099549185>

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[snow path]

wondering if anyone can help me with d

[snow path]

this is my work so far

so if this is right, i've found one complex number that satisfies this. i'm wondering how i might find others

assuming this is correct at all

i am not confident in what i have so far either

[grizzled halo]

d or e?

[snow path]

d!

oh

sorry

yes it's e

[grizzled halo]

ok

from your 4th line to your 5th line, remember that pi/6 is the same as pi/6+2pi, pi/6+4pi,...

[snow path]

yes

[grizzled halo]

so we'll express that as $\theta=\frac13(\frac {\pi}6+k2\pi)$

[twin meteor]

chlamydia

[snow path]

makes sense.

[grizzled halo]

that gives 3 unique answers

[snow path]

gah. but im not seeing why that's the case. isn't that just one unique answer?

[grizzled halo]

you can try thinking about it on the unit circle: you're adding k2pi/3 to your first answer

because it's 2pi/3, it takes 3 times for it to circle back to your first solution

[snow path]

oh, i see!

thank you

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[terse forum]

Reflection in the x-axis-Vertical Translation 2 units up

[terse forum]

for Quadratic Fn I did

$f(x)=-x^2+2$

[twin meteor]

Akira 🍉

[terse forum]

is that right

[peak axle]

Yup

[terse forum]

thanks

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[hollow shell]

.reopen

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[alpine mica]

It was wrong when i put it in, didnt really knew what process i was supposed to do first and if i was supposed to go further, excuse my equations being broken into 2 lines

[alpine mica]

<@&286206848099549185>

[grizzled halo]

you're applying product rule wrong

[alpine mica]

How so

[grizzled halo]

$\frac d{dx}f(x)g(x)=f'(x)g(x)+f(x)g'(x)$
which is

[twin meteor]

chlamydia

[grizzled halo]

$(x^2-7x+6)^4\frac d{dx}(4x+6)^3+(4x+6)^3\frac d{dx}(x^2-7x+6)^4$ here

[twin meteor]

chlamydia

[grizzled halo]

and then chain rule for each

[alpine mica]

so for example would the derivative of (4x+6)^3 be 3(4x+6)^2 or (4)^3

or something else

[alpine mica]

question above this reply

[grizzled halo]

3(4x+6)^2 *4 because you need to diff the inside too by chain rule

[alpine mica]

oh okay

[grizzled halo]

g(x) was 4x+6 here, so g'(x)=4
this doesn't mean multiply the other part by 4 too

[alpine mica]

where

[alpine mica]

where are you seeing this

could we do an example problem

[alpine mica]

(4x + 3)^3 (x2 − 5x + 3)^4 like this, so i can see the steps

nvm figured it out

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[inland latch]

I am confused with how I got this incorrect.

*Instructor does not want us to simplify.

I am mainly confused with approaching 2 inner terms.

[inland latch]

Uhm, you unfortunately closed this channel for someone else to use.

[alpine mica]

oh my bad

i think that was a photo that got posted late my bad

[inland latch]

No worries!

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@inland latch Has your question been resolved?

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@inland latch Has your question been resolved?

[inland latch]

<@&286206848099549185>

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@inland latch Has your question been resolved?

[vast shale]

Not want to simplify into exponent form? Not really a simplification, just writing it differently

I'd say turn it into exponent form then chain rule

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[unborn wharf]

Could I get help on part b of #10

[slim blade]

set up your initial inequality statement then answer it

[unborn wharf]

How

[slim blade]

what is the inequality for less than 80

[unborn wharf]

X > 80

[slim blade]

flip your sign

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[dim quail]

No idea how to proceed

[dim quail]

,rotate

[split wind]

factorize the numerator

[dim quail]

Thanks

I got it

.close

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[visual kayak]

Hey

[visual kayak]

Is it possible to show that sqrt(3)-sqrt(2) is an algebraic number here?

[dark kiln]

put it into wolfram

it will say it's root of 1 - 10 x^2 + x^4

[visual kayak]

I want to prove it

@dark kiln like I want to find the polynomial in another way

[dark kiln]

okay, i don't know how hopefully someone comes

[visual kayak]

Alright thank you

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@visual kayak Has your question been resolved?

[split wind]

the usual, or more like intuitive, way is to try out all combinations of √3 and √2

i.e.
√3+√2
√3-√2
-√3+√2
-√3-√2

[split wind]

use these as the roots of a polynomial

[split wind]

as to construct this
@visual kayak

[visual kayak]

Seems helpful

But is there any chance I can reach the polynomial directly without guessing?

[visual kayak]

Imagine we didn't know about this, how can we find it

[split wind]

even if i don't know this, i would do it

[split wind]

this way

to see

real coeff quadratics are of conjugated pairs

and also

(√3-√2)²

=5-2√6

which looks so much like a root of a quadratic equation

that's why i say it's intuitive

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[inland kite]

@hexed shadow I don’t know how to use one variable to represent the product of three consecutive integers

[inland kite]

Like using a variable expression thingy

[hexed shadow]

I've written a bunch of leading questions that might help with the answers spoiled, the final question fully answers + spoils the "product of three consecutive integers"

You could represent a number that is double the number a by 2a.
You could represent a number that is seven bigger than a by (a + 7).
How do you represent a number that is one bigger than a? ||a + 1||
How do you represent a number that is two bigger than a? ||a + 2||
How do you represent the number that is an integer multiplied by an integer one bigger than it multiplied by an integer two bigger than it? ||a(a+1)(a+2)||

[inland kite]

But how do I know the values of the integer

In the questions, it wasn’t stated

[hexed shadow]

You don't! That's why we use the free variable $a$ to represent an unknown number.

[twin meteor]

NarrowAdder#9135

[inland kite]

How do Ik if the second integer is eg 2 bigger

It’s 3 unknown integer, no?

[hexed shadow]

by the definition of the question, a consecutive integer is the integer that is one bigger than the other

[inland kite]

Oh

[hexed shadow]

so 3,4,5 are consecutive integers, but 7,9,11 are not

[inland kite]

I hate terminalogy

I got it

Thx

[hexed shadow]

I call these kinds of questions "definition hell" questions, they are truly the worst :P

Your welcome! Have a good one.

[inland kite]

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[half summit]

A student runs 9.0 m [W] and then turns and runs 12.0 m [N]. If he is able to do this in 5.0 s, what is his average velocity?
I calculated the hypotenuse with pyth, and it's 15, so I divided by the time which is 5, so the answer is 3.0 m/s?

[vale frigate]

yes 3.0 m/s along a certain direction

[half summit]

ah alr, for the direction is it 53 degrees?

tan 12 / 9

9*

[vale frigate]

,calc (atan(12/9)*180)/pi

[twin meteor]

Result:

53.130102354156

[vale frigate]

yes

[half summit]

ah nice

[half summit]

that's between W and N right?