help-10

[obtuse pebble]

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[shadow lake]

hello can I ask for help?

[signal ledge]

ofcourse you can

[shadow lake]

i jsut wanna clarify, how did the critical points become (-1,0) and (1,-4) , i understand the 1 and -1 part its from the (x-1)(x+1) from the first derivative right? how about the 0 and the -4? where did they come from? thank you!!

[quaint hinge]

the 0 and -4 are y-values

plug -1 and 1 into your f(x) equation

remember that critical points are points where your function (in this case f(x)) hits a local min/max (which is the casual definition)

taking the derivative gives you the x-value of those points

then you plug them back in to f(x) and get your y-values

[shadow lake]

Ohh i see it makes sense now, thank you thank you sooo much!!

[quaint hinge]

no prob!

[shadow lake]

for the point of inflection, is it always the y-intercept of f(x)? is it fine to ask the concept behind it

the y intercept and the double derivative of f(x) is equaled to zero right is the point of inflection

[quaint hinge]

it's not necessarily the y-intercept

in this case, f''(x) = 6x

but what if f''(x) was 6x - 100 (which could come from a different polynomial)

all you want to check is where the second derivative is equal to 0, it doesn't necessarily mean that x = 0

[obtuse pebble]

@shadow lake Has your question been resolved?

[obtuse pebble]

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[lavish nymph]

can someone help I have the slope -9/2 so now what

[versed pier]

oh no

you need the gradient p sure

if I remember correctly

[lavish nymph]

what

[versed pier]

oh wait sorry I thought it had 3 variables

[wispy bramble]

wait why again

yea its just y in terms of x

the x does look like a z tho

[lavish nymph]

uh

so what do I do

[versed pier]

are you familiar with calculus

[lavish nymph]

yea

I got the deriv of it

which was 2/9

and then I made it -9/2

why

[versed pier]

okay yeah

now just make a line

[lavish nymph]

wdym

[versed pier]

y = -9/2(x-0) + 2/3

or sm

[lavish nymph]

ok

then what

[versed pier]

then you rearragne and solve

assuming you calculated the slope right and stuff

[lavish nymph]

so -9x/2 + 2/3

@versed pier

[wispy bramble]

that's your answer yeah

[lavish nymph]

ok now what do I do with that

[wispy bramble]

-9x/2 + 2/3 = y

y + 9x/2 = 2/3

multiply by 6 on both sides
6y + 27x = 4

or 6y + 27x - 4 = 0

which is option C

@lavish nymph

[lavish nymph]

are you for sure

[wispy bramble]

is this for a test

[lavish nymph]

no its my homework

but I only have one attempt

[wispy bramble]

yeah pretty sure it's correct

[lavish nymph]

@versed pier could you confirm because ive been getting different answers from others

[wispy bramble]

i just checked it on desmos

[lavish nymph]

ok so its c

[wispy bramble]

yea

[lavish nymph]

omg ty so much

ive been waiting for like 2 hours for a answer

evewryone giving me different stuff

❤️

[wispy bramble]

do .close if ur problem was solved

[lavish nymph]

.close

[obtuse pebble]

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[autumn spade]

I found the A^T*A matrix

2 2 0 1
2 2 0 1
0 0 0 0
1 1 0 2

now for finding the eigen values i was a little stuck since the calculations of A-lambda(I)'s determinant was a bit daunting

so i searched the net

and found this

i figured that the same solution can be applied to my problem

but i dont really get the answer here

[autumn spade]

so can anyone please help and explain this to me?

[obtuse pebble]

@autumn spade Has your question been resolved?

[autumn spade]

<@&286206848099549185>

[obtuse pebble]

@autumn spade Has your question been resolved?

[obtuse pebble]

@autumn spade Has your question been resolved?

[autumn spade]

<@&286206848099549185>

[obtuse pebble]

@autumn spade Has your question been resolved?

[obtuse pebble]

@autumn spade Has your question been resolved?

[obtuse pebble]

@autumn spade Has your question been resolved?

[autumn spade]

<@&286206848099549185> anyone?

[urban ridge]

There are definitely tricks to calculating the eigenvalues more efficiently for some matrices, but here i'd actually say calculating the determinant isn't so bad

[warm shale]

ryc

ryc

ryc

[urban ridge]

at that point, i'd just go ahead and do a usual 3x3 determinant. i'd also keep in mind that if mu = 2, then the first 2 rows are the same, so i know mu = 2 is going to make the 3x3 determinant 0. that'll give you another factor of (mu - 2) you can pull out (and you're left with a quadratic)

Here's another way to handle this matrix which uses the technique you found online

there's one important thing to remember: the eigenvectors of a symmetric matrix are orthogonal to one another

so if you know one eigenvector, then if P is the orthogonal projection onto that eigenvector, then (A + P)v = Av + Pv = Av + 0 when v is a different eigenvector.

it also works if we scale P

for your matrix, we can quickly see two eigenvectors:v1 = (0 0 1 0)^t, and v2 = (1 -1 0 0)^t

let me know if you want to see how this works or if you prefer the other way

[urban ridge]

the corresponding projections are v1 v1^t and v2 v2^t (well, im not dividing by the norm squared cause im going to scale it later anyway)

that gives us $P_1 = \begin{pmatrix} 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 0\end{pmatrix}$ and $P_2 = \begin{pmatrix} 1 & -1 & 0 & 0 \ -1 & 1 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0\end{pmatrix}$

[warm shale]

ryc

[urban ridge]

is that ok so far?

[urban ridge]

oh i didnt finish my point here. my point is that this means that v is still an eigenvector of A + P. so we can change A by P, and then still find the same v when we find eigenvectors.

[autumn spade]

how did you get this?

[urban ridge]

i looked for eigenvectors with eigenvalue 0

in particular, one column is 0, so i know that i can get a 0-eigenvector from that

and then also the first 2 columns are repeated. so if i subtract one from the other, i get 0.

[autumn spade]

0 is an eigen value cus the determinant would be 0 right?

[autumn spade]

what do you mean by this?

[urban ridge]

yeah, but also zero's an eigenvalue because Bv1 = 0 (which is 0*v1)

(im writing B to be the matrix A^t A here)

[urban ridge]

B has its first 2 columns both (2 2 0 1)^t. so if i take 1 of column 1, and -1 of column 2, i get 0.

that's what led me to pick v2 = (1 -1 0 0)^t as another eigenvector

[autumn spade]

oh i get it

so v1 and v2 are two eigen vectors with eigen value 0?

could we not have taken (-1 1 0 0) too then?

[urban ridge]

yeah, that would be fine too

sorry i went to have lunch and stuff

[urban ridge]

ok, so now that we have these matrices, P1 isn't very useful because B already has a 0 in the spot we can adjust with P1

but P2 is more useful

in particular, if we add 2P2 to B, we get

$\begin{pmatrix} 4 & 0 & 0 & 1 \ 0 & 4 & 0 & 1 \ 0 & 0 & 0 & 0 \ 1 & 1 & 0 & 2\end{pmatrix}$

[warm shale]

ryc

[urban ridge]

which is going to be much easier to take the determinant of. well, we still need to subtract lambda, but when we do, we still have tons of 0's

it's important to note: you should not pay attention to the eigenvalue you get for this matrix that corresponds to the eigenvector (1, -1, 0, 0)^t

we changed that eigenvalue by 2

or, ok, you can pay attention to it, but you have to subtract 4 at the end from that one (you're gonna get an eigenvalue of 4 where you should have gotten 0)

this is because (B + 2P2)v2 = Bv2 + 2 P2 v2 = 0 + 4 v2 = 4v2. whereas Bv2 was just 0

[autumn spade]

makes sense

[obtuse pebble]

@autumn spade Has your question been resolved?

[obtuse pebble]

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[tall zephyr]

how do you answer this?

[tall zephyr]

im only having problems on the process

[ember frost]

differentiate y

the point (a, f(a)) is an inflection point if f'(a) = a

[obtuse pebble]

@tall zephyr Has your question been resolved?

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[vital patio]

is this correct

[ember frost]

no

[wheat dust]

how did you go from the first line to the second?

[iron eagle]

$\log_{a}{b} - \log_{a}{c} = \log_{a}{\frac{b}{c}}\ log_{3}{9x} - \log_{3}{(x-8)} = \log_{3}{\frac{9x}{x-8}}$

[vital patio]

what about the 4

[wheat dust]

what is a logarithm

[ember frost]

the 4 stays where it is

(x - 8)

[warm shale]

Tangerine

[iron eagle]

therefore we have\ $\log_{3}{\frac{9x}{x-8}} = 4\ \frac{9x}{x-8} = 3^{4}$

[warm shale]

Tangerine

[iron eagle]

should be easy from now

[vital patio]

oop i dont understand lol ima just leave it blank

[rich plume]

well, it would be better if you find the restrictions on x pre-hand

[ember frost]

$\a^x = b if and only if x = \log_{a}b$

[wheat dust]

no i was asking him lol

to let him understand

and not just give him the answer

[ember frost]

ah oops my bad

[iron eagle]

😭

[wheat dust]

okay so

in your class or whatever you learned the properties of logarithms right

[iron eagle]

$\log_{a}{b} - \log_{a}{c} = \log_{a}{\frac{b}{c}}$ have you learned this rule

[warm shale]

Tangerine

[vital patio]

yes i have that in my notes

[iron eagle]

yes so now in your case, a = 3, b = 9x, c = x-8

[vital patio]

but idk how to use it on this lol

ok

[iron eagle]

ignore the 4 on the right first

[vital patio]

Ok

[iron eagle]

so by using the rule, we combine these two logarithms into one

[vital patio]

yes

[iron eagle]

$\log_{a}{b} - \log_{a}{c} = \log_{a}{\frac{b}{c}}\ log_{3}{9x} - \log_{3}{(x-8)} = \log_{3}{\frac{9x}{x-8}}$

[vital patio]

thats the final answer right

[warm shale]

Tangerine

[iron eagle]

no you are still looking for x

remember this is an equation

[vital patio]

oh ye

[iron eagle]

do you understand up to this step

[vital patio]

idk how to find x

[iron eagle]

yes ill get to that

do you understand up to now though

[vital patio]

yes

[iron eagle]

ok so now we add back the right hand side

$\log_{3}{\frac{9x}{x-8}}=4$

[warm shale]

Tangerine

[vital patio]

yes

[iron eagle]

now you have to understand what logarithms are

[vital patio]

its

log

[iron eagle]

$log_{n}{x}= y$ means to find a number y where $n^{y} = x$

[vital patio]

ahh

[warm shale]

Tangerine

[vital patio]

so i make it to exponential?

[iron eagle]

you have to reverse the process

$\log_{3}{\frac{9x}{x-8}}=4$ means that $3^{4} = \frac{9x}{x-8}$

[warm shale]

Tangerine

[vital patio]

ohhhh

i get it 😎

[iron eagle]

to put in general terms, if $\log_{a}{b} = c$, $a^{c} = b$

[warm shale]

Tangerine

[iron eagle]

and now your equation is\ $\frac{9x}{x-8} = 3^{4}$

[warm shale]

Tangerine

[iron eagle]

you should know how to solve this right

[vital patio]

yes

i think

[iron eagle]

ok find x

[vital patio]

i simplify 3⁴ and cross multiply correct

[iron eagle]

yes

[vital patio]

😱😱😱

thank u

[iron eagle]

[vital patio]

@iron eagle hey

[iron eagle]

yes

[vital patio]

I do the same on this?

[iron eagle]

yes you combine the two logs first

[vital patio]

so it will be log 12x³/27xy²=a

[iron eagle]

the right side is a^0

[vital patio]

so is 1

[iron eagle]

yes

[vital patio]

ok

[iron eagle]

so $\frac{12x^{3}}{27xy^{2}} = 1\ 12x^{3} = 27xy^{2}$

[warm shale]

Tangerine

[vital patio]

i forgor this

[iron eagle]

what are you trying to find here though

[vital patio]

X

[iron eagle]

x

ok

$\frac{12x^{3}}{27xy^{2}} = 1\ 12x^{3} = 27xy^{2}\ \frac{x^{3}}{x} = \frac{27y^{2}}{12} \ x^{2} = \frac{9y^{2}}{4}\ x = \sqrt{\frac{9y^{2}}{4}}\ x = \frac{\sqrt{9y^{2}}}{\sqrt{4}}\ x = \frac{3y}{2}$

a

[vital patio]

i divide 12x to 27xy?

[warm shale]

Tangerine

[iron eagle]

move all the x terms to one side first

[vital patio]

why?

[iron eagle]

because you are looking for x

you cant leave your answer for x with x in it

[vital patio]

ohh

[iron eagle]

it has to be expressed in terms not containing x

[vital patio]

i didnt know u can just remove it and place it to other

[iron eagle]

so you combine all the xs together

[iron eagle]

its just dividing x from both sides

[vital patio]

the √9y² not gonna cancel the √ and ²?

[iron eagle]

thats what I did

$x = \frac{\sqrt{9y^{2}}}{\sqrt{4}}\ x = \frac{3y}{2}$

[warm shale]

Tangerine

[vital patio]

Oooooooo

Okk i get it thx

[iron eagle]

np

[vital patio]

.close

[obtuse pebble]

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[noble lake]

i know to use this identity :tan(A - B) = (tan A - tan B) / (1 + tan A tan B)

but slightly confused

[obtuse pebble]

@noble lake Has your question been resolved?

[willow crater]

first u need to make angle smaller

[noble lake]

minus by 360?

[willow crater]

yes

[noble lake]

okie one sec

[noble lake]

255 195 / 435 375

tan 255 - tan 195 / tan 435 + tan375

[willow crater]

u can minus 360 again in denominator and for numerator u can minus 180

[noble lake]

okie lemme try

tan 75 - tan15 /tan75 + tan15

[willow crater]

15 and 75 are complementary angles so do u know which property is to be applied here

[noble lake]

hmm im not sure i just know they add to make 90

[willow crater]

can u write this in the form of sin and cos functins

[noble lake]

oo im a bit confused as in sin75=o/h?

[willow crater]

no

do u know that tan=sin/cos?

[noble lake]

yes

[willow crater]

and do u know that tan(90-theta)=cottheta

[noble lake]

familiarish

[willow crater]

and cot=cos/sin

[noble lake]

yes

[willow crater]

so u can write this as tan(90-15) - tan15/tan(90-15)+tan15

which is cot15-tan15/cot15+tan15

now u can write cot15 and tan15 in terms of sin15 and cos15

[noble lake]

cot15= cos15/sin15

tan15=sin15/cos15

[willow crater]

yes

[willow crater]

substitute those values into this

[noble lake]

cos15/sin15 - sin15/cot15 / cos15/sin15 + sin15/cot15

[willow crater]

do u know the formula for cos(a+b) and sin(a+b)

[noble lake]

sin(x ± y) = sin x cos y ± cos x sin y
cos(x ± y) = cos x cos y ∓ sin x sin y.

[willow crater]

if u do know it then u can solve this now

[willow crater]

its sin15/cos15 not cot15

[noble lake]

ah yes sorry spelling mistake

[noble lake]

ah okay im just confused on how to sub it in

[willow crater]

?

[noble lake]

do i have to make it the same denominators

[willow crater]

yes

[noble lake]

like cos^2 15 -sin^2 15 / sin^2 15 x cos^2 15

divided by the same

[willow crater]

why do u have square in denominator

i mean multiplication

it shoulb be sin^2 + cos^2

which is equal to 1

so u just have to simplify the numerator now

i gtg now

[noble lake]

why would it be this

[noble lake]

ah okay well thank you for your help

[obtuse pebble]

@noble lake Has your question been resolved?

[noble lake]

.close

[obtuse pebble]

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[still hamlet]

A box contains 6 black and 5 yellow marbles. Two marbles are drawn from the box in succession without replacement. What is the probability of getting black on the second draw, given that it is yellow on the first draw?

[past sand]

What do you think?

[still hamlet]

I'm not sure 6/10?

help me pwease

[past sand]

I mean yeah you're correct

Why doubt?

[still hamlet]

that is the pard part when solving math :((

thanks for the reassureance I just need emotional support

.close

[obtuse pebble]

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[obtuse pebble]

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[dense lodge]

Don’t get why there isn’t another product in the answer

[urban ridge]

What does it mean for u and v to be orthogonal?

[dense lodge]

Ohhh

U^T*v =0

So u^tV = v^TU = 0?

[urban ridge]

Yeah

That's right

[dense lodge]

Tyyy so much

.close

[obtuse pebble]

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[cerulean fable]

Hello! I have a abelian group (G, +) and need to prove that Nil={x∈G:∃n∈N∗ : n⋅x=0G} is a subgroup of G. Here is what I've done so far. It looks completely wrong, at the end I'm just showing that a=b= OG. Anybody got any idea ?

[brave bramble]

So you're creating a new set E, and trying to show that E = Nil?

You're much better off assuming a ∈ Nil, b ∈ Nil, then showing (a + b) ∈ Nil

If a ∈ Nil, then there's some natural number n, such that na = 0.

If b ∈ Nil, then there's some natural number m, such that mb = 0.

Is a + b ∈ Nil? If so, there's some natural number that multiples a + b and takes it to 0. What is that number?

@cerulean fable

[obtuse pebble]

@cerulean fable Has your question been resolved?

[cerulean fable]

is this number (ma-nb) ?

assuming that ma=0 and nb= O I reversed the order

[obtuse pebble]

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[cerulean fable]

.reopen

[obtuse pebble]

✅

[brave bramble]

ma - nb is not a natural number

I'm looking for a natural number that, when multiplied by a + b, gives 0. Keep in mind, you do have that na = 0, mb = 0.

[cerulean fable]

(n+m) ?

[brave bramble]

Well, let's try it!
(m + n)(a + b)
= ma + mb + na + nb
= ma + 0 + 0 + nb

Not quite everything goes away

Good guess though, we're close to something that works better

Try mn

[cerulean fable]

thank you!

.close

[obtuse pebble]

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[grave trout]

hello

[grave trout]

I need help with thos

[timid silo]

prussia

[grave trout]

yessir

[timid silo]

wondering where the russian in p-russian come from

[final thunder]

Don’t ping helper when u have even posted the question

[grave trout]

oh ok

[grave trout]

help

Help me please

<@&286206848099549185>

[final thunder]

Find the probability that it isn’t green or purple first

[grave trout]

15/20

I think

[final thunder]

Right

[grave trout]

is that my answer?

[final thunder]

No you’re doing it 10 times

So times it by 10

[grave trout]

150/200

[final thunder]

Which is 7.5

[grave trout]

so 7.5

is my answer

[final thunder]

Think so

[grave trout]

ok ty

[obtuse pebble]

@grave trout Has your question been resolved?

[obtuse pebble]

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[pseudo gulch]

I dont know what my teacher did at the marked step. Can anyone please help?

[tardy epoch]

,tex .cts

[warm shale]

riemann

[obtuse pebble]

@pseudo gulch Has your question been resolved?

[obtuse pebble]

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[cursive mirage]

For question 16 do I count f(0) or no? Is zero considered even?

[cursive mirage]

Because if I counted f(0) I get 0.625 and if I didn't I get 0.5

[obtuse pebble]

@cursive mirage Has your question been resolved?

[cursive mirage]

.close

[obtuse pebble]

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[umbral hornet]

A ship leaves the harbour at 1 pm at 12 km/h travelling N 15 deg W. At 2:30 pm a second ship leaves the same harbour and travels S 75 deg W at 15 km/h. How fast are the ships separating at 3:16 pm?

[umbral hornet]

what am i doing wrong here?

the answer is supposed to be 16.89

for context, i set the distance ship 1 has travelled as a and distance ship 2 has travelled as b

time (t) is how long the 2nd ship has been travelling for, so in relation to that, i set (t+1.5) has the time ship 1 has been travelling for

oh crap nvm

it's a problem with my calculation of time for a

,close

.close

[obtuse pebble]

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[honest flicker]

Idk what to do

Idk how to do dimensional analysis

[chrome narwhal]

Do you know how speed distance and time are related?

[honest flicker]

Uhhh

Distance is speed times time right

And u can like divide

I think

[chrome narwhal]

Ok yeah, so you know that d=v*t

Now you know both of their distances and both of their speeds, so you can work out how long it takes them both to get there

[honest flicker]

How

[chrome narwhal]

Apologies I think I misread the question to begin with give me a second to work through it, it’s worded pretty confusingly

Ok yeah so we know how to calculate distance when we know velocity and time

[honest flicker]

[chrome narwhal]

And as time goes on this distance from where they are to the university decreases

So we need to create a function of their distance to the university based on time, so how might we do that?

[honest flicker]

Uhhh

149-95x

170-110x

[chrome narwhal]

Yeah exactly

[honest flicker]

Also they wanted me to use dimensional analysis 😭 😭 😭 😭 😭 but this is fine

That stuff

[chrome narwhal]

Ok that’s fine, after all your numbers you just write the units, so you’d have

149Km - 95Km/h*th

[honest flicker]

NOOO I DONT WANT TO USE IT

ANYWAYS

[chrome narwhal]

And you see this is actually a function of distance

[honest flicker]

Idk wat to do know

[chrome narwhal]

But as I said we’re interested in finding the time when the equation (149-95t)<(170-110t)

So how would you solve for the time such that this is true?

[honest flicker]

Uhhhhhhhhhh

I have no clue

[chrome narwhal]

Imagine the inequality was an equals sign, what would you do then?

[honest flicker]

I still wouldn't know what to do😭

Do I get t by itself

Fr

[chrome narwhal]

Yeah that’s it

[honest flicker]

Uhh I got 15t<21💀

[chrome narwhal]

Yeah that looks right

That gives t<21/15 which is roughly 1.4 hours or so

[honest flicker]

Oh

Do I put 1.4

@chrome narwhal

[chrome narwhal]

I’m not sure that would depend on your instructor, 21/15 or whatever that is in a decimal representation to a certain number of significant figures may be preferred

[honest flicker]

Rip I got it wrong😔

Incorrect inequality sign

[chrome narwhal]

Yeah you need to be careful of that, remember that if you multiply by a negative sign, or if you invert fractions you need to swap the direction of the inequality

[honest flicker]

But I didnt😭

[honest flicker]

This is correct right frfr

[chrome narwhal]

Well how did you calculate it? Me doing your homework doesn’t help you and isn’t interesting for me lol

[honest flicker]

Djhdjsbsjdbd

[honest flicker]

Is this one right frfr

[honest flicker]

<@&286206848099549185>

[honest flicker]

<@&286206848099549185>

[willow crater]

hey

[honest flicker]

Henlo

[willow crater]

what do u need help with

[willow crater]

its right

[honest flicker]

Ty

[honest flicker]

Idk wat to do

[willow crater]

can u find the number of scens as a function of time

[honest flicker]

Wat

[willow crater]

like the amount of kitchen scenes rendered is 540+90t since 540 were initially rendered and additional 90 are rendered each minute

did u understand this

[honest flicker]

Yes

@willow crater

[willow crater]

yes

[honest flicker]

But how is that the number of scenes as a function of time

There's 2 scenes

[willow crater]

well we are taking the 2 scenes separately snce they are different

u cant add the amount of kitchen scenes rendered to the garden ones

why would u add them

[honest flicker]

Wat

[willow crater]

can u derive an expression for the amount of garden scenes rendered?

[honest flicker]

Yes

[willow crater]

then do it

[honest flicker]

60t+960

[willow crater]

right

[honest flicker]

This is wat u said😭

[willow crater]

sorry mb

i am often told that i am not good at explaining stuff

[honest flicker]

Now wat

[willow crater]

well now its given that the kitchen and garden scenes rendered are same after some time so we can just do 960+60t=540+90t from here we can get the value of t at which they are equal

did u understand this?

@honest flicker

[honest flicker]

Why

[willow crater]

read the last para of the que

it asks after how much time will the amount of scenes rendered be same

n1=540+90t=amount of kitchen scenes rendered

n2=960+60t=amount of garden scenes rendered

now we do n1=n2

since the amount of scenes rendered is same

[honest flicker]

Oh

[willow crater]

i cant simplify it more than this

hope u understood

[honest flicker]

I got t=14

@willow crater

[willow crater]

thats correct

[honest flicker]

Wat Abt this

[honest flicker]

<@&286206848099549185>

[old dagger]

I got u

[honest flicker]

Is this right

[old dagger]

yep

well doen

anything else?

[honest flicker]

yes

One last one

[old dagger]

ok

[honest flicker]

Oki lemme read it rq

MY CONNECTION

NOOOOOO

Bsck

It's B right @old dagger

[old dagger]

r u good haha

yeah its B 👍

[honest flicker]

WOOOOOO

[old dagger]

haha

anything else

[honest flicker]

No

[honest flicker]

RAAAA

Ty

Just had to make sure

[old dagger]

haha well done

[honest flicker]

.close

[obtuse pebble]

Channel closed

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[old dagger]

cya

[obtuse pebble]

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[wild vigil]

Hello

[wild vigil]

So in translation

[versed pier]

https://nohello.net/en/

don't ever do this

but go on

[forest sinew]

damn take it easy geez

[exotic creek]

☝️🤓

[wild vigil]

A cup of tee sits in a room with 20 degrees celsius. At the beginning the tee had a temperature of 90 degrees after 15 min it was 54 degrees. The formula to be used is Temperature of the object = Roomtemperature +( Original temperature - room temperature) * e^-k*time in hours after the beginning of the cooldown. k is a constant that varies on how good the object "keeps" heat.

[forest sinew]

differential equations

[wild vigil]

Okey so i tried translating to the best of my abillities

[forest sinew]

the problem is to determine k?

[wild vigil]

yes

[forest sinew]

so, youre given some information, how much have you been able to write in equation form?

[wild vigil]

so what i got is

ah wait i messed something up

ok now i got it

so

[forest sinew]

so you have some information

at t=0 and at t=0.25

[wild vigil]

54= 20+(90-20)+e^-k*15

[wild vigil]

but im guessing thats wrong

[forest sinew]

its not 15

you said time is in hours

[wild vigil]

mhmmm true

where does the 54 then go?

[forest sinew]

it stays where it is

[wild vigil]

okey

[forest sinew]

the only thing there that is wrong is the 15

it should be 0.25

[wild vigil]

okey imma try and see if i can do sumn

okey so the next step is maybe to do ln on both sides to eliminate the e on the one side and just get the -k*0,25 standing alone

[forest sinew]

yup

[wild vigil]

okey so now i did plus k on each sides and then - ln (T)

leaving me with

k=25 - ln (T)

But i doubt thats right

[forest sinew]

huh? T?

whats T

@wild vigil

sorry im driving around

[obtuse pebble]

@wild vigil Has your question been resolved?

[wild vigil]

ah sorry im reading it straight from the book how its written

54 i mean

@forest sinew

[obtuse pebble]

@wild vigil Has your question been resolved?

[obtuse pebble]

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[glossy yacht]

why must there be a non trivial solution?

[glossy yacht]

det(lambda I - A) = 0 which is fine, but what is special about the eigenvalues?

not all singular matrices A have infinite solutions to Ax=0

[obtuse pebble]

@glossy yacht Has your question been resolved?

[obtuse pebble]

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[fickle cave]

how do you solve this?

[olive rover]

👍

[obtuse pebble]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[fickle cave]

1

[olive rover]

oh

[subtle sinew]

Do you know your prefix conversions?

[olive rover]

K = ?

[subtle sinew]

Like converting from KOhms to Gigaohms or Megaohms, etc

[fickle cave]

i've done but not like this questions

how do you do that

[subtle sinew]

It's not any different

What's Kohms?

[fickle cave]

1000

x1000

[subtle sinew]

Yeah K is kilo

So 1000

Convert that to Gigaohms

Can you do that?

Can you convert 900 Kohms to Gigaohms

[fickle cave]

0.900, 000 Gigaohms

[subtle sinew]

How did you get that?

[fickle cave]

0.009*

Giga ohms*

[subtle sinew]

Not quite

Almost

[fickle cave]

I moved from the the decimal place at 9 and moved left 3x

oh

that would be Mili ohm then mb

gotta move it 6x over right?

[subtle sinew]

It would be Mega, not milli

[fickle cave]

mega*

so 0.000009Giga ohm

[subtle sinew]

No

You should know this chart

[fickle cave]

k

[subtle sinew]

From kilo to mega, how much are you changing by and in what direction?

[fickle cave]

your going left

[subtle sinew]

How much, meaning how many place values

[fickle cave]

by +3

[subtle sinew]

So 900 KOhms in MegaOhms is what?

[fickle cave]

0.009M ohm

[subtle sinew]

Why did you move the decimal point 6 times?

You just said it was 3 places

Because it's 900 Kohms

[fickle cave]

oh yes mb

0.9M ohm

[subtle sinew]

What about Kohms to Giga?

How many places and in what direction?

[fickle cave]

3 left

[subtle sinew]

KiloOhms and Giga

It is not 3

[fickle cave]

oops

6*

read that wrong sry

[subtle sinew]

So then 900 Kohms in gigaohms is what?

[fickle cave]

0.0009G ohm

[subtle sinew]

What about Kohms to Ohms?

[fickle cave]

900 000 ohms

[subtle sinew]

And last one, Kohms to milliohms

[fickle cave]

900,000,000.0miliohm?

[subtle sinew]

Yes

[fickle cave]

:))

[subtle sinew]

So you convert 900 Kohms to all the other unit that the answer choice has, which one is the correct conversion?

[fickle cave]

giga

[subtle sinew]

Yes

[fickle cave]

yayy

tyy

[obtuse pebble]

If you are done with this channel, please mark your problem as solved by typing .close

@fickle cave Has your question been resolved?

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Please don't occupy multiple help channels.

[subtle sinew]

Please stop opening new channels and just wait patiently in your channel for help

However long it takes

[teal turret]

Ppl wait days

[subtle sinew]

Like #help-12 lol

[warm canopy]

Okay Nanno below this line post your full question and where you are stuck and wait for someone to provide help to you, however long this takes. I will close your other channel, please do not open another

[inner stratus]

there are missing informations

It says more milk so how much milk does an adult already drink

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[ocean nexus]

Anyone know how I would go about this? I am wondering if there is a method to find k rather than guessing and checking, i.e. _ x _ = 36k, and _ + _ = 8. Thanks
Find two values of k so that each trinomial can be factored over the integers.
Q. 36m^2 + 8m + k

[ocean nexus]

is there like a method to find k since the numbers are big so idk how you would simply guess the values

[obtuse pebble]

@ocean nexus Has your question been resolved?

[ocean nexus]

yoo i actually found the strat: if any gr 10 like myself who was stuck on the above problem here the strat.
36m^2 + 8m + k = 4 (9m^2 + 2m + k/4). From 9m^2 + 2m + k/4 --> (m + a) (9m + b) --> 9m^2 + 9am + mb + ab = 9m^2 + m (9a + b) + ab
Let 9a + b = 2,
Let k/4 = ab
Let's pick any value of a and b that = 2, so a = 1, b = -7 --> 9a + b = 2, 9(1) + (-7) = 2, 2 = 2
Since 2 = 2, we sub in our values of a and b since it is true.
k/4 = ab, k/4 = (1)(-7), k/4 = -7, k = -28
Therefore, k = -28

We can show it is factorable: 36m^2 + 8m + k = 36m^2 + 8m - 28 --> 4 (9m^2 + 2m - 7)
_ x _ = - 63 --> 9 x - 7 = -63
_ + _ = 2 --> 9 + (-7) = 2
So, 4 (9m^2 + 9m - 7m - 7), 4 [9m (m +1) - 7 (m + 1)], 4 (m + 1) (9m -7)
And then just pick two other values of a and b to find another value of k

.close

[obtuse pebble]

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[steel wave]

Someone help plzzzzz

[obtuse pebble]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[steel wave]

2

[subtle sinew]

What kind of triangle is that?

[steel wave]

Isosceles

[subtle sinew]

And that means what?

[steel wave]

Angle A and C are equivalent

[subtle sinew]

And?

[steel wave]

Side AB and CB are equivalent

I think

[subtle sinew]

And if they are the same, that means you can do what?

[steel wave]

Isolate X

Oh wait what

I got the correct answer this time

I need help with another problem

[subtle sinew]

What is it

[steel wave]

I’m pretty sure I got the angle measures wrong

Answer is suppose to be 60

Oh wait

[subtle sinew]

Are you sure that's the correct answer?

[steel wave]

Yeah

My teacher gave me whole answer sheet

I see what I did wrong now

[subtle sinew]

Angle B isn't 40

[steel wave]

Yeah

It is 100

Ima leave this help channel up and this time ima actually try on a problem for at least 5 minutes before I ask for help

[subtle sinew]

You can close it and then come back when you get really stuck and open a new channel

[steel wave]

Ok

.close

[obtuse pebble]

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Closed by @steel wave

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[frosty venture]

can someone help me with a math question

[obtuse pebble]

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/

[frosty venture]

This is the question

[subtle sinew]

,rotate

[obtuse pebble]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[frosty venture]

i dont know where to begin

[subtle sinew]

Is that not your work?

Because it looks like you know how to begin

[steel wave]

Assuming u got the slope, use point-slope form to solve

[frosty venture]

i got it wrong

[subtle sinew]

Well, this part is wrong. I'm assuming that says -23/8 + 80/8?

[frosty venture]

ik the answer but idk how ppl got oit

[subtle sinew]

First question is, is this your work?

Or someone else's?

[frosty venture]

yes

mine

heres my friend's

[subtle sinew]

Second question

[frosty venture]

the correct answer is 1197 over 664

😞

[subtle sinew]

.

[frosty venture]

i think i did the calculation wrong for that

oops

..

[subtle sinew]

Yes that's one of the things I am trying to point out

You weren't doing the process wrong, you were doing the algebra wrong

[frosty venture]

oh

let me try to solve this one more time

thank you for correcting me on that

[frosty venture]

wait how did it go to -6640 over 664 - 855 over 664

[subtle sinew]

Did you find the proper value for the slope?

[frosty venture]

yes

i got the answer

:))

[subtle sinew]

Do you know how to find the y intercept?

I'm assuming you know the general equation of a line, y = mx + b

And you found m

[obtuse pebble]

@frosty venture Has your question been resolved?

[obtuse pebble]

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[proven olive]

hello

[proven olive]

Find the dimensions of a rectangle (in m) with area 1,728 m2 whose perimeter is as small as possible. (Enter the dimensions as a comma separated list.)

how do i solve this

[past pecan]

What have you tried so far

[dense imp]

start out by calling one of the sides the name of a variable, say x. Since the area of the rectangle must be x * the other side = 1728, it automatically constrains the other side to being 1728/x. see if that helps you get started. also, what math level is this for? are you able to use calculus concepts?

[proven olive]

yea

calc 1

optimization

[past pecan]

Then what soosh said is good

Area = lw = 1728 and Perimeter = 2(l+w)

[proven olive]

alright let me errase what I have

ohhh fuck i get what you mean lol

.close

[obtuse pebble]

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[dusk widget]

!status

[obtuse pebble]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[dusk widget]

2

So I let x be in span(S1 ∩ S2)

then x = a1u1 + ... + anun, where a1,...,an are elements of F, and u1,...,un are all of the elements of S1 ∩ S2

where do I go from here?

[versed pier]

Let $x \in span(S_1 \cap S_2)$

[warm shale]

nosqldb

[versed pier]

okay

now you simply show that $a1u1 + ... + anun \in span(S1)$

[warm shale]

nosqldb

[versed pier]

and $a1u1 + ... + anun \in Span(S_2)$

[warm shale]

nosqldb

[versed pier]

@dusk widget this proof is kinda given

[dusk widget]

i got nvm

since ui is in S1, x is in span(S1), and since ui is in S2, x is in span(S2)

.close

[obtuse pebble]

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[bronze sky]

need to find that angle

and i dont really know hwere to start

[south inlet]

do you know sine, cosine, and tangent?

[bronze sky]

yes

[south inlet]

can u give me the equation of each

[bronze sky]

this would be cosin eright

[south inlet]

yes

[bronze sky]

wym

[south inlet]

its fine, it seems you already know to use cosine

so what would cos(theta) be equal to in this case?

[bronze sky]

arent i supopsed to set it up like cos(theta) = 4/5

[south inlet]

yes

[bronze sky]

what next

[south inlet]

so thats all you need

[bronze sky]

ru fr

[south inlet]

you just need to isolate theta

yes

[bronze sky]

wait

since its theta would it be inverse cos

so cos^-1

[south inlet]

yes

[bronze sky]

am i supposed to put theta into desmos or what

[south inlet]

you have a calculator?

[bronze sky]

yea

[south inlet]

you have a inverse cosine function on it

probably

[bronze sky]

yeah

im just using desmos

[south inlet]

oh ok

you could directly put it in desmos

[bronze sky]

uhh

let me look for theta

or can i just put like x

[south inlet]

yeah it doesnt matter what the variable is

[bronze sky]

liek this

[south inlet]

no

because you already did the inverse cosine, but you kept it on the left side of the equation

if you inverse cosine of both sides, on the left side it would leave you with x, and on the right side, it would be cos -1 (4/5)

[bronze sky]

so what should i do from here, im not sure

[south inlet]

ok so we have initially

cos(x) = 4/5

we want to isolate x

so we take inverse cos of both sides

the cosines cancel out on the left side, leaving us with x

and on the right side, it leaves us with cos -1 (4/5)

[bronze sky]

ohhh

ohhh

[south inlet]

so, you can just put cos -1 (4/5) into desmos

[bronze sky]

so are we dividing by cos -1

or multiplying

[south inlet]

not really

its just wrapping both sides of the equation by cos inverse

[bronze sky]

ok so now im just left with cos -1 (4/5) = x

[south inlet]

yes

[bronze sky]

ok then just input that

?

[south inlet]

yes

[bronze sky]

i got 0.644

[south inlet]

yea

[bronze sky]

does that sound right

aye w

ok

but what if the 4 and 5 were flipped

so i had cos-1 (theta) = 5/4

[south inlet]

hmm

one problem

the previous answer is wrong

desmos is by default in radians

not degrees

[bronze sky]

oh yeah my bad

forgot to change

so

36.8698976458

[south inlet]

yeah

[bronze sky]

so what ab this

[bronze sky]

.

[south inlet]

it wouldnt be cos-1(theta) = 5/4

its just cos(theta) = 5/4

cos is just adjacent / hypothenus

[bronze sky]

but like say it was

or are u saying it snot possible

wait im a dumbass

LOL

ok im gonna keep this open for a little longer i need to write this down but thanks

[obtuse pebble]

@bronze sky Has your question been resolved?

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[stray cosmos]

m = 30 kg
θ = 26°
a = 2.5 m/s2
μ = 0.58

[rich plume]

what is your question?

[stray cosmos]

We need to find the pull of this. I have found Fg, which is 294.3. Then I found Force normal which was 129.012. Then I used Ff=UFn to find Ff, which was 74.826.

no clue where to go from here

[rich plume]

first of all I'd recommend drawing a fbd of the diagram

[stray cosmos]

yea thats what I drew too

[rich plume]

so, see that mg has a slant component along the friction

[stray cosmos]

I think so

[rich plume]

that component would be mgsin(theta)

Now, for the friction, it is given by UN

So calculate the normal force

[stray cosmos]

wait is this refering to the line that goes perpendicular to the object?

[rich plume]

no

along fritction

[stray cosmos]

oh, force parralel. I guess I did solve for that at 129.012. I used that as my foce normal for some reason at first

[stray cosmos]

so I have 129.012 for force parralel, 153.41 for foce friction, and 294.3 for force gravity

[rich plume]

Okay I'm trusting you on this one

can you draw a diagram and label what forced you mean

[stray cosmos]

like this

plus force friction

[obtuse pebble]

@stray cosmos Has your question been resolved?

[obtuse pebble]

@stray cosmos Has your question been resolved?

[obtuse pebble]

@stray cosmos Has your question been resolved?

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[mortal thunder]

I did everything right got the problem correct but i wanna better understand it for my own learning on like the interpretation

<@&286206848099549185>

[willow crater]

what do u want to understannd

[mortal thunder]

Like understanding what my answer means to the problem

Whats the 22.5 represent

And stuff

[willow crater]

22.5 represents dy/dx when y=45 and x=1

[mortal thunder]

I know that but i meant more specific to the actual word problem about the business cards and stuff

[willow crater]

?

[mortal thunder]

The cost is y

The x is the business cards

[willow crater]

ohhh

i dont know how to explain this one

sorry

[mortal thunder]

Np

<@&286206848099549185>

.close

[obtuse pebble]

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[obtuse pebble]

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[chilly crater]

I rely need help

Anyone

[ember frost]

whats the formula for the area of a triangle and a rectangle?

[chilly crater]

Tri 1/2x bxph

Rec b X h

[ember frost]

correct, now do the calculation for both shapes

what do you get?

[chilly crater]

1/2 x 8 x 6x

5(4x-1)

[short ore]

ye

[ember frost]

now transform both into ax + b form

[chilly crater]

??

20x-5

[timid silo]

ar tri = 1/2 * 8 * 6x = 24x

[ember frost]

simplify them

[timid silo]

ar rect = 5 * (4x - 1) = 20x - 5

[ember frost]

whats 1/2 x 8 x 6?

[timid silo]

area of triangle

[chilly crater]

24

[ember frost]

correct!

[chilly crater]

Then

[timid silo]

areaTriangle = areaRectangle + 10

[ember frost]

according to the question, the area of the triangle is 10cm2 greater than that of the rect

[ember frost]

^

now plug that into the equation and solve for x

[chilly crater]

Oh

[timid silo]

24x = (20x - 5) +10

24x = 20x + 5

[chilly crater]

Ohk

[timid silo]

24x - 20x = 5

4x = 5

x = 5/4

[chilly crater]

Omg

Tysm

. Close

.close

[obtuse pebble]

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[obtuse pebble]

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[jolly olive]

there are two sets given
A := {6 , 4 , 2 , 0 , 2} and
B := {1 , 4 , 9 , 16 , 25}.
if its possible i have to creat funktions that have following charactaristics (i may use a tabel) and if it isnt possible to creat a function i have to give a reasoning.

(i) g1 : A → B, so that g1 is surjectiv and not injektiv.
(ii) g2 : A → B, so that g2 is injektiv and not surjektiv.

[jolly olive]

how to get a funktion

[obtuse pebble]

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