help-10

[jagged falcon]

It's the cos x that gives 0, not the product of magnitude

Do you know how to calculate scalar product of vectors without knowing the angle between them?

[rough pecan]

√ (3^2 - m^2 -3^2 )
√ (-m^2)

the 3^2 minues from the other 3^2

[jagged falcon]

Yeah the product of magnitudes is not 0, their scalar product is

[rough pecan]

sorry whagts the differnece between their scalar product and the normal product

[jagged falcon]

Also incorrect. It is sqrt((3)^2+(-m)^2+(-3)^2)

[rough pecan]

ah ok

[jagged falcon]

By normal product I take it you mean product of numbers in R. We do not define product on vectors in R^n like that. One of the products we define is scalar product. The scalar product of ai+bj+ck and di+ej+fk is (ad+be+cf)

If both of these are perpendicular, this product should be zero

[rough pecan]

ohh ok so in this case
its 5x3 + 3x-m + 1x-3

oh ok i just did that and got m=4

thank you so much

i didn even need the magnitude at all

[obtuse pebble]

@rough pecan Has your question been resolved?

[obtuse pebble]

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[safe lodge]

I need help with the solution of the following fourier series task. I think I understood the general concept of fourier series, but I have a problem with identifying odd and even functions. Maybe someone could help me do understand these type of questions better ( PS: Englisch is not my first language)

[warm canopy]

Have you tried drawing it?

[warm canopy]

And then it also needs to repeat every 2π

[safe lodge]

Yes, it would look the same between 2pi and 4 pi

I dont know how to draw it in - 2 pi direction

[tardy epoch]

take your graph and shift it left by 2pi

[obtuse pebble]

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@safe lodge Has your question been resolved?

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[glass dagger]

can you use a math editor to format your math?

or latex

[pseudo swift]

or post a pic of the problem if you have one

@solemn osprey

seems weird enough yea

[solemn osprey]

in otherwords x^2y''+xy'+y=0=sqrt(5x)

for second order differential equations

where Ay''+By'+Cy=0 is the homogenous form, I just don't know if the sqrt(5x)=0 is extraneous or not

[pseudo swift]

0=sqrt(5x) what

[solemn osprey]

yeah there are two equals

[pseudo swift]

seems fucked up

[solemn osprey]

it could be another way to write a system of equations, not sure

he says it's on purpose

[pseudo swift]

you can't have both of them true at the same time though

we're talking about a functional equation

you don't have sqrt(5x) = 0 for any x

[solemn osprey]

yeah I'm pretty baffled

[pseudo swift]

¯_(ツ)_/¯

yeah idk what your prof is on

seems like good stuff

[solemn osprey]

I wonder if he wants this to work like compound inequalities

[pseudo swift]

is it really a differential equation then

the guy just invented a new field "today imma teach you differential inequations"

[solemn osprey]

no idea, probably just gonna have to take the loss

[pseudo swift]

yea

[solemn osprey]

.close

[obtuse pebble]

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[small cave]

To select a team, some rules must be respected. All teams have 7 members and a maximum of 2 girls.
Elsa's class has 28 students, 11 of which are girls.

Elsa's team won the tournament. John is part of the team. A photo will be taken with the team members side by side. Determine how many different photographs can be taken, knowing that Elsa and John are not together?

[small cave]

I think the answer is 6C2 * 5! .

Am I right?

<@&286206848099549185>

[obtuse pebble]

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@small cave Has your question been resolved?

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[subtle gull]

I have 4 values how do i make the compound sol

[obtuse pebble]

@subtle gull Has your question been resolved?

[obtuse pebble]

@subtle gull Has your question been resolved?

[ripe terrace]

are you trying to solve x⁴+3x²-4 = 0 for x ?

if not then what equation you are trying to solve ?

[ripe terrace]

and wdym by compound solution ?

[subtle gull]

X+yi

Img number

[ripe terrace]

hmm okay (although the prefer the term complex solution or solution simply)

[ripe terrace]

^

[obtuse pebble]

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[marble crest]

If T(t0) = <2,3,4> then which of the following could be the osculating plane to r(t) at t0?

Answers:
a. 3x+y+z=2
b. x+2y-2z=7
c. x+y+z=5
d. 3x+4y-z=8
e. 2x-y-z=0

[marble crest]

Don't know what to do at all 😭

[abstract flame]

the tangent vector has to be contained in the oculating plane

and you have all the equations of the planes

so you can find vectors that are normal to those planes

and those vectors must be orthogonal to T(t0)

[marble crest]

Ohh okay ty

@abstract flame So the normal vector for answer choice a would be <3,1,1,> right?

[abstract flame]

yeah

[marble crest]

Ty

[obtuse pebble]

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[vast flare]

I'm a bit confused

[vast flare]

Apparently the answer is x <= 5

Pls help

[vivid cedar]

did you try

|x+5|<=2x

and then u can do

x+5<=-2x and x+5<=2x

and then ucan see which one exists

@vast flare

so x<=5/3 or x>=5

i dont get how the answer is x<=5 though

[vast flare]

Same

[vivid cedar]

wait lemme do it on paper

1 sec

[vast flare]

Desmos and all calc says x<=5

Oh wait I put the signs wrong

[vivid cedar]

it should be x>=5 or x<=5/3

[vast flare]

But it says only x>=5

[vivid cedar]

are you just solving for x

[vast flare]

Yes

[vivid cedar]

just x

uhhh

hmm

they should both work

[vast flare]

But desmos refutes the 5/3 version

[vivid cedar]

send a screenshot

[vast flare]

Explain that please

[vivid cedar]

what

well

that is saying x>=5

yea

i was right

cause the shaded part

is greater than

or equal to

5

[vast flare]

But what about 5/3?

[vivid cedar]

uhhh idk tbh im not that smart

like sometimes when you get two answers

1 of them doesnt work

[vast flare]

Yea but why for this case?

[vivid cedar]

i have no clue

im only 13 💀

[vast flare]

Wait how do you know about abs values then?

That's year 11 material

[vivid cedar]

what

idk

my friends did it in grade 6

all my friends smarter than me 🥲

[vast flare]

Which country you from?

[vivid cedar]

this is algebra one right

[vivid cedar]

america

[vast flare]

Interesting

[vivid cedar]

its just simplifying the two sides

no clue why desmos doesnt accept the other thing tho

maybe someone else can tell

[vast flare]

Let's wait for an expert

[vivid cedar]

yea

k gotta study for a test

cya

[vast flare]

Cya

[vivid cedar]

gl finding the answer

[vast flare]

Apparently Microsoft Math agrees too.

And Symbolab

So -5/3 is somehow dejected

<@&286206848099549185>

[timid silo]

how can I help you ?

[vast flare]

Figure out why x >= -5/3 cannot exist

[timid silo]

what is the exact question ?

[vast flare]

See up

[vast flare]

This one

Working out and question provided

[vast flare]

And why x>=5 is the only sol.

<@&286206848099549185>

[timid silo]

alright I think I got it

[vast flare]

Yay

[timid silo]

for the inequality to be satisfied you need to find the values of x that will make 2x >= abs(x + 5)

so, if you try and negative values for x the inequality will not be satisfied as 2x will be negative while abs(x + 5) is always positive

that way -5/3 is not a solution

[vast flare]

Ahhhh!

You're a genius

[timid silo]

now you get 0 and all positive values remained

[timid silo]

nah, not exactly 😅

[vast flare]

Thx tho

.close

[obtuse pebble]

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[timid silo]

anytime

[obtuse pebble]

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[fathom flicker]

I am trying to find all real $x$ where $$\sum_{n=0}^{\infty}2^nx^n$$ converges. I was hoping someone could check my work. I did the ratio test, so,

[warm shale]

austinu

austinu

austinu

[fathom flicker]

so that is the interval of all real x where the sum converges, by the ratio test.

is that correct?

[tardy epoch]

So far so good

[fathom flicker]

Is there more I have to do? I thought that was all of it

[tardy epoch]

Endpoints

[fathom flicker]

oh right

|L|=1 is inconclusive

so I have to check that

so when x=-1/2 and x=1/2

Okay so

[warm shale]

austinu

austinu

[fathom flicker]

the first sum is greater than or equal to the harmonic series for all n. By the comparison test it diverges.

the second sum, idk how to determine if it diverges or converges. All I have access to is ratio/root/alternating series tests, all of which are inconclusive

[tardy epoch]

Limit test

[fathom flicker]

I haven't proven that yet

so I can't

I have that series xn converges => lim xn = 0

that gives series xn diverges => lim xn != 0

but not the other direction

so it isn't helpful here right

because it isn't an if and only if statement

[tardy epoch]

It is an if and only if

[fathom flicker]

no because what about the harmonic series

lim xn = 0 but series DNC

[fathom flicker]

are you sure? I don't think it is

[tardy epoch]

Right

You got it backwards

[fathom flicker]

cause then you could negate it and conclude the harmonic converges

[fathom flicker]

I haven't proven that yet

[tardy epoch]

I find that hard to believe

[fathom flicker]

I have this

series xn converges => lim xn = 0

doesn't negating that give me series xn DNC => lim xn !=0

and not the other way around

the divergence test above is the other way around

[tardy epoch]

What exactly were you taught

[fathom flicker]

Well I mean a lot so I'm not sure what you are looking for me to say. but ill try to list a few things

the series converges if the limit of its partial sums converge

[tardy epoch]

In this image

[fathom flicker]

I just drew this

to show my confusion

[tardy epoch]

So you weren't taught any of those?

[fathom flicker]

No, the top line is what you gave

and the rest is me showing why I am confused

I've been taught that the harmonic diverges, I have that proof. And comparison/root/ratio tests

[tardy epoch]

Use this to prove by contradiction

[fathom flicker]

okay

I can do that

but that isn't the same as the 'divergence test' is it?

[tardy epoch]

They could be equivalent

[fathom flicker]

could be isn't the same as that they are though

okay ty riemann

I guess I am still a little confused about the difference going on there, but my question is solved

.close

[obtuse pebble]

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[willow lynx]

can somebody explain how to solve this

dont know how

[obtuse pebble]

@willow lynx Has your question been resolved?

[boreal geyser]

The red and shaded area represents all the values for y. first, find the equation that represents the dashed line

you are given two points. how can you find the equation of the line?

[willow lynx]

the slope is -1/6x

[boreal geyser]

correct i just relized all the answers have that equation

[willow lynx]

lol

i already knew how to do that bit though

kind of meant this sorry

and

[boreal geyser]

ok do you know what a dashed line means?

[willow lynx]

none of the points on the line will satisfy the inequality

[boreal geyser]

correct, so which symbol would represent that? the ones with an equal or the ones without?

[willow lynx]

without

[boreal geyser]

ok, so we can eliminate A and C

[willow lynx]

its probably B then

[boreal geyser]

now, the shaded area is above the line, so all y values must be...

[boreal geyser]

Correct!

[willow lynx]

ty i had a few more questions so i can really understand this

[willow lynx]

what does it mean when the area above is shaded

[boreal geyser]

If the area shaded is above the line, then all values above that line (greater than the equation) satisfy the equation. If the area shaded is below the line, then all values below that line (less than the equation) satisfy the equation.

[willow lynx]

shading above means greater than while shading below means less than. In addition, we should also take the boundary of the region into account, where a solid line means equal to, while a dashed line means not equal to.

i see

thanks

[boreal geyser]

the + 1 is the y intercept in the equation y =mx + b

[willow lynx]

ah okay, thanks

.close

[obtuse pebble]

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[gleaming rose]

what is this question asking me to do?

[gleaming rose]

sorry if its blatant

and also i think ms is miliseconds however i dont know what cs is

is it centiseconds

[royal basin]

yes, centiseconds

[gleaming rose]

so for the first one would i want to convert to kiloseconds? since its 957000

[polar fossil]

sure that would work

[royal basin]

yes, 957 ks

[gleaming rose]

now is there an easy way to convert these?

or kinda intuition

i have these tables

like is there a way to use these values in my chart against the starting value ?

[polar fossil]

just try the two of them on either side of your exponent and see which one works

[gleaming rose]

wait wym?

[royal basin]

ignore the ones for 10^±2 and 10^±1 btw

[polar fossil]

like if you have 3.8 x 10^16 g then try converting into Pg and try Eg

[gleaming rose]

because they wont be within those values?

[gleaming rose]

for this part

[gleaming rose]

so the two areas nearby?

like for example peta, and exa?

[polar fossil]

yeah

[gleaming rose]

so would three would like deka?

i mean b

whoops

[gleaming rose]

would that be an option?

[gleaming rose]

when you said avoid those two

would that mean deka isnt an option for b

.close

[obtuse pebble]

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[jovial coyote]

Ive done all the other questions, the answer i got is -3.51, can you tell me what i did wrong please?#

[kind hawk]

you didn't show any work so how should we do that

[jovial coyote]

ah right

hol on

[kind hawk]

hmm, -3.51 is an approximation to x^3+4x^2-6=0. Maybe they messed up

I assume this is newton, but I don't really wanna plug stuff in to check

[jovial coyote]

so im right and the website is wrong?

ig thats a possibilty

yup it is definently -2.51

3*

alr i'll figure it out eventually lol

thank u for ur time

.close

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[half quartz]

Could someone remind me the rules for this equation?

like, why is this true?

[warm shale]

beard420

beard420

[obtuse pebble]

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[coarse shuttle]

I'm trying to find the general solutions for this algebreically, but i messed something up:
tan(x + 𝜋) + 2 sin(x + 𝜋) = 0

My work is below (sorry about the messy handwriting)

[coarse shuttle]

I used reduction formulas

and then the tangent quotient identity

other than that I just used algebra

does anyone know why I'm missing some answers?

[tulip prawn]

@coarse shuttle you divided 2sin(x) from both sides. How do you know that it is possible?

[coarse shuttle]

oh i see

[tulip prawn]

Is your question answered?

[coarse shuttle]

Partially. I see where I went wrong, and I’m trying to figure out a way around it. I think I found a way, but I don’t know if it will fix my mistake.

so I’m going to solve it that way and see if I get my other answers. If I don’t, I’ll try to figure out where I went wrong from there.

[tulip prawn]

OK, sure. Do you want to close the issue with .close or leave it open?

[coarse shuttle]

I was going to leave it open in case it didnt work

but do you think I should close it and just open a different one if I get stuck again?

[tulip prawn]

Both works

We're not having a help-forum drought so you could leave it here.

[coarse shuttle]

ok. I'll leave it open then

yeah i got it this time

thank you so much :)

.close

[obtuse pebble]

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[civic socket]

!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'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

@sharp whale Has your question been resolved?

[obtuse pebble]

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[teal python]

I dont know if its yes or no can someone give me a hint or tell me if im right

[ruby path]

What's the most recognisable property of an odd function

[teal python]

um

[ruby path]

f(-x) = ...

[haughty coyote]

I feel like this depends on the definition of odd function

Depending on whether it forces that 0 be in the domain or not

[ruby path]

The reason for it going through the origin or the fact that it does go through the origin

[ruby path]

hmm

$f(x) = \frac{|x|}{x}$

[warm shale]

neonperseus

[teal python]

-f(x)

[ruby path]

0 not in the domain but still odd

[ruby path]

yeah good

so what does it mean if I add a constant to any function

[teal python]

you move it

[ruby path]

if I have f(x) = sin x, what does it graphically mean for f(x) + 5

yeah precisely

it moves up

[teal python]

yeah

[ruby path]

now if you have a constant term is it ever possible for f(-x) to be -f(x)

[teal python]

oh wait

no that I think about it the function 1/x doesnt go through the origin

[ruby path]

it doesn't indeed

[teal python]

ok I get your point thanks

.close

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[jagged onyx]

Pls help I have no Idea where to even start off

[jagged onyx]

i tried substituting values for n

didnt seem to work

[haughty coyote]

There's literally no solution between 4 and 8

[jagged onyx]

yea

exactly

<@&286206848099549185> Pls Help Have been waiting for 15 minutes

[haughty coyote]

I don't know what you're expecting

You know there's no solution

So it's impossible to draw any of the mentioned conclusions because they're all wrong

[jagged onyx]

The answer is B apparently

In the key

[violet kindle]

Really?

Im getting smth different

[jagged onyx]

Idk for sure

?

[violet kindle]

Oh wait

Integer

What

Yeah theres no solution when n is an integer

Is that a typo?

[jagged onyx]

no i don't think so

i might be wrong

.close

[obtuse pebble]

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[teal python]

hey @ruby path

remember that problem u helped me with earlier and said the answer was no

well I got a diffrent perspective

would this be right or wrong?

btw anyone else that wants to pitch in the question is

[high lily]

wrong

[sage geode]

The domain of the function may not contain 0 btw

[high lily]

^

[obtuse pebble]

@teal python Has your question been resolved?

[teal python]

yeah but ive been thinkin about the edge case 1/x

@high lily @hazy oyster

[sage geode]

That's a counterexample too though

Wdym

[obtuse pebble]

@teal python Has your question been resolved?

[teal python]

ohh u were the person who agreed with me saying no

ok

.close

[obtuse pebble]

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[knotty sedge]

Hello everybody, for the past few days I am unable to solve this exercise featured in Advanced high school mathematics by David Surowski. The exerise goes as follows:

I am aware that the solution could be really simple, it is just that I haven't stumbled upon it yet.

[knotty sedge]

I tried to prove that the triangles are isosceles, although to no avail

[obtuse pebble]

@knotty sedge Has your question been resolved?

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[summer lynx]

Hey uhm, I have a question. When im looking at an alternating series

[summer lynx]

Im supossed to either use Leibniz or Neccesary condition, right?

Idk if the second one is called like that

[warm shale]

totomc

[warm canopy]

Depends what you mean by "supposed to", those are certainly things you can try yeah

[summer lynx]

oh yeah Im mostly talking about borders

[summer lynx]

But I dont get the difference between these two

In order to use any of those the limit needs to be 0, right?

[fathom flicker]

suppose $$\sum_{n=1}^{\infty} a_n (-1)^n$$ converges. This implies that $$lim_{n\to \infty} a_n (-1)^n=0$$

[warm shale]

austinu

[fathom flicker]

alternating series test will tell you this happens when a_n is monotonic decreasing -> 0

[summer lynx]

the thing is I dont get when to use leibniz or the neccesary condition

[fathom flicker]

what are those?

[summer lynx]

maybe im confused af

[warm canopy]

Check necessary first, as if it fails that then you don't need to check leibniz

[summer lynx]

Sure

[warm canopy]

If it passes, it doesn't tell you it converges, so you might want to try and check with leibniz

[summer lynx]

ooh

and if I goes to 0 but I cant use leibniz?

[warm canopy]

🤷‍♀️

Try anything else

[summer lynx]

but what else can you do for alternating series

[fathom flicker]

alternating series test

[warm canopy]

This is leibniz

[fathom flicker]

ah

[warm canopy]

You can try ratio

Just throw any test at it

(Actuslly I think there are two tests attributed to leibniz but I assume you mean alternating series) thinking of Cauchy, the bastard

[fathom flicker]

i mean the one about if you have series of x_n (-1)^n then this converges if sequence of x_n is monotonic decreasing to 0

[warm canopy]

Mhm that's leibniz alternating series, and is what I assume OP is referring to

[summer lynx]

yes

sorry for not using the proper names

[obtuse pebble]

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[unreal whale]

So I have the work for this problem and got 1/2 idk if it’s correct

[royal basin]

,rccw

[royal basin]

no, incorrect

[unreal whale]

How

[royal basin]

$2^a + 2^b + 2^c = 2^1$ doesn't mean $a+b+c=1$

[warm shale]

Ann

[unreal whale]

But all the bases are the same

[royal basin]

you're trying to take log_2 of both sides, yes?

[unreal whale]

Why log again?

[royal basin]

that's how you go from 2^a = 2^b to a = b

by taking the log of both sides

[unreal whale]

Oh

[royal basin]

it doesn't work if there is a SUM of powers on either side

like for example

2^4 + 2^3 + 2^3 = 2^5

does NOT mean 4 + 3 + 3 = 5

[unreal whale]

Oh

Okay what happens when u take the log of both sides

I need a refresher

[hybrid gull]

,tex .log rules

[warm shale]

shenny17

[unreal whale]

Then what?

[royal basin]

as-is? you get $\log_2(2^{2x} + 2^{2x+2} - 2^{2x-2}) = 1$, which doesn't help you.

[warm shale]

Ann

[unreal whale]

Yea

Is the answer weird?

[royal basin]

i don't know what that question is supposed to mean

but here is what you could do to solve the equation $4^x + 4^{x+1} - 4^{x-1} = 2$:

write $4^{x+1}$ as $4 \cdot 4^x$ and $4^{x-1}$ as $\frac{1}{4} \cdot 4^x$, to get $$4^x \cdot \paren{1 + 4 - \frac{1}{4}} = 2$$

[warm shale]

Ann

[royal basin]

@unreal whale

[A] I do not understand what you've written.
[B] I understand what you've written, but I don't see how to continue.
[C] I understand what you've written and am continuing from it now.

[obtuse pebble]

@unreal whale Has your question been resolved?

[unreal whale]

B

[hybrid gull]

You can start by simplifying @unreal whale

[royal basin]

specifically simplifying the 1 + 4 - 1/4 here, as doing anything else is basically like going directly backward.

[hybrid gull]

^

[unreal whale]

Then what

[hybrid gull]

Continue solving for x?

ya gotta figure this out somewhat for yourself my friend

[royal basin]

show what you've got.

[unreal whale]

Never mind I’ll ask for help later thanks tho

I don’t have time right now

.close

[obtuse pebble]

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[fringe rivet]

I am not really sure what it means by unique

How can i show creativity if they're just equations

[fierce geyser]

It says it in the instructions

The word problems should be created by you and have a unique description

[fringe rivet]

wdym by a unique description

[devout harness]

I know a situation where you might wanna solve for the maximum on a quadratic equation. Suppose you have a monopoly on some product, with a linear relation between the price you set and the amount you'll sell, and a constant cost....

can you continue on what I was going for?

[fringe rivet]

Oh so you need almost like a reason for why you need to make an equation

[devout harness]

yeah

[fringe rivet]

i can def use this

so basically you want me to find the best price to sell the most amount?

[devout harness]

to make the most money, yes

[fringe rivet]

ya thats simple enough

thanks

[devout harness]

np

[fringe rivet]

.close

[obtuse pebble]

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[fringe rivet]

.reopen

[obtuse pebble]

✅

[fringe rivet]

did i do this correct?

so the zeros are -2 and 6

and passes through 1,4

[obtuse pebble]

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[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'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

[timid silo]

2

[obtuse pebble]

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

[timid silo]

I get confused where we assume |g(x) - M | < |M|/2

[fathom flicker]

what is your definition for limit convergence?

[timid silo]

I started with taking delta > 0 such that if 0 < |x - a| < delta, then there must be |g(x) - M | < epsilon

But it didn't worked

[fathom flicker]

We say $f(x)$ converges to $L$ is as $x\to c$ $$\forall \varepsilon >0 \exists \delta >0$$ s.t. $0<|x-c|<\delta \implies |f(x)-L|<\varepsilon$

[warm shale]

austinu

[fathom flicker]

does this look familiar

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[gloomy comet]

guys i have a question is there a way to use the log base number on keyboard

[gloomy comet]

for example for exponent

i do ^

[fathom flicker]

just write log_b()

with the underscore representing underscript

[gloomy comet]

ok got it thank u

[fathom flicker]

the b representing the base

and then the argument of the log would go inside the ( )

[gloomy comet]

can u send me a ss on how that would look like on wolfram

[fathom flicker]

log_5(25)

$\log_{5}(25)$

[warm shale]

austinu

[fathom flicker]

log_5(25)

like that

[obtuse pebble]

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[obtuse pebble]

@meager elm Has your question been resolved?

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[glossy grove]

cos x - sec x = 4 sin x . Solve for 0<= x <= 360

[glossy grove]

So my method is cos x - 1/cos x = 4 sin x

then I multiply everything by cos x

cos^2 x - 1 = 4 sin x cos x

cos^2 x -(sin^2 x + cos^2 x) = 4 sin x cos x

-sin^2 x = 4 sin x cos x

4sin x cos x + sin^2 x = 0

sin x(4cos x + sin x) = 0

sin x = 0 or 4 cos x + sin x = 0

sin x = 0 or tan x = -4

Is this correct?

from there x = 0 or 2pi or pi

My other question is since I multiply everything by cos x, wont there be an answer for cos x?

[weary delta]

Looks fine to me but there are infinite solutions not 3

[glossy grove]

the question wants Solve for 0<= x <= 360

[glossy grove]

How about the step where I multiply everything by cos x

wont cos x give a solution too?>

[weary delta]

It won't change the set of solutions

[prime reef]

cosx is assumed not to be 0 since it s in the equation at the denominator

[prime reef]

maybe assumed isnt a good word here, we need cosx to not be 0

[weary delta]

You do make an assumption so I guess the word choice is fine

[glossy grove]

I see, makes sense

but the cos x wont give me another set of solutions yea

[prime reef]

an assumption is when you think something is true without being sure

cosx can not be 0 so i m not really assuming

a good example of this is when you make an assumption to solve a problem, you want to prove the statement A is true so you assume that A is not true and you want to get to a contradiction, the fact that you are assuming that means that you don't really know whether A is true or not, but here that isn't the case

there is no "cosx could be 0" scenario

[glossy grove]

cos(x-45) = sin x. Solve for 0<=x<=360.

How would I do this question

I used addition formula and expanded the cos function

[weary delta]

Convert the cos into a sin?

Or the sin into a cos?

[prime reef]

yeah that should be a better method

sinx=cos(pi/2-x)

[weary delta]

After that arccos/arcsin of both sides, since the domain is restricted you should get the answers right away

[glossy grove]

How do I convert cos(x-45) into sin

The formula sheet says cos(x-45) = sin x

but then I will get sin x = sin x

[prime reef]

the formula sheet should say cos(pi/2-x)=sinx

cos(90-x)

[glossy grove]

Oh am I suppose to change the right hand side, sin x = cos (90 - x)

then cos inverse both sides

x - 45 = 90 - x

brilliant! thank u

[prime reef]

eeehh

[glossy grove]

x = 135

[prime reef]

i dont like it

[glossy grove]

am i suppose to have 2 answers for this?

[prime reef]

lets say cosx=cos45

what is x

[glossy grove]

45

[prime reef]

arent there more solutions?

[glossy grove]

and 315

[prime reef]

so you got cos(x-45)=cos(90-x)

you arent sure if there are more solutions or not

[glossy grove]

yeah

there should be I think

[prime reef]

do you know the general solution to this?

[glossy grove]

because question wants 0<= x <= 360

[glossy grove]

45+ 360n, 315+ 360n ?

but if I got the answer as 135

[prime reef]

yeah looks ok...a better way to write this is 360k+-45

[glossy grove]

Can't I say 2nd and 3rd quadrant

So x =135 and 225

[prime reef]

what would the general solution to this be

btw i just realised u got 2x=135 so x= 135/2

[glossy grove]

Will it be 135/2 +- 360k

[prime reef]

since you have cos(x-45)=cos(90-x) you will have x-45=360k+- (90-x)

so x-45=360k+90-x => 2x=360k+135, x=180k+135/2

and x-45=360k-90+x which gives -45=360k-90 which is not possible

so x=180k+135/2 is your GENERAL solution

but you want x to be between 0 and 360 so what do u do

[glossy grove]

Let k be 1

And 0

To get 2 solutions

[prime reef]

yeah

the "nice" way to do this is 0<x<360 => 0<160k+135/2<360 => -135/2<160k<360-135/2

and you find the acceptable values for k from there

but when you just want the answer it s much faster to never do this, but good to know exactly what to do if you are confused or unsure

[glossy grove]

Thank you so much, this helps alot with my understanding

👍

[obtuse pebble]

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[obtuse pebble]

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[tacit briar]

what is the expected value of head when you flip 2 fair coins?

[tough stirrup]

75% I believe

[tacit briar]

Wrong

[keen quarry]

1/2?

[tough stirrup]

.5 + (.5*.5) is it not?

TT, TH, HT, HH

[obtuse pebble]

@tacit briar Has your question been resolved?

[tacit briar]

It’s 1 bruh

[nocturne minnow]

If you know the answer, why did you open a channel?

[obtuse pebble]

@tacit briar Has your question been resolved?

[obtuse pebble]

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[long hedge]

why does an exponential have to be positive

[grizzled shore]

because $e^{\text{real number}}>0$ for all real numbers

[warm shale]

frosst

[long hedge]

in english

we know it needs to be positive

[grizzled shore]

a positive number

to the power of some other (real) number

is always bigger than 0

,calc 0.5^0.01

[warm shale]

Result:

0.99309249543704

[long hedge]

ok captn obvious

[grizzled shore]

well, that's why this is true

[long hedge]

why does the base have to be pos

[grizzled shore]

because if you had say -1 as your base

then -1^2 is 1

but -1^3 is -1

[long hedge]

so its just because we want it to grow

[grizzled shore]

also, -1^0.5 becomes undefined unless you extend to imaginaries

[obtuse pebble]

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[stable apex]

a always 2?

or the previous value?

and what is n?

is that the index position?

[strange frost]

a is the first value of the sequence. I think question #2 has a typo, the first term should be 107 otherwise it doesn’t make sense

[strange frost]

Yes, the “nth term”

[stable apex]

so this is the common equation for finding the sequence?

[obtuse pebble]

@stable apex Has your question been resolved?

[whole dock]

What do you mean by "this"

[whole dock]

It's for finding the nth term of the sequence

[stable apex]

ok

thank you so much

.close

[obtuse pebble]

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[timid silo]

A motor boat whose speed in still water is 18 Km/hr takes 1 hour more to go 24 km upstream that to return down to the same spot. Find the speed of the stream.

[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'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

[timid silo]

3

I got an answer but I'm told it's wrong

[timber island]

i see

can u show ur working?

how u got ur answer i.e.

[timid silo]

well... i did that in rough section😕

[timber island]

sed. do u remember ur answer?

[timid silo]

i got an equation 540 + 84x - x^2

[timber island]

i see

[timber island]

well 24/t = 18+x and 24/(t+1) = 18-x

so 24/t + 24/t+1 = 36

[timid silo]

oh shit

i realized my mistake

[timber island]

so t = 1 (hour) or -0.6 hour

[timber island]

what was it?

[timid silo]

i wrote - instead of +

mistake in sign

sed life:/

[timber island]

it happens

well good u found ur mistake

are u able to get the correct answer now?

[timid silo]

yup

its 6

[timber island]

nice

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

polid

[obtuse pebble]

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[spring goblet]

Can I please have some help on this question?

[obtuse pebble]

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

[spring goblet]

I am unsure how to attempt the question but have considered 8-H as the empty space

for part b) 96 is the volume but I am unsure why it asks to minus 1/3s^2(8-H)

also, which part am i differentiating?

I have also considered the rate as being dV/dT

for part a) am i able to sub in 6 for s and show when h = 0 s = 6

[obtuse pebble]

@spring goblet Has your question been resolved?

[bold bane]

Do you understand how similar triangles applies here?

[obtuse pebble]

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[marsh summit]

Hello, I am having trouble with this pattern, may someone help me

And maybe give me some tips on finding patterns quicker, as a have an upcoming exam

I*

[winter radish]

5 + 6 + 7 = 6*3
9 + 2 + 7 = 6*3
11 + 6 + 8 = 7*3

14 + 4 + 12 = 30

30 = 10 * 3

[candid yarrow]

you can use backslash to escape

[winter radish]

thx

[candid yarrow]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[winter radish]

ah srry

[marsh summit]

ahh ok

do any of you have any tips of finding patterns quicker?

[candid yarrow]

try adding the numbers, finding their differences, or multiplying them

otherwise, there isn't a fixed way to solve these

and you likely won't see them again at a higher level, since they can have multiple answers

[marsh summit]

ohh ok

thank you

.close

[obtuse pebble]

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[obtuse pebble]

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[merry vault]

I need to get the basis of this vector space

Can someone give me an algorithm of how I can do that

I am lost on how to proceed

[brisk grove]

try to isolate z from x + y - z = 0

find the general form of a vector in your subspace

[merry vault]

wdym with general form

oh hm

x+y = z
so (x,y,x+y,w) or?

do I have to find a generating system?

.close

[obtuse pebble]

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[brisk grove]

yes

try to express that as a linear combination

[merry vault]

.reopen

[obtuse pebble]

✅

[merry vault]

a(1,0,1,0) + b(0,1,1,0) + c(0,0,0,1)

.close

[obtuse pebble]

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

Hello, I need help

[timid silo]

Can someone please explain to me why the fourth line shows the anti differentiated substituion thingy as added rather than minused

Like it is anti differentiated and then the upper and lower bounds replace x as normal\

but why is it added instead of minused

bc the definite integral formula is F(b) - F(a) iykiwm

[kind hawk]

there is a minus in the antiderivative itself

[timid silo]

OHHHHH

[kind hawk]

it would be -(-cos(...))

[timid silo]

I AM BLIND

thank you lol ;-;

.close

[obtuse pebble]

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[strange sequoia]

Hey i need to know wheth3r im doing the right thing

[strange sequoia]

Thanks

Let me know if you don't understand something. Cheerd

Cheers*

[candid yarrow]

have you learnt polar form yet?

[strange sequoia]

Yes i did

[candid yarrow]

you can use it here

[strange sequoia]

But the question says working entirely in cartesian form

[candid yarrow]

to check your answer

[strange sequoia]

oh oh fair enough, but is wht im doing correct?

or nah?

[candid yarrow]

I think so

[strange sequoia]

alright thanks, real quick tho...how does the sqroot 2/2 10 work

is tht an improper fraction?

or do i js times sqroot 2/2 and 10 to get like a proper number

coz whn i try to solve this on the calc, it doesnt let me

[candid yarrow]

they are the same thing

[strange sequoia]

ye but like the calc doesnt like it js like tht

[candid yarrow]

what did you enter into the calculator

[strange sequoia]

it gives me a syntax error

[strange sequoia]

hol up lemme show u

[candid yarrow]

was it “10sqrt(2)/2”

[strange sequoia]

thts wht i entered

[candid yarrow]

because it means multiplication

[strange sequoia]

ye...

so how do i enter it?

like

whts the correct way?

[candid yarrow]

enter it as if it were multiplication

because that’s what it is

[strange sequoia]

so put a * in the middle?

[candid yarrow]

yes

[strange sequoia]

gotcha

thank you!

appreciated

[candid yarrow]

did this work?

[strange sequoia]

i got 7 sqroot2 / 20

i dont have the ans key so i cant tell if its right

but thts wht i got

[candid yarrow]

even if you don’t have that, you can still try verifying by using the polar form

[strange sequoia]

how do i do tht

cant recall

polar form is the sin cos one right?

[candid yarrow]

yes

[strange sequoia]

so r is

sqroot of a^2 +b^2 right?

but thn whts theta

[candid yarrow]

arctan ( b/a), if you remember

[strange sequoia]

oh ye true

and thn to divide them

i js normally divide it on the calc ye?

[candid yarrow]

what do you mean

[strange sequoia]

holup

illl do it an get back to u

so i got this

[timid silo]

Imagine using a cg50 smh

You do A levels, right?

[strange sequoia]

i use to a ti but it isnt charged atm lol

[timid silo]

Ah ohk nvm

[candid yarrow]

try to use exact form instead of decimals

[strange sequoia]

gotcha but how do i divide that

like i got tht ans then?

[candid yarrow]

divide what?

[strange sequoia]

like tht

[candid yarrow]

go back and replace all decimals with their original form

[strange sequoia]

its only one decimal...the 53.13 one

[candid yarrow]

[candid yarrow]

does that contradict what I said

[strange sequoia]

nah im js saying

[candid yarrow]

do you know how to divide polar forms?

[strange sequoia]

do u just uhh divide the r and subtract the theta?

yes pre sure but thn i end up with 0.5 (8.13010235 cos theta - i 8.13010235 sin theta)

[candid yarrow]

use exact forms, not decimals. arccos 0.7071 is unclear, but arccos sqrt(2)/2 is clearly 45°

[strange sequoia]

ok ok

thanks

.close

[obtuse pebble]

Channel closed

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[strange sequoia]

.reopen

[obtuse pebble]

✅

[strange sequoia]

is this correct?

[candid yarrow]

5/11 ≠ 0.45

You used decimals instead of the exact form, you could use ≈ instead of =

[strange sequoia]

oh ok ok

[candid yarrow]

writing 5/11 cis -pi/6 is perfectly fine

[strange sequoia]

aight thank u

[candid yarrow]

otherwise it all looks correct

[strange sequoia]

thanks

[candid yarrow]

has your question been resolved? @strange sequoia

[strange sequoia]

yes thank u

[candid yarrow]

.close

[obtuse pebble]

Channel closed

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[obtuse pebble]

Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[glacial tree]

Is this the correct answer? Since the answer for solving the equation is )20+_ sqrt-404 ) /6

[obtuse pebble]

Please don't occupy multiple help channels.

@glacial tree Has your question been resolved?

[fierce geyser]

Top G

[obtuse pebble]

@glacial tree Has your question been resolved?

[glacial tree]

.close

[obtuse pebble]

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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[glad jungle]

Why is N an empty set?

To me it honestly makes no sense

[hollow wind]

Maybe they made a mistake or something because I also can't see why N is an empty set

[trim portal]

for all t in R

[glad jungle]

Shouldn't it be an infinity set?

[glad jungle]

But in what way would that make it an empty set?

[trim portal]

It's set of all x in R^2 that satisfy following property:( x = t[1, 1] for all t in R)

does there exist some pair of numbers which equals t[1, 1] for all values of t?

which equals 1*[1, 1], 4*[1, 1], -6*[1,1]... at the same time

[glad jungle]

Ah right, only [0,0] i guess

[hollow wind]

This is not what "for all" means in set theory though

[glad jungle]

To be honest I do think he is right tho

Just don't really know about the [0,0] case

[trim portal]

What's your interpretation?

[trim portal]

x=[0,0] wouldn't work. [0, 0] doesnt equal 1*[1, 1]

[hollow wind]

The usual interpretation is that this is a line of y = x

[glad jungle]

ah ye haha indeed

[glad jungle]

That's why there is "some" in the question above

[hollow wind]

Yeah, that's just a really odd way to phrase it, is this pre-university?

[trim portal]

I dont think it's odd actually

maybe it would be clearer with parenthesis

but otherwise it seems ok

[hollow wind]

I've personally never seen it, any time I've seen "for all" it's meant the same as "∀"

[trim portal]

it means

[glad jungle]

I have no clue, was helping someone else but found it strange in the beginning aswell, but for me MethIsAlwaysRight his explanation makes sense

[trim portal]

N = {x ∈ R^2 : ∀(t ∈ R)(x = t*[1, 1] ) }

[trim portal]

this set should be equal to empty set

[hollow wind]

No, that's my point, it doesn't mean that

Because that's not an empty set

[trim portal]

You claim that this is not an empty set?

consider x = [1, 1]. Now in order for it to belong to that set, it must be true that ∀(t ∈ R)(x = t*[1, 1] )

i.e ∀(t ∈ R)([1, 1]= t*[1, 1] )

now consider t=4, in order for condition above to be satisfied, this particular example t=4 must be satisfy (necessary condition)

hence [1, 1] must equal 4 * [1, 1]

which is not true, so [1, 1] isnt in that set

[glad jungle]

Alright thanks for the help @trim portal , you guys close the channel after you done with your convo?

Or can I close it now?

[trim portal]

You can close it I guess

[glad jungle]

Alright, thanks!!

.close

[obtuse pebble]

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[true spire]

i simply dont remeber calculating with cyclic numbers i guess

when i look it up modulars come up and i dont jazz about it...

[royal basin]

cyclic numbers?

also is that . meant to be multiplication?

so $0.2\overline{7} \cdot A = B$

[warm shale]

Ann