help-23

[obtuse jackal]

Base completion theorem ? I.e. that any free family can be completed into a base by adding some other elements to it ?

[obtuse jackal]

Given a basis already exists

[solemn epoch]

So I could use this basis completion theorem?

[obtuse jackal]

Depends on whether you've seen it

But honestly that's interesting theory to know (to really get a good graso of linalg) but here it's much faster to just directly prove it's spanning

[solemn epoch]

Yeah I kinda agree. So to prove spanning, do I have to show each set is contained in the other?

[obtuse jackal]

No, just that, by definition, span(your 3 vectors) contains S

[solemn epoch]

How would I show that?

[obtuse jackal]

That's another good thing to know

Span(A) = Span(Span(A)) contains Span(some vectors of Span(A))

[obtuse jackal]

Thus it suffices to show that you can construct u, v, w

[solemn epoch]

Cause I was thinking that the second set of vectors can be shown to be a linear combination of the first set of vectors just by distributing arbritary coefficients and showing that the second set of vectors is a linear combination of the first set (defintion of span).

I was just struggling to really show that the first set spans the the second one

[obtuse jackal]

Do you understand that? If so, is this what you're struggling to show ?

Cause your explanation has me a little confused as to how to interpret it

[solemn epoch]

What I was trying to say is that basically I can show a(u + w)... for some a in R, and then I can distribute and collect like terms to show that we have (a +b)u which is just a linear combination of u which is in the span of the first set of vector u

[obtuse jackal]

Why would showing that be a proof ?
||You've got it in reverse||

[solemn epoch]

I would say that it was one part of the proof with the second part being the other way around

Which I assume covers the reverse part?

[obtuse jackal]

Just do it rather than making complicated plans for simple things

But all you want is to express u, v and w in terms of these 3 vectors. That shows it's a spanning family.

[solemn epoch]

Alright lemme see if I can do that

.close

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[safe radish]

Please don't occupy multiple help channels.

[novel magnet]

im kinda stuck after this

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[upbeat ridge]

Can anyone help me with these two questions?

[upbeat ridge]

For question number 1, I'm not sure which form to use

Should I be using recursive or explicit and why?

[sweet mica]

Explicit better because you directly substitute 20

If recursive you have to calculate a20 with a19 with a18 with a17...

[upbeat ridge]

How do I know the common ratio?

I don't know the value of the 1st term

[safe radish]

@upbeat ridge Has your question been resolved?

[hardy crescent]

first term * ratio^4 = 45
first term * ratio^7 = 360
find first term and ratio from this then find 20th term

[safe radish]

@upbeat ridge Has your question been resolved?

[upbeat ridge]

I know the equation, but how do I get the ratio?

first term * ratio^4 = 45
first term * ratio^7 = 360
first term * ratio^20 = Final answer

[hardy crescent]

first term * ratio^7 = 360
first term * ratio^4 * ratio^3 = 360
45 * ratio^3 = 360

magic

[upbeat ridge]

What can I do with that

[hardy crescent]

find ratio

[upbeat ridge]

How?

[hardy crescent]

ratio^3 = 360/45
ratio^3 = 8
ratio = 2

find first term by putting this value in either given equations and find first term the 20th term

[upbeat ridge]

Ah okay, thanks

.close

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[wraith swift]

mind explaining the wordings?

[wraith swift]

anyone

?

[nova creek]

,rotate

[nova creek]

What exactly are you confused about?

[wraith swift]

the wordings

I can't make out what the second method with graph is trying to convey

[nova creek]

We have the graph y = |x| and y = 5

[wraith swift]

where did the y=5 come from? isn't module function just y=|x|?

[nova creek]

The solution to |x| = 5 is where the two graphs intersect

y = 5 comes from how we're solving |x| = 5

[wraith swift]

can you elaborate?

[nova creek]

The solution to f(x) = g(x) is the x value(s) where f(x) and g(x) intersect. Just let f(x) = |x| and g(x) = 5

[wraith swift]

where f(x) and g(x) intersect

is this a method or rule or something?

I never seen it before 🤨

[wraith swift]

so x for f(x)=-5 and g(x)=5?

it should come out (5,5)then tho

[nova creek]

Well, we're setting the y values of the functions equal; that's what f(x) = g(x) means. We are also trying to find the points where the x values are equal; those x values are the solutions to f(x) = g(x). If the x value and the y value are equal, then they're the same point

[nova creek]

No; -5 ≠ 5. f(x) = |x|

[wraith swift]

umm

im not so sure I know you are trying to convey.

you can try to use computer functions to elaborate if u wish i am a programmer

[nova creek]

If two functions intersect, then they share a point. Thus, the y value and the x value of that point is the same

Let's try the other way around. How would you find the points where y1 = f(x) and y2 = g(x) intersect?

[wraith swift]

not sure how, I just started with functions

[nova creek]

Well, if the functions intersect, then at that point, they have the same y value, right?

[wraith swift]

can you give an example?

on desmos maybe?

[nova creek]

Gimme a sec

[wraith swift]

kk thnx

[nova creek]

You see how the red and blue lines intersect at x=1?

[wraith swift]

yea

iam following you

then

[nova creek]

Do you see how, at the point where they intersect, the point on both graphs are the same? If they weren't the same they wouldn't be intersecting

In other words, if the blue line is f and the red line is g, then f(1) = g(1), because they intersect at 1

[wraith swift]

yea one is (-1,5) and other is (1,5)

[wraith swift]

so we are proving them same or something?

[nova creek]

? Neither my graph nor your graph intersects at (-1, 5) or (1, 5)

[wraith swift]

sorry

not this one

[nova creek]

Mine intersects at (1, 1), while yours intersects at (-5, 5) and (5, 5)

[wraith swift]

yea

i got that

[nova creek]

Point is, if they intersect, they share the same point, yeah?

[wraith swift]

yea

they intersect

they share the same image you mean??

[nova creek]

So, in regards to this comment, the y values of the functions are equal at that point? Aka, y1 = y2?

[wraith swift]

yep

[nova creek]

And if y1 = f(x) and y2 = g(x), then f(x) = g(x)?

[wraith swift]

yea

true

[nova creek]

Thus, if we want to find the points where f and g intersects, we have to solve f(x) = g(x)

[wraith swift]

they produce the same result no matter what yes

[wraith swift]

yea but what is the point of all this??

[nova creek]

We can go the other way around too. If we want to solve f(x) = g(x), then we can just find the points where f and g intersect

In our case, if we want to solve |x| = 5, we can just find the points where y = |x| and y = 5 intersect

[wraith swift]

yea I get that

[nova creek]

And the intersection points are x = -5 and x = 5

[wraith swift]

but why are we doing all this?

the concluding statement says there are solutions but isn't a function only supposed to have one image?

[nova creek]

Wdym?

[wraith swift]

why are we proving f(x) = g(x)?

[nova creek]

Because the question wanted us to solve |x| = 5

The graphical interpretation of this statement is the intersection of |x| and 5

You were confused about the graph, no?

[wraith swift]

nah i was confused about why are we doing what we are doing

and where does it all connect

a little bit about the graph too yea, but mostly that

[nova creek]

The problem told us to solve |x| = 5. We are solving that because it told us to. There are two ways to do it: algebraically or graphically

[wraith swift]

wait a second again

|x|=5 means??

[nova creek]

The graphical method is to find the intersection between |x| and 5. Why? Because of this comment

[wraith swift]

i mistook it for (x)=5 🤦🏻‍♂️

(i know what |a| does, mod function right)

[nova creek]

Mod function?

[wraith swift]

modulus?

f(x)= |x| y=positive value of x right

[nova creek]

I see. There's another function called the modulo which gives the remainder after dividing. I got confused

[wraith swift]

yea

[nova creek]

The similar names make me think there might be a connection between the two, but that's irrelevant for this problem

[wraith swift]

yea

[nova creek]

Is there any more confusion?

[wraith swift]

yea i still wonder what is that

why we do it i mean

[nova creek]

Why we do what?

[wraith swift]

I'm confused on why do we do what we do for given question
I am not so sure about the question itself

[nova creek]

What do you mean "why we do what we do?" What are we doing that you are confused about?

[wraith swift]

explain the question

that shall solve it

what does it ask us to do?

[nova creek]

Solve |x| = 5

[wraith swift]

is it asking us to prove |x|=5

[nova creek]

It's hard to prove that, because |x| and 5 are two different functions

[wraith swift]

im not sure what this is

[nova creek]

It wants to know what x values give us 5. The solution are -5 and 5. Why? Because |5| = 5 and |-5| = 5. Why isn't, say, 4 a solution? Because |4| = 4 ≠ 5

[wraith swift]

AH

FINALLY

I GET IT

It wants to know what x values give us 5

you could have told me earlier

😂

[nova creek]

Yes. It might be more general to say what x values make both sides equal, because you may have an x value on both sides

[wraith swift]

https://tenor.com/bdOF4.gif

.close

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[pseudo verge]

hi

[pseudo verge]

can someone check my answers?

i have two answers for this one. i'm unsure about it

[sacred wren]

for every monomial, if it has an x, differentiate with a dx at the end, if it has a y, differentiate with a dy, then solve for dy/dx

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[brisk nimbus]

I am looking for the lower and upper quartile for this data. Since 4 is the median, should I exclude it and only use the yellow part for Q1 and red for Q3?

[cobalt parrot]

no do not exclude it

[brisk nimbus]

so Q1 is the median of the first five, and Q3 the median of the last five

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[pastel vessel]

Hey how do I use the "bsplinecurve" command in WolframAlpha? Whenever I try to use it WA doesn't interpret it.

[final halo]

Have you looked at the documentation?

[pastel vessel]

Yes, it didn't really help.

[pastel vessel]

How do I make multiple inputs as shown in the example?

[final halo]

First line of code in the example

[pastel vessel]

What about it?

[final halo]

What are you asking?

[pastel vessel]

I am asking, how do I make an input myself using bsplinecurve with my own control points?

[final halo]

And what exactly in that example is not helping you to do that? pts is a list of control points

[pastel vessel]

This

[final halo]

That is a matrix, not a list of points

Do it the same way the example does

[pastel vessel]

I literally copied it from the example

[final halo]

It looks like you're using wolfram alpha, which is not wolfram

I think its a mathematica function

[pastel vessel]

Oh, so I suppose there isn't one for WA.

Thanks for the help anyway.

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[oblique citrus]

Hi ! I was wondering why $y'+2y = x^2$ and $y'-2xy =0$ were considered first order linear differential equations, but $xy' -3y = x^2$ isn't ?

[flat frigate]

Nini

[obtuse jackal]

are you sure about that ?

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[oblique citrus]

it's what my exercise tells me..;

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[plucky elk]

Show the original question

[sweet mica]

It is a linear equation since it involves linear combinations of ${y^{(i)}}_{i=0}^\infty$ over a ring of derivable functions

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[flat frigate]

Categorist

[solid horizon]

How would you reflect something over a curved line (if you can)?

[ionic jasper]

yo can anyone help me with a trig question

oh nvm

[ionic jasper]

use formula ig

[solid horizon]

what formulae?

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[signal granite]

Prove that the solution set of a system of linear equations does not change if you perform an elementary
row operation of type III (Ri → Ri + λR)

[signal granite]

How would i go about this?

a tip i got: show that s is a solution of a system of linear equations S1 if and only if s is also a solution of the system S2. S2 being S1 after the row operation Ri → Ri + λR

but i have no idea how id do that

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[signal granite]

.close

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[livid knoll]

how to find tangent line

so i can find the rate of change

[buoyant shadow]

it's like, on top of that line

it's already straight

[livid knoll]

o

how to find its slope

from that sketch

it might be inaccurate

the

sketch

[buoyant shadow]

you don;t get anything else

have to trust the sketch

[livid knoll]

oki

[buoyant shadow]

draw a line with a ruler to the x=2 line

[livid knoll]

ty

.close

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[slow basin]

Does anyone know a formula for this question? I could really use some help! Thank you!

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@slow basin Has your question been resolved?

[slow basin]

The formula I think is used in this problem is h/a + h/b = 1
But I don’t know how to plug the number into the equation.

[fierce ore]

I think you can solve it like this

Suppose both have a time function for the amount of work done

f(t) = t/60
g(t) = t/240

f(t) +g(t) = 5t/240

So you would need 240/5 minutes for the work to be done

So 48 minutes

I don't know if it's right but at least it somewhat makes sense

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[tulip axle]

Idk, this seems like an exam

We are not allowed to help

Nor would we want to help

In this case

[spark vine]

This is not an exam

this is a practice paper

[tulip axle]

Well, the chart is self explanatory

If 120 watched james bond, how many watched spiderman?

[spark vine]

I just cant figure out the 2 boxes

got it right

nvm

.cloe

.close

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[vagrant sand]

What is the probability the outcome of rolling two 6-sided die is an odd number?

[vagrant sand]

would this be 3/4?

[tulip axle]

1 1
1 2
2 1
1 3
3 1
1 4
4 1
1 5
5 1
1 6
6 1
2 2
2 3
3 2
...

Think you can see the pattern

Just get the odd ones, divide by the total

[cedar rover]

What the probability of rolling a single 6-sided dice and getting an odd number?

@vagrant sand ?

are you there?

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[trail schooner]

Could someone please explain how to find “the function rule k(x)”

One question I had was where they got the 1 from in the solution

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[trail schooner]

<@&286206848099549185>

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[trim silo]

hey everyone! this is for my calc 2 class and I got the answer of 0.7275. I dont feel this is right and the question is also asking for volume. Does that matter? Thanks!

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@trim silo Has your question been resolved?

[vocal portal]

but in a certain manner

[vocal portal]

how would it be different from left endpoint method?

[trim silo]

Like this?

[vocal portal]

seems good

[trim silo]

ok thanks so i guess the final answer would be 0.7275 mm^2

.close

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[lean otter]

$$\left(\frac{\sqrt{2}+1}{\sqrt{2\ -1}}\right)^2+\left(\frac{\sqrt{2}-1}{\sqrt{2+1}}\right)^2+2\cdot \frac{\sqrt{2}+1}{\sqrt{2\ -1}}\cdot \frac{\sqrt{2}-1}{\sqrt{2+1}}$$

[flat frigate]

ItzGriz

[lean otter]

why is it

just

not

\solve

/close

.close

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[safe radish]

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[turbid osprey]

how would i set this up?

[leaden canyon]

find the number of possible committees with no art students

[buoyant shadow]

and also commitees with no additional constraints

[turbid osprey]

23?

18 with noner

[leaden canyon]

a committee has 4 students

[turbid osprey]

oh

no art would be 4

with extra 2 ppl

so 5?

[leaden canyon]

haev you learned combinations/permutations

[turbid osprey]

i kinda started

but he said to do this

[hybrid mauve]

ive got some summer school course for math because i barely failed it

and this question

oooh this question

[lean chasm]

@hybrid mauve #❓how-to-get-help

[hybrid mauve]

shit man

[turbid osprey]

i just dont know what to do

[leaden canyon]

then lets start with finding the total number of committees possible

[turbid osprey]

6

[leaden canyon]

without consideration of whos an art student/drama/band

how did you get that

[turbid osprey]

a comm has a max of 4

but like there 3 extra

missing 1

[leaden canyon]

3 extra?

[turbid osprey]

yea

[leaden canyon]

wdym

[turbid osprey]

8+10+5=23

[leaden canyon]

yes

[turbid osprey]

/4

is 5.75

but i just made the .74 into another group

[leaden canyon]

thats the number of committees that you can split them into

[turbid osprey]

because the other 3 has no where to go

[leaden canyon]

we are trying to find all possible committees

[turbid osprey]

wdym but all?

[leaden canyon]

imagine you want to create a group of 4 people

and you want to select the people from a pool of 23 people

how many different groups of 4 can you make?

[turbid osprey]

6

5

5

[leaden canyon]

hmm... idk how to explain this well

[true ingot]

iirc isn't there just a formula for this

[leaden canyon]

its combinations

[true ingot]

yeah

[turbid osprey]

so nCr?

[true ingot]

yeah

[leaden canyon]

but trying to teach the reasoning behind it

[turbid osprey]

but how would i set it up?

i dont know what n and r are

or like represeting

[true ingot]

well n is just the total number of students

cause that's all of the elements in the set

or am I tripping

[leaden canyon]

yes

[true ingot]

then r is how many you "pick"

[leaden canyon]

you need to first find the total number of possible committees

[turbid osprey]

so n would be all and r will be the grouop?

[leaden canyon]

then find the total number of possible committees excluding any art students

and subtract them for the answer

[turbid osprey]

so it would be 23N5?

[leaden canyon]

23c4

[turbid osprey]

C

why 4?

[leaden canyon]

the committee is 4

idk where you got 5 from

[turbid osprey]

the possible groups

[turbid osprey]

=8855

[true ingot]

It's been a while since I've done this, but isn't the easiest way to solve this just finding how many combinations of the 3 other spots aside from the art student spot

so 18C3

then multiply it by 5 for each of the 5 art students?

I mgiht be wrong

[turbid osprey]

umm idk

[turbid osprey]

^?

[leaden canyon]

ok what does 23c4 give you

[turbid osprey]

8855

[leaden canyon]

i mean what does that number represents

[turbid osprey]

ummm the amount of ppl that can fit in a group

[leaden canyon]

no that would be 4

[turbid osprey]

outcomes

of the 23?

[leaden canyon]

can you clarify a bit more?

[turbid osprey]

like could be like 1 from each class into a group or like 2 and 2 or 3 and 1

like if u had the word cat

uncan write it 6 ways

[turbid osprey]

smt like that

[leaden canyon]

yeah its the total number of possible committees

i have to go. the answer is 23c4-18c4. 18 because you remove the art students from the selection pool

[turbid osprey]

oh

ok thanks

[true ingot]

oh wait it's at least 1 art student I'm smooth brained

[turbid osprey]

lol

[true ingot]

but yeah that's correct since 23c4 is the total number of groups

then 18c4 is the total number of groups without an art student

[turbid osprey]

so no 5?

[true ingot]

no

where di the 5 come from

[turbid osprey]

groups

[true ingot]

?

you're making 1 group of 4

[turbid osprey]

like the possible groups

of 23

[true ingot]

they're asking how many possible groups of 4 can you make for that one group

yeah

so

23 is the total number of ppl

you need to pick 4 people from those 23 people

to make your group

[turbid osprey]

yea and the possible groups that can be made is 5

[true ingot]

why

[turbid osprey]

23/4 5

with 3 extra

[true ingot]

what

[turbid osprey]

nvm im lost

[true ingot]

I thin kyou need to reread your question

they're not asking how many ways you can make 5 groups of 4

they're asking you how many ways you can make 1 group of 4 out of 23 people

[turbid osprey]

yea LOL lost

but thanks

[true ingot]

ok well the answer is just 8855 - 3060

if you need it

[turbid osprey]

yea and its 5795

so n would be the total?

and r will be the amount it is divding?

[true ingot]

what

n is the ttoal number of ppl

and r is the committee size

[safe radish]

@turbid osprey Has your question been resolved?

[safe radish]

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[fathom kayak]

"These sets are disjointed" Does that mean all of them have to be disjointed?
If i understand its Pairwise disjoint, because B⊂A, but A∩C ∪ B∩C = Ø

[peak estuary]

they are not pairwise disjoint because like you said B is a subset of A

"these sets are disjointed" is ambiguous

it probably means pairwise

[fathom kayak]

Might be fault of my translation

I've got two questions(T/F)
these sets are disjoint
these sets are pairwise disjoint

Since there are 3 sets its confusing.

[peak estuary]

well like I said the first question is ambiguous and I don't wanna answer it. the answer to the second question is false because B is a subset of A

[safe radish]

@fathom kayak Has your question been resolved?

[safe radish]

@fathom kayak Has your question been resolved?

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[cunning aurora]

could someone briefly explain how an exponential function works? preferably in a manner which could be understood by an individual who is not very mathematically inclined

[worthy hemlock]

You could probably watch videos instead. There are tons of good videos that explain that well

[safe radish]

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[analog flare]

You should prob write 3 theta as 2 theta + theta

[timber atlas]

Ok

Sin 2 theta cos theta + theta

Now what?

[true juniper]

Once you recognise its sin compound angle you can work from there

[timber atlas]

Hmm..ok

So now I expanded and have:
2 sin theta cos^2 theta + theta

[safe radish]

@timber atlas Has your question been resolved?

[safe radish]

@timber atlas Has your question been resolved?

[safe radish]

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[flint nest]

I have the equation 10x + 6 = 5x +6

[flint nest]

my answer is the solution set is ø

the computer says i'm wrong

why am i wrong?

[plucky elk]

x=0

[light shoal]

subtract 5x+6 from both sides

[flint nest]

2x = x

or i mean 5x = x

5 * 0 = 0

[light shoal]

how did you get 5x = x

[flint nest]

I get it

huh h

[iron snow]

Do you mean 5x=0?
if you subtract 5x+6 from both sides then that's what you should get

[flint nest]

ohhh yeah

brain no thinky

yes yeah that makes sense

[safe radish]

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[stray storm]

What is a congruence test

and where is A

[upbeat swan]

its what you use to prove that triangles are conguent

[stray storm]

yup

how would you do that

like

[upbeat swan]

look what elements they have in common

[stray storm]

same angles

symmetrical

what does it mean "which congruence test"

how would you apply

SSS,SAS

and where is A

[upbeat swan]

if triangles have all sides conguent, then the test is side side side

or sss

[stray storm]

oh

a means angle then

[upbeat swan]

if they have 2 sides and 1 angle

its sas

side angle side

[stray storm]

so

it would be SSS?

What does RHS mean doe

[upbeat swan]

idk

look it up

[stray storm]

ok

thanks

SSS is correct right?

ill assume yes

.close

[safe radish]

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[upbeat swan]

it's not

[stray storm]

Its not???

.reopen

[safe radish]

✅

[stray storm]

but they have the same side lengths

[upbeat swan]

how do you know

[stray storm]

ye

good point

[upbeat swan]

im only seeing equal angles

[stray storm]

im just looking at it

[upbeat swan]

look at the angles

[stray storm]

you can prove line SQ is same for bothe right

S

[upbeat swan]

yeah

you dont need to prove

[stray storm]

ok

thats one S

[upbeat swan]

yes

[stray storm]

ok

[upbeat swan]

then you dont have more sides

you only have angles

so

[stray storm]

so

[upbeat swan]

whats the test

[stray storm]

AAS

[upbeat swan]

yeah

[stray storm]

yes but

why cant you prove SP

u technically can right

[upbeat swan]

sp what

[stray storm]

line sp

[upbeat swan]

what with line sp

[stray storm]

isnt that a S too

[upbeat swan]

you dont know its congruent with anything

[stray storm]

wdym

[upbeat swan]

i mean

the question doesnt tell you sp is congruent with anything

[stray storm]

i dont understand but ok

[upbeat swan]

.

how do you not understand

[stray storm]

it doesnt explicitly tell us anything does it

[stray storm]

im braindead

[upbeat swan]

here

rps = qtx

right?

[stray storm]

yup

[upbeat swan]

ok

and you are saying ps = xt

out of nowhere

[stray storm]

oh

oh

[upbeat swan]

see?

[stray storm]

ok

[upbeat swan]

you dont know that

[stray storm]

thanks

but wait

its not sealed right

so with the same angles it has to be the same length

since they both have to go to one point

[upbeat swan]

no it doesnt

[stray storm]

ok

ill just

stop asking

.close

[safe radish]

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[upbeat swan]

.reopen

[safe radish]

✅

[upbeat swan]

see now?

they dont have to be the same lenght

[stray storm]

ah

i get it

thanks

.close

[safe radish]

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[upbeat swan]

np

[safe radish]

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[stray storm]

,rotate

[stray storm]

Help pls

Is there any way to do it apart from trial and error

[potent roost]

maybe write it as a function of x

[stray storm]

like?

[potent roost]

y = (120-3x)/4

[stray storm]

oh

ya

[potent roost]

now plug in x's from 1

[stray storm]

??????

pls slowdown

oh

like

1

2

3

4

5

[potent roost]

yes

[tawdry needle]

You see 30 and 0 is an option
The way you can get the next option is to reduce 4y by multiples of 4 and then checking if you can get an x value that works
For the x value to work you need the 120-4y to be divisible by 3

[stray storm]

?????

im so confused

[tawdry needle]

So 4y itself needs to be divisible by 3

[stray storm]

please explain

why

[tawdry needle]

Answer is 15 ?

[stray storm]

dude i dont want the answer

i wanna learn

how did you get that

[tawdry needle]

Ye but if you know the answer tell me if this is correct

[potent roost]

so we have $y = \frac{120-3x}{4}$

[stray storm]

Ok

[flat frigate]

Swas.py

[potent roost]

lets factor a 3

[tawdry needle]

So i can explain without the chance of my explanation being wrong

[stray storm]

why does it equal that

[potent roost]

$y = \frac{3}{4}(40-x)$

[flat frigate]

Swas.py

[lean otter]

💀

[stray storm]

what

pls slow down

[potent roost]

3(40-x) is 120 - 3x correct?

[stray storm]

yup

[potent roost]

so 3/4(40-x) = (120-3x)/4

[stray storm]

yes but

lemme just type the original question

[potent roost]

no need for that

[stray storm]

3x+4y=120

so

[potent roost]

yes

[stray storm]

its

wait

how did you get to 3(40-x)

[potent roost]

3x+4y=120
we subtract 3x
4y= 120 - 3x
we factor a 3
4y = 3(40-x)
we divide by 4
y= 3/4(40-x)

Okay?

[stray storm]

whats factoring

oh

wait nvm

yup

[potent roost]

now we know x is a positive integer

[stray storm]

shouldn't 40-x/4 too

[potent roost]

no

[stray storm]

y

[potent roost]

3/4(40-x)/4 would mean 16 in the denominator

[stray storm]

nono

like

[potent roost]

I can do this if you want
(3(40-x))/4

but its the same thing

let me just use latex

[stray storm]

i dont see how its the same thing

[potent roost]

$\frac{3(40-x)}{4}$

[stray storm]

y=(3(40-x))/4

[flat frigate]

Swas.py

[stray storm]

yup

[potent roost]

now x is a positive integer

[stray storm]

yup

y=that

[potent roost]

can you see that after x goes above 40 we'll get negative values for y

[stray storm]

yup

[potent roost]

so we only need to look at numbers from 1 to 40

[stray storm]

yup

so we trial and error that?

[potent roost]

we can get some more intuition, though

[stray storm]

how

[potent roost]

we have to make sure 3(40-x) is divisible by 4

in order for y to be an integer

[stray storm]

why

[lean otter]

Integers are full numbers

No decimals

[stray storm]

yup

[lean otter]

No reminders

So it cant br something like

[stray storm]

yup

yup

[lean otter]

7/4

[stray storm]

yup

[lean otter]

yup

[potent roost]

3(40-x) now this needs to be a multiple of 4 so (40-x) needs to be a multiple of 4

since 3 isn't a multiple of 4

[lean otter]

You're now just finding values of x for which 40 - x is a multiple of 4

[stray storm]

i dont get it

[lean otter]

Which part

[stray storm]

everything

[potent roost]

bruh

[lean otter]

[lean otter]

I bruhed irl

Okay so you have

[stray storm]

i get the algebra part

but

[potent roost]

do you understand till here?

[stray storm]

ya

[potent roost]

and the fact that x can only be from 1 to 40

[stray storm]

yup

[potent roost]

alright

so we need to ensure that 3(40-x) is divisible by 4

[stray storm]

y

oh wait

ya

[potent roost]

is 5 divisible by 4?

[stray storm]

no

so it has to equal

a multiple of 4?

[potent roost]

yes 3(40-x) has to be a multiple of 4

[stray storm]

so

[potent roost]

can 3*(a number not a multiple of 4)
ever be a multiple of 4?

[stray storm]

4,8,16,20,24,28,32,36,40

[stray storm]

yes

[potent roost]

how

[stray storm]

3*8

wait

wait

no

[potent roost]

8 is a multiple of 4

[stray storm]

12

[lean otter]

8 is a multiple of 4

[stray storm]

no

[potent roost]

yes so it cant

[lean otter]

You literally listed it

[stray storm]

so no

since

3*12 is invalid too

[potent roost]

yes

[stray storm]

so no

[stray storm]

no

[potent roost]

so we have deduced that if 3(40-x) a multiple of 4 then (40-x) has to be a multiple of 4

okay?

[stray storm]

yup

wait

that means x must be a multiple of 4 right

so its 36,32,28,24,20,16,12,8, or 4

[potent roost]

yes you are correct

[stray storm]

yahoo

[potent roost]

thats it

[stray storm]

do i just plug all of those?

[potent roost]

for x yes

and you get ys

but

you dont need to find those ys

[lean otter]

Dont even need to plug them

[potent roost]

cuz the question asks for how many

[lean otter]

Just count how many valid x

[stray storm]

oh

[lean otter]

Yee

[stray storm]

so

[potent roost]

just count these 36,32,28,24,20,16,12,8,4

[stray storm]

i just count how much then div by 2

[lean otter]

Why divide

[potent roost]

no dont divide

[stray storm]

cuz it says pairs

how many pairs

[lean otter]

Pairs of x and y

[potent roost]

each x gives a y

[stray storm]

oh

[lean otter]

Every x has a y

[potent roost]

that makes it a pair

[stray storm]

so the answer is a 9

yahoo

thanks guys

.close

[safe radish]

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[potent roost]

,w positive integeral solutions 3x+4y=120

[flat frigate]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Swas.py#7370

[potent roost]

💀

[safe radish]

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Send your question here to claim the channel.

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[lean otter]

hello

[lean otter]

hello

bye

i need to do this and im confused

i know its done similar to this

but im confused-

[quasi bison]

do you know how to do multiplication like this in base ten?

[lean otter]

yes yes

[quasi bison]

right well it works exactly the same in hex

addition and multiplication of digits just works somewhat differently

[lean otter]

where im stuck at is if the number is higher than 16 i have to convert it to hexa am i correct?

[quasi bison]

you are working in hexadecimal...

if you want to do the digit-by-digit multiplication in base ten to make it easier for yourself then by all means do so

but you will have to convert back into hexadecimal regardless of the value

[lean otter]

(o.o;)

[quasi bison]

ok yeah sure

that works

[lean otter]

the thing is

idk how that is working

like culd u help me get the idea in my mind?

[quasi bison]

when you say "idk how that is working", do you mean "i don't understand how 143_10 becomes 8F_16, 140_10 becomes 8C_16 etc." or do you mean "i don't understand why we have to do these conversions in the first place"?

[lean otter]

the first one

[quasi bison]

so what you're saying is, you have forgotten how to convert between decimal and hex.

https://www.google.com/search?channel=trow5&q=how+to+convert+between+decimal+and+hex

[lean otter]

yes-

[quasi bison]

in the general case it involves a bunch of long division

there are also shortcuts for base sixteen specifically (namely, convert to binary first then convert bin to hex which is easy)

[lean otter]

is it

answer devided by 16

and the reminder x16?

[quasi bison]

it's remainder, not "reminder". a reminder is something you put on your phone to make sure you don't forget the doctor's appointment.

and in this particular case, when the number you're converting has at most two digits in hexadecimal,
yes, the first digit is the quotient by 16 (i.e. the number divided by 16 and rounded down) and the second is the remainder.

[lean otter]

okay thankyou wonderful person

did i go wrong anywhere?

the brakets are after converting to hexa

anyone here?

hello-

[quasi bison]

isn't it B.8 rather than 8.B

[lean otter]

OH

my bddd

um this is kind of hard...

whats 2+2c in hexa? 4c?

this?

hello anyone here q-q?

i need help or a step by step guide on how to do this please

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

it has not been resolved T-T

[worthy hemlock]

It's like regular multiplication, except you're in a different base

[lean otter]

where did my answer go wrong?

[worthy hemlock]

You have to do a few extra steps, by converting from base 16 to base 10, to do the multiplication

[lean otter]

im following this

[worthy hemlock]

What does (2) = 32 mean?

[lean otter]

it means when we convert 32 to hexadecimal its 2

[worthy hemlock]

No, it's not

[lean otter]

wait..

wait wait wait

is it 20???

[worthy hemlock]

Yes

[lean otter]

OH

[lean otter]

so do i add these after converting?

[worthy hemlock]

As mentioned, multiplication in base 16 is the same concept and process and multiplication in base 10, except you convert base 16 to base 10 first to make it easier

[lean otter]

sooo

should be correct now yes?

[worthy hemlock]

Nope

[lean otter]

how come

[worthy hemlock]

When you do regular base 10 multiplication, can you have 32 in the ones place?

[worthy hemlock]

Because it's wrong

[lean otter]

i am aware its wrong-

how is it wrong-?

[worthy hemlock]

.

[lean otter]

i am confused-?

[worthy hemlock]

When you do regular base 10 multiplication, for instance, 24 * 8, you do 4 * 8 first, making that 32, can you place value of 32 in the ones place?

[lean otter]

i am still confused-?

im unfimiliar with maths so idk what ones place is

[worthy hemlock]

Have you never seen this before?

[lean otter]

so the first digit

wait

am i suppose to keep the thing in ones place and carry

and add it to the other place while multiplying

?

[worthy hemlock]

Yes, that's how multiplication works

[lean otter]

AH

[worthy hemlock]

It seems like you need a review on multiplication

[lean otter]

i am really forgetful trust me-

so for the first thing

its a 0 yes?

[worthy hemlock]

0 in what base?

Like are you using 32 in base 10 or 20 in base 16? You just saying 0 means nothing because there's not enough context

[lean otter]

ah sorry

since its 20

and 2 got carried over

[worthy hemlock]

That is the first step, continue and finish the problem

[lean otter]

am i doing smth wrong again?

it should be A+c+2

[worthy hemlock]

Where is A coming from?

I don't even understand your process

[worthy hemlock]

As asked before, do you know how to do regular multiplication?

[lean otter]

AH

sorry i forgot again

its another 0

cuz the 1 in 10 gets carried over

am i correct?

q-q im really sorry im bad at thiss

[lean otter]

alright

can we change the question to

this?

🤯 i dont like mathsss

[safe radish]

@lean otter Has your question been resolved?

[spiral crescent]

What is the problem

[safe radish]

Channel closed

Closed due to timeout

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[safe radish]

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[tawdry jackal]

Need help:
my thought process:
ive tried differentiating x = cos (xy)
=> 1 = -sin(xy) * d(xy)/dx
solving this led me to dy/dx = (-y-1)/x

[tawdry jackal]

i hope the question is clear enough to be read. my bad if it isnt

[final halo]

Show more of your work, your first line is correct

[tawdry jackal]

one sec

1 = -sin(xy) * [y+x dy/dx]

1 = (-sin(xy) * (y) - x dy/dx * sin(xy)

x dy/dx * sin(xy) = -sin(xy) (y) - 1

dy/dx = [-sin(xy) (y) -1] / (x * sin(xy)

now what do i do

"solving this led me to dy/dx = (-y-1)/x" i found the mistake here, but i still cant get the 'prove that' answer

[final halo]

So something useful here will be that $\sin^2(\theta)+\cos^2(\theta) =1$

[flat frigate]

ΣAC

[tawdry jackal]

um.. im dumb. i cant seem to find where

[final halo]

You've got sin(xy) floating around

If we could write that in terms of cos(xy) that'd be great because cos(xy)=x

[tawdry jackal]

hm

Oh

so like sin(xy) = root(1-(cos(xy)^2)

[final halo]

Yes

It seems like we're also going to be off by a negative and I can't see why right now

[tawdry jackal]

im slightly bad at english. off by a negative? you mean were a bit off the final answer expected only due to a negative sign

am i right?

[final halo]

Yeah, right now our answer is going to be the negative of the one given i think

[tawdry jackal]

wait. why is cos(xy) = x

i dont think ive come accross that one before

[final halo]

Look at the question

[tawdry jackal]

OH

so right now, my final step is :
[-(root(1-x^2) - 1] / (x (root(1-x^2)))

so i think im off by a "Y' and minus

so maybe, can the question be a bit wrong?

i assume the book is old (about 7 to 8 years atleast). of which the image is taken from

[final halo]

You dropped the y

It should be there

[tawdry jackal]

oh

[final halo]

I think the question is incorrect yes, I just did the question myself

[tawdry jackal]

ah yes

[tawdry jackal]

i missed it in this step

[tawdry jackal]

thank you for your help, a lot.
this was my first time actually asking help and it was fun

im worried a lot of questins might be wrong in similar pattern,

cus this was the first question:

and i had banged my head for the first equation

thank you again

.close

[safe radish]

Channel closed

Closed by @tawdry jackal

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[final halo]

Riemann check me

[tawdry jackal]

should i reopen?

.reopen

[safe radish]

✅