help-10

[bleak steppe]

.close

I can't close it?

[sinful kraken]

Its already closen

[bleak steppe]

Oh, well then, uhm, let me just

[sinful kraken]

U cant

[bleak steppe]

I think I'm the one who broke this sorry

[sinful kraken]

U did t

Didnt brake it

[obtuse pebble]

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[finite flame]

If i am given two points lets say $(x_1,y_1)$ & $(x_2,y_2)$ how to find a line passing through these two points

[warm shale]

ron143

[finite flame]

I have 1 more doubt

,tex If i am given a equation of circle and a point $(x,y)$ outside of circle then how to find equation of tangent passing through the point

[forest sinew]

u use a formula

[warm shale]

ron143

[finite flame]

What is the formula

[obsidian isle]

ok let's go through this in a systematic way.

how can we parametrize a circle?

[finite flame]

Meaning?

[obsidian isle]

express any point on the circle as a function of a single variable t

such that (x,y) = (x(t), y(t))

[finite flame]

Oh not in that form

(x-a)^2 + (y-b)^2 = r^2

This form

Hey don’t bother about 1st question i just want 2nd one

I got 1st one

[rapid pumice]

whats (7x - 8) + 2x + 20)?

[obsidian isle]

if (x-x0)^2 + (y-y0)^2 = r^2, then (x,y) = (rcos(t) + x0, rsin(t)+y0)

so now we have two points

(rcos(t) + x0, rsin(t) + y0)
(x1,y1)

[finite flame]

But here t is variable right?

Let’s take an example to simplify I guess

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

And point (4,5)

[obsidian isle]

wait this is way simpler than i'm making it out to be i'm sorry

[finite flame]

Ouhh

[obsidian isle]

(x-a)^2 + (y-b)^2 = r^2

assume that y = mx + c

then you get a quadratic in x

[finite flame]

But there’s two tangent right

Oh ya

Nvm

Continue

?

[obsidian isle]

that becomes a mess because of the offset

a little substitution will make this a lot cleaner

let X = x-a, let Y = y-b

then X^2 + Y^2 = r^2

now assume Y = mX + c

[finite flame]

Ya

[obsidian isle]

X^2 + (mX + c)^2 - r^2 = 0
X^2 + m^2X^2 + 2cmX + c^2 - r^2 = 0
(1+m^2) X^2 + (2cm) X + (c^2-r^2) = 0

we only want this quadratic to have one solution, so let's set the discriminant equal to 0

[finite flame]

Why one solution?

We need both equation right?

[obsidian isle]

(2cm)^2 - 4(1+m^2)(c^2-r^2) = 0
4c^2m^2 = 4(1+m^2)(c^2-r^2)
c^2m^2 = (1+m^2)(c^2-r^2)
c^2m^2 = c^2 - r^2 + m^2c^2 - m^2r^2
c^2 - r^2 - m^2r^2 = 0
c^2 = r^2 + m^2r^2
c^2 = r^2(1+m^2)
c = +-r sqrt(1+m^2)

the plus or minus accounts for the two tangents. but we only want each tangent to touch the circle at exactly one point

[finite flame]

Ohh umm kk

Ya right

[obsidian isle]

now this gets a bit messy

we have found the constraint on c with the discriminant of the quadratic, now we will plug it back in

(1+m^2) X^2 + (2cm) X + (c^2-r^2) = 0

[finite flame]

Where to plug it in?

Ohh

How do we solve next

[obsidian isle]

wait actually do you know calculus

[finite flame]

I know but I don’t think we are supposed to do here calculus

Cause its 11th std concept where calculus was not taught

[obsidian isle]

https://sites.math.washington.edu/~conroy/m120-general/circleTangents.pdf

this quadratic shit is so damn messy. finally found a clean solution

find (a,b) given (c,d) such that:
a^2 + b^2 = r^2
b/a = -1/((b-d)/(a-c))

[obtuse pebble]

@finite flame Has your question been resolved?

[obtuse pebble]

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[shut lily]

when listing down the sample size does order matter? like in a problem where I flip 2 coins should i list HT and TH seperately?

[grizzled lily]

Yes

Since your looking for every possible combination

[shut lily]

icic thanks, i appreciate it

.close

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[timid silo]

can anyone help me with theory of equations

[timid silo]

<@&286206848099549185>

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[terse juniper]

I've got this problem:

"You roll a six-sided fair dice and sum up the values until you throw a value that is equal or less than your last throw. (For example, you could throw 2, 3, 5, 5 and the sum would be 15)"
What is the probability that there are exactly two throws?
What is the probability of each possible sum?

This problem is related to combinatorics, isn't it? I just can't wrap my head around the way this is supposed to be calculated.
I know that the least amount of throws you can make is two (any two same numbers) and the maximum amount of throws would be 7 (1, 2, 3, 4, 5, 6, 6)
Based on this, the lowest sum is 2 and the highest is 27

[royal basin]

hmm

gonna try to list all possible roll seqs

...which is probably going to be very long and tedious

can't see a good way to calculate this

[terse juniper]

Yeah, been doing it for a moment now and this definitely doesn't seem to be the "correct" way to do this.

[obtuse pebble]

@terse juniper Has your question been resolved?

[obtuse pebble]

@terse juniper Has your question been resolved?

[terse juniper]

<@&286206848099549185> I don't have enough paper to list all the sequences , pls help

[obtuse pebble]

@terse juniper Has your question been resolved?

[obtuse pebble]

@terse juniper Has your question been resolved?

[frosty schooner]

I have an idea

[terse juniper]

Do tell please

[frosty schooner]

I will draw, if you are not in a hurry

[terse juniper]

No prob, any help is appreciated

[frosty schooner]

Well, it turned out to be questionable. The thing is, I cant figure out the rules for subtracting. It is easier to figure out combinations of crosses, than it is for combinations of numbers, but still hard. May give it another approach later. Hope the following mess helps :)

[terse juniper]

Thank you, I'll look into this

[terse juniper]

.close

[obtuse pebble]

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[eternal nexus]

Would someone please explain me intuition of this rule?

[eternal nexus]

What is actually happening here?

[somber mural]

You integrate the function with respect to t

You should get a function in terms of x

Then you differentiate with respect to x

[eternal nexus]

Yes, I realize that.

But why this is true?

Would you please elaborate?

[white stag]

because when you go to plug in values for t after taking the antiderivative, one value will be x, and the other will be 1. from there the portion where you plugged in 1 will disappear, along with the integration constant, due to the differentiation with respect to x treating them as constants, and therefore being derived to zero. from there you should be left with only some function in terms of x.

[eternal nexus]

Thank you @white stag 🙂

.close

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[obtuse pebble]

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[fathom lion]

.close

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[simple obsidian]

.close

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[rigid gust]

How can I factories this quadratic?

[thick oracle]

ok

[strong vale]

Every quadratic can be written as $(x-A)(x-B)$

[warm shale]

azeem321

[thick oracle]

nope

this cant be factorised

sorry

im not joking

some cant be factorised

[rigid gust]

Can you factories the following

[thick oracle]

maybe

[strong vale]

Every quadratic can be factorized. However, your factors might be complex

[thick oracle]

nope

[rigid gust]

Then how can I factories the above two quadratic?

[strong vale]

,w solve 3x^2-x+4=0

[thick oracle]

see

cant factories

[warm shale]

Results provided by WolframAlpha

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

Requested by azeem321#9772

[thick oracle]

limited

what grade are you in

[rigid gust]

11

[strong vale]

have u learned complex numbers

[thick oracle]

ok

yes

he has

[strong vale]

if you have learned complex numbers then they would expect u to facotrize that

if not, then fine you won't be expected to facotrize

[rigid gust]

They are not in my syllabus but I know that i = sqrt(-1)

[thick oracle]

then you have no chance

just leave them

[rigid gust]

Then can I solve the above limit without using complex numbers

[thick oracle]

yes

[rigid gust]

How ?

[strong vale]

Do you know the limit is asking?

[thick oracle]

wha

t

eh

you need to try to factorise

[strong vale]

No you don't

Mike

[thick oracle]

?

in order to solve

[strong vale]

bro

[thick oracle]

what

[strong vale]

Limited, do you know how to do long division?

[rigid gust]

Yes

[strong vale]

ok divide the top polynomial

by the bottom

the quotient is the limit

alternatively, multiply top and bottom by $\frac{\frac{1}{x^2}}{\frac{1}{x^2}}$

[warm shale]

azeem321

[strong vale]

Factorizing will yield no results for this limit

[thick oracle]

it will

[strong vale]

ok solve it by factorizing

[thick oracle]

ok

[rigid gust]

Is the answer 1.5

[strong vale]

yh

[rigid gust]

Thanks both of you

[thick oracle]

ok

np

[rigid gust]

.close

[obtuse pebble]

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[wanton kraken]

quick question

[wanton kraken]

how do you get 5-3a<-1 out of "a>2"

using the properties of inequalities

[spiral maple]

Algebra

[wanton kraken]

no shit

[spiral maple]

Well yeah, but that's the answer to your question

How do I get from equation A to equation B? Algebra

[wanton kraken]

can u stfu

thanks

[spiral maple]

Post your attempt if you're unsure of the steps.

[wanton kraken]

I am stuck

it might be obvious

but my brain is fried from all the other problems

I've solved for the day

[spiral maple]

.

[frosty schooner]

Seems kinda random. It's just two true inequalities. Like, what is the task?

[spiral maple]

If you haven't attempted it, do so before you ask for help.

We can't help a blank slate.

[wanton kraken]

using the properties of inequalities, I have to get 5-3a<-1 from a>2

but I'm stuck

[frosty schooner]

If it is "Given A arrive to B" kind of task, then algebra it is, truly
Let me try to help

Aight
Lets move by bits to the victory
If a>2, and you have 3a in the end, what would you write down with it? Ignore minus for now

[wanton kraken]

both sides multiplied by 3

but it's -3a

so changes the direction

[frosty schooner]

And you are left with..?

[wanton kraken]

oh then add 5

[frosty schooner]

Perfect!

[wanton kraken]

ty

.close

[obtuse pebble]

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[long tangle]

I need help with exercise 35. I don't understand how to rearrange quadratic equations, I have no idea how to even start

[woven socket]

In this case, "rearranging" means "finding an expression of the form", e.g. for the a. it means finding an expression of the form ax² + bx +c

[long tangle]

yes, but how do I do that

[woven socket]

Let's take the example of the a., the function g :
You should expand the (x+5)², and try to put the x² together, the x together and the numbers together

Try to develop g(x)

[long tangle]

then I get x² + 10x + 25

and then the -9 right

so is x² + 10x + 16 then the answer?

[woven socket]

Yes, that's right !

Now, for h you should develop the (x+3)(x-4), and then apply the (-2) factor

[long tangle]

alright

then I get x² - x -12 and do I then multiply the whole thing by -2?

[woven socket]

Yep

[long tangle]

so -2x² +2x +24

[woven socket]

That's it

[long tangle]

okay thank you so much

[woven socket]

(I mean, you did all the work...)

[long tangle]

.close

[obtuse pebble]

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[sonic turtle]

Would someone be able to help me, I need help figuring out how to properly show all steps of my work

[sonic turtle]

One sec

I’ll send a picture of my work in a sec

[short spruce]

looks good

[sonic turtle]

I know that 2 is the answer without even doing this math

It’s a fairly simple problem

But how do I show my work

I haven’t done logs in a long time

[short spruce]

that's good enough

[scarlet gale]

Your work there is good.

[sonic turtle]

Do you think it would be easy for other students to comprehend

[short spruce]

as long as they know how to rewrite exponential equations logarithmically

[scarlet gale]

The only thing is that the side n was on switched, so it's a little strange, but still understandable.

[sonic turtle]

Do you see the third line, is it even necessary for me to switch to that with a log

[sonic turtle]

Ok

[scarlet gale]

You can make it more explicit, too.

[sonic turtle]

How

Can you show me an example

[scarlet gale]

log₁₀(10ⁿ) = log₁₀(100)

Just do the same step to both sides without skipping ahead.

[sonic turtle]

Ok

[scarlet gale]

Then you get n = 2 on the next line.

[sonic turtle]

Lemme try one sec

[sonic turtle]

Nice username btw LOL

[short spruce]

it fits me

[sonic turtle]

So when you take log of a 10

The log cancels out right

Cause the base of log is 10

[scarlet gale]

Yes, that looks good. Now it's clear you're doing the same thing to both sides each time.

[short spruce]

yeah

[sonic turtle]

Okay

Thank you guys <3

[scarlet gale]

You're welcome.

[sonic turtle]

What about this one

I am actually confused how to solve it

[scarlet gale]

You can take the 100 out of the logarithm.

log₁₀(1200)
log₁₀(12 · 100)
log₁₀(12) + log₁₀(100)
log₁₀(12) + 3

[sonic turtle]

Would that be a 2

Instead of three

@scarlet gale

[scarlet gale]

Oh, right.

[sonic turtle]

Does this look right?

Students can’t use calculators on this

So is this the most simplified form?

[scarlet gale]

Yes, there's an alternative as well.

[sonic turtle]

Mhm?

[scarlet gale]

log₁₀₀(1200)

The way you can get that is.

2y = log₁₀(1200)
y = log₁₀(1200)/2
y = log₁₀(1200)/log₁₀(100)
y = log₁₀₀(1200)

The last line is the change of base rule.

[sonic turtle]

Okay

[scarlet gale]

y = log₁₀₀(12) + 1 also.

Depends on which you see as simpler.

[sonic turtle]

How do I do this one

I have no idea

[somber mural]

So you need to isolate x @sonic turtle

[somber mural]

Correct

You can Technically shorten it by 1 step

Take log base 2 of both sides instead

You'll get x immediately

[sonic turtle]

OOOOOHHHH

OMG

Okay

I didn’t think of that

Ok one sec

So is this right

[somber mural]

Ye

[sonic turtle]

Okay thank you so much

[somber mural]

Np

[scarlet gale]

And then 1/16 is 2 to the what power?

@sonic turtle

Or, alternatively, what power of 2 is 16?

[sonic turtle]

Hi

Sorry I’m back

Ummm

[sonic turtle]

4

[somber mural]

What about this

@sonic turtle

[sonic turtle]

One sec

Idk

[somber mural]

What happens if the power is negative

Like 2^-1

[sonic turtle]

So 2^-4

Is 1/16

[somber mural]

Yes

So x = ?

[sonic turtle]

-4

[somber mural]

Yes

[scarlet gale]

Looks good.

[obtuse pebble]

@sonic turtle Has your question been resolved?

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[sonic turtle]

Thank you guys for the help

[obtuse pebble]

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[zenith kraken]

Abstract algebra continuous function norm uniform convergence question - can someone please check this for me?

[obtuse pebble]

@zenith kraken Has your question been resolved?

[zenith kraken]

<@&286206848099549185>

[sterile wyvern]

@zenith kraken are you trying to show that F is continuous?

[brave bramble]

So I agree that part i works

And you need to show that part ii isn't bounded

I don't follow part ii

[obtuse pebble]

@zenith kraken Has your question been resolved?

[obtuse pebble]

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[austere smelt]

I feel like an idiot for still forgetting how to do this, how do you convert an angle value to a Vector2 relative to up? So a 90 degree rotation would be equal to (1, 0) for example, and 45 degress (0.5, 0.5).

[main lodge]

I believe that would be (sin(theta), cos(theta))

[austere smelt]

Ah, thank you very much.

[main lodge]

Np

[austere smelt]

.close

[obtuse pebble]

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[main lodge]

Oops sorry, when you said (0.5, 0.5) are you sure you didnt mean (1/sqrt(2), 1/sqrt(2))?

[austere smelt]

Honestly, not sure. Probably. I really suck at vector math. Your answer was enough for me to find my old code for this though, so it's all good.

[main lodge]

Oh cool

[obtuse pebble]

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[velvet hawk]

am i stupid or did my teacher put the wrong answer

[broken night]

if ur just multiply the fractions it would be 1/18

[velvet hawk]

yea i did that but it says its wrong

[broken night]

do u have the beginning of the question with the amounts of marbles listed?

[velvet hawk]

its the first one in the row

you have to get it out of the picture

[broken night]

oh ok so in the picture I see only 9 marbles, where did u get 12 from?

[velvet hawk]

i see 10...

wtf

my brain

idfk where i got 12 from

lemme try with 10

[broken night]

nah ur right I enlarged it to check lmao

I see 10 now

lmk what you get

[velvet hawk]

kk

OH MY GOSH I DID IT

[broken night]

2/25?

[velvet hawk]

yea

[broken night]

nice good job

[velvet hawk]

fuck i spent 2 hours using the wrong numbers

[broken night]

ive been there bro

[velvet hawk]

ive done it way too many times

once i thought a k was a 4

[broken night]

oh damn that sucks

[velvet hawk]

atleast it wasnt on a test

well anyways thanks for your help

[broken night]

true but ur teacher is kinda doing u dirty for making you count from a tiny pic

yea ofc

[velvet hawk]

thats true tho

imma close the channel now

bye

[broken night]

bye

[velvet hawk]

.close

[obtuse pebble]

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[valid phoenix]

what is the cdp equation of binomial distribution?

[valid phoenix]

is it this function?

[forest sinew]

looks like sum of binomials?

cdp

what do you mean cdp

what does it stand for

[valid phoenix]

CDF* typo

my bad

[spiral maple]

then yes

$F(x):=P(X\leq x)$

[warm shale]

Mosh

[civic zealot]

Yes, the CDF of any discrete function is $F(x) = P(X\leq x) = \sum_{n\leq x}P(X=n)$

[warm shale]

Zybikron

[valid phoenix]

thanks what about the CDF of geometric distribution

is it just 1 - (1-p)^x

[spiral maple]

You can google that

[valid phoenix]

👍

[obtuse pebble]

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[stable gale]

.close

[obtuse pebble]

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[strong vale]

yes

approach was perfect

not sure why u put 90 twice tho @stable gale

[obtuse pebble]

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[elder spear]

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

I need help finding the domain and range for this

[short spruce]

do you know what domain and range are

[timid silo]

Not really 😪

[short spruce]

perhaps google that

[timid silo]

Gotcha!

I still don’t get it😀

Wait I think I might

Would the domain include-3

[short spruce]

yes

[timid silo]

Ok ok would it also have infinity since -3 is the only point

[short spruce]

?

i'm not sure what you mean by that

[timid silo]

Is the domain just -3?

[short spruce]

no

the domain includes -3, but the graph covers much much more than that

[timid silo]

Yes so would it be like (♾,-3)

[short spruce]

does it go to infinity?

[timid silo]

I mean it looks like it does

[short spruce]

what direction is it going in?

[timid silo]

The left

[short spruce]

which covers what type of numbers?

[timid silo]

Negative

[short spruce]

so, care to redo your answer?

it's not infinity, but close

[timid silo]

-8?

[short spruce]

is 8 supposed to denote infinity lol

[timid silo]

No😪

[short spruce]

it's going in the negative direction... forever

so what is it going towards

[timid silo]

-♾

[short spruce]

yep

[timid silo]

Ok ok

Thank you

For the range it doesn’t go past 2 or -2 but I don’t think that’s right

[short spruce]

think about what that graph is doing

if you were to expand it out

[timid silo]

It will keep going up

[short spruce]

(and down)

[timid silo]

So just (♾,-♾)

[short spruce]

normally the lower number is represented first

[timid silo]

Oh ok thank you

Alright awesome

How do I close it?

[short spruce]

.close

[timid silo]

.close

[obtuse pebble]

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[obtuse pebble]

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[long root]

I not sure if I am going crazy or the textbook is wrong but the gradient is 1 when x-interpect = 1 and the y-intercept = 1.... right?

[long root]

the text book is saying its -1

Question 7c)

[teal prawn]

that equation becomes y = -x - 1

[long root]

I got the equation to become y = -x +1

thats what I did @teal prawn

[teal prawn]

the question says x + y + 1 = 0

[long root]

ohhhhhhh

I am so dumb

sorry....

thank you for pointing that out

.close

[obtuse pebble]

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[subtle tusk]

Can someone help me with this?

[naive owl]

is that a test

[obtuse pebble]

@subtle tusk Has your question been resolved?

[subtle tusk]

no

it’s a question from previous year question bank

which was asked for 10 marks

[subtle tusk]

<@&286206848099549185>

[obtuse pebble]

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[obtuse pebble]

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[compact shadow]

By definition, those are 3+(1+2+…+5) independent linear equations, so 25-3-(1+…+5)=7

[compact shadow]

.close

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[worn onyx]

help

[worn onyx]

bout kepler gravity

sattelite orbiting 🌍 at height of 600 km, if centripetal acceleration of sattelite is 7.80 m/s^2 ,calc the linear speed

i use a=v^2/r

but got wrong

[tardy epoch]

What r did you use

[worn onyx]

6.37×10^6

r

[tardy epoch]

How'd you get this number

[worn onyx]

given in the question

[tardy epoch]

Show the question

[obtuse pebble]

@worn onyx Has your question been resolved?

[obtuse pebble]

@worn onyx Has your question been resolved?

[obtuse pebble]

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[past granite]

I don't get why the x component is equal to m(a cos 50)

And how does the second line come about?

[frosty schooner]

Draw a right triangle please. If you have worked with vectors before, you would know that legs of triangle would sum up to vector on hypotenuse

[past granite]

Yes I understand that

[frosty schooner]

That is to say, v_x + v_y = v
Good?

[past granite]

Yup

[frosty schooner]

Now, tell me, how to express leg through hypotenuse knowing angles?

[vast wren]

Have you tried drawing the components of each force? You will see that F(1) has no effect on a(x)

[past granite]

Yeah I was thinking that

[frosty schooner]

So you are left with F_2x = m * a_x right

[past granite]

Yes

[frosty schooner]

Now, you cant compute a_x?

[past granite]

Oh is that why it's a cos 50?

[frosty schooner]

Because it is in a right triangle, it is a handy proection, yes

[past granite]

Great! I understand it now

Thank you @frosty schooner @vast wren

[frosty schooner]

👍

[vast wren]

[past granite]

.close

[obtuse pebble]

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[dusky hearth]

hey 🙂

[dusky hearth]

what is the lowest value of n such that an algorithm that has a runtime of 100(n^2) will run faster than an algorithm with a run time of 2^n on the same machine?

i tried solving this and got n= log100 + 2logn

but idk how to proceed

[obtuse pebble]

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[obtuse pebble]

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[golden heron]

Hello, I am trying to show that this is logically equivalent, am I doing it right?

[lucid flame]

yes but you accidentally put a not symbol on the 3rd line

[golden heron]

Oohh, okay lemme fix it, thanks!

Oh nvm, wait imma try it

Here, Is this correct?

[obtuse pebble]

@golden heron Has your question been resolved?

[golden heron]

I also have another answer, lemme write it quick

Here's my other solution

I don't know which to use

[obtuse pebble]

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[golden heron]

.reopen

[obtuse pebble]

✅

[golden heron]

<@&286206848099549185>

I have two answers, which is correct?

[uncut galleon]

How do you get from the 1st to the 2nd line in the first answer ?

oh ok

sry my bad

[golden heron]

The question is to show that this are logically equivalent, sorry I forgot to include it.

[uncut galleon]

yh nvm

i get that

I'd do it this way :
$$\neg p \to (q\to r)\equiv (\neg p\lor q)\to r$$
imbricated implications
$$(\neg p\lor q)\to r\equiv q\to (\neg p \to r)\equiv q\to (p\lor r)$$

[warm shale]

Silfer

[uncut galleon]

there is something weird in your answers

you start from the answer to get to the start

but both answers seem correct to me

[golden heron]

I use this table for the laws

Can you do the step by step process, because I can't understand it

our prof told us to always include the laws for every steps

[obtuse pebble]

@golden heron Has your question been resolved?

[uncut galleon]

Ho my bad, implicated implications are in the lesson my teacher gave me but i'll prove it : Using implication twice
$$p\to(q\to r)\equiv \neg p \lor (\neg q \lor r)$$
Using associativity and commutativity :
$$p\to(q\to r)\equiv (\neg q \lor \neg p)\lor r$$
Using associativity and then implication twice :
$$p\to(q\to r)\equiv q\to (p\to r)$$

[warm shale]

Silfer

[obtuse pebble]

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[timid silo]

Can somebody please help me with this

[thick oracle]

ok

so

there are 2 cases

[timid silo]

okay

[thick oracle]

solve each one

[timid silo]

I computed first one, x is greater than or equal to 2,5 and 6

will the second one be relevant since x is a real number

[thick oracle]

yeah

[timid silo]

so x is either great than or = to 2,5,6 or less than 2,5 & 6?

[thick oracle]

what

thats not how you rite it

[timid silo]

can you please tell then

[thick oracle]

ok

solve the first

eh

ill just solve it in paint

1 sec

[timid silo]

stream it?

[thick oracle]

ok

i cant stream

[timid silo]

np

[thick oracle]

this is for the first

second

[timid silo]

got it

I'll try to solve it by myself now

[timid silo]

what will be the final answer though

[thick oracle]

third

idk

[timid silo]

?

[thick oracle]

forth

now

between 1 and 2

[timid silo]

which option

[thick oracle]

now intersec

t

and find the answer

ill let you

so? whats the answer

hello?

[timid silo]

yeah I am trying

I am bit of a beginner so a lil confused

give me a min pls

[thick oracle]

intersect the 2 above

sure

you just need to put them next to eachother

)

[timid silo]

x E [2,5] U [6, infinity]

?

[thick oracle]

yes

but

at 5 and at infinity its )

not ]

or [ if you want

[timid silo]

what topic does this belong to btw

I studied this long back in school

now I need this for a test

[thick oracle]

inequalities and intervals

[timid silo]

thanks so it'll be option 4 right?

[thick oracle]

yes

[timid silo]

Thanks a lot fren

[thick oracle]

ok

is it good?

corrrect?

[timid silo]

yes

[thick oracle]

ok

nice

[timid silo]

I have a few more

let's discuss them other time

[thick oracle]

i cant

[timid silo]

oh sorry

[thick oracle]

i have to eat

maybe after

[timid silo]

sure please

[thick oracle]

ok

[timid silo]

can I add you as a fren?

[thick oracle]

yes

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[swift wing]

Hi
I'm need to prove that you can't define an implication or a disjunction by using an alternative and a conjunction
How can I prove this problem?

[obtuse pebble]

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[obtuse pebble]

@swift wing Has your question been resolved?

[obtuse pebble]

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[pearl dirge]

can anyone point me to a resource (or even shed some info here) how you can go about including a variable outside of a radical into a radical?

for example, y * sqrt (16 - y^2)

is there a way to include the y within the sqrt(16 - y^2)?

[cunning quail]

y * sqrt (16 - y^2) = sqrt(y^2(16-y^2))

[teal prawn]

yeah y = √(y^2)

and use radical laws

[pearl dirge]

wow

Okay. thanks a ton!!

.close

[obtuse pebble]

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[teal prawn]

Although ig √(y^2) is technically |y| so be careful about losing info about the sign

[pearl dirge]

well, since there is a y already contained within the sqrt(), then would you not be able to already be able to determine that ?

[teal prawn]

if y were to be negative and you squared it and included it into the sqrt and for some reason, decided to bring it out

you would have to consider both signs ig

that creates some extraneous solutions?

[pearl dirge]

hmm, youre right. interesting point

[teal prawn]

its not y that is contained it is the square of y that is contained

[pearl dirge]

i overlooked that

[teal prawn]

$y \Rightarrow \sqrt{y^2} = |y| ≠ y$

[warm shale]

kinglacto

[teal prawn]

you can still include it though

[obtuse pebble]

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[zealous crow]

hi can anyone help me understand where im going wrong, i think i got b wrong

[woven socket]

The 2c at b. is wrong

You're multiplying the (x, y) by c, not the f((x, y))

Which in fact proves that f is not a linear transformation since f(c(x, y)) != cf((x, y))

So, in b. First and third answer are wrong

[zealous crow]

ohh ok so is a and c correct but in b the problem is they aren't equal

[woven socket]

Yes, and also that the first answer in b is incorrect

[zealous crow]

L what did i miss

[woven socket]

The first answer of the a.

Again, you're adding (x1, y1) and (x2, y2)

So it should be 6(y1+y2)-7(x1+x2)+2

(So they're, again, not equal)

[zealous crow]

oh oki how does this make it a lin transformation

[woven socket]

Well, it's not a linear transformation

Because f(x+y) != f(x) + f(y) and f(cx) != cf(x)

[zealous crow]

is that the only way to distinguish if its a lin transformation

[woven socket]

For a function to be a linear transformation, you need these two conditions

If one of them is not verified, then it's not a linear transformation

Another thing is f(0) = 0

[zealous crow]

what's this

[woven socket]

Well, a linear application always send the 0 of the first vector space to the 0 of the second vector space

[zealous crow]

i think i get it, so for any function where x = 0, f(0) = 0

[woven socket]

No, for any linear transformation

[zealous crow]

bc it's a another condition of lin transformations?

[woven socket]

No, it's something you deduce from the to conditions I mentionned

f(0) = f(2*0) = f(0) + f(0)

So you must have f(0) = 0

[zealous crow]

ah i think i got it, is there anything else i should know about lin transformations

[woven socket]

That's the main things you need to know I think

(For now)

[zealous crow]

ok ty i got the problem correct

.close

[obtuse pebble]

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[strange cape]

31

[strange cape]

I have no idea where i wrong

doing question 31

[hasty linden]

@strange cape check how you set up your integral

[obtuse pebble]

@strange cape Has your question been resolved?

[strange cape]

yes i have no idea whats worng

[hasty linden]

your intergral should be [0,2] + [3,-1]

[strange cape]

sorry still have no idea...but i gonna sleep its 2am here lol

.close

[obtuse pebble]

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[timid silo]

how would a be done for this?

[gloomy valve]

So x, y, z give you the number of rooms of each of the three categories

Now you need to express the two conditions (max number of beds) and (max area) in terms of x, y, z

[timid silo]

so one equation would be x+y+z = 60

15x + 25y +40z = 700

5x + 9y +15z = p?

<@&286206848099549185>

[gloomy valve]

first one should be x + 2y + 4z <= 60

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

is the 2nd one

15x + 25y + 40z <=700

[gloomy valve]

@timid silo Yup

and 5x + 9x + 15z is what you want to maximize

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[timid silo]

im struggling to understand this problem and how to solve it (discrete math)

[timid silo]

any advice how to start?

[novel knoll]

Understand the definition of A_i?

[timid silo]

you mean ai = a1 U a2 U a3 etc?

[novel knoll]

No I mean you are given definitions of A_i

I ask if you understand it

[timid silo]

sort of

like the first one A is an integer, between 0 and i

idk really struggling here tbh

[novel knoll]

Not an integer

A_1={0,1}

[timid silo]

so b. A_1 = {0,1} c. = (1,∞)

im just confused how to find union/intersection from them

[novel knoll]

Do a) first?

What is union of A_1 A_2 and A_3?

[timid silo]

i think this, correct?

so i just need 2 answers per letter?

[novel knoll]

What?

[novel knoll]

A_1 is this

Figure out what A_2 and A_3 is

[novel knoll]

Tell me answer to this union

Notice a pattern

And answer the question

[timid silo]

{0,2} and {0,3} so {0,1} U {0,2} U {0,3}

so {i, i+1, i+2}

[novel knoll]

Simplify it

[novel knoll]

And no

A_2 and A_3 are not that

[timid silo]

oh would a_2 just be {1,2} lol

[novel knoll]

No

Read the statement of A_i

Can you say in words what it means?

Well it even tells you exactly the elements in it after the equality sign

[timid silo]

{2} and {3}

those are my final guesses for a_2 and a_3

also appreciate your help @novel knoll we didnt learn this in class so gotta self learn it

[novel knoll]

Its really just reading

If the first equal sign is confusing

Just read the last equal sign?

It says exactly the elements in A_i

[timid silo]

right, so i get A_i = {0,1,2,3,4,...,i}

[novel knoll]

So can you answer correctly what A_2 and A_3 is?

[timid silo]

A_2 = 2

A_3 = 3

[novel knoll]

No

[timid silo]

lol

help meout bro

[novel knoll]

A_i ={0,1,…,i}

So if i=2 we stop at 2?

So A_2 is?

[timid silo]

0,1,2...

{0,1,2}

[novel knoll]

Yes

[timid silo]

then {0,1,2,3}

i got you now man

for a_3

[novel knoll]

What is this union then?

[timid silo]

my question now is how many answers do I need for each letter question?

since its asking this

[novel knoll]

4?

[timid silo]

so the union would be {i, i+1, i+2, i+3}

[novel knoll]

Where does i come from?

No i in A_1 or A_2 or A_3 is there?

How does i magically appear?

[timid silo]

{0,1} U {0,1,2} U {0,1,2,3}

that wouldbe the union of a_1 a_2 a_3 then..

[novel knoll]

And simplified?

[timid silo]

{0,1} U {0,2} U ... U {0,n}

is that how i would simplify it friend?

[novel knoll]

What is a union?

[timid silo]

it is a collection of sets

i think im just trying to figure out how to format it

[novel knoll]

If you can’t answer what this is simplified you clearly don’t understand what union is

[timid silo]

{0,1,2,3,4,5,...,i}

[novel knoll]

.

[timid silo]

{0,1,2,3} for that set

correct?

[novel knoll]

Yes

[timid silo]

{0,1,2,3,4,5,...,n}

so would this be my answer for union to N?

[novel knoll]

Yes

[timid silo]

@novel knoll thanks for the help brother 🤝

last question, would this be the answer for the union to infinity?

{0,1,2,3,4,5,...,n,...}

just with the additional dots added

for my second answer

[novel knoll]

What is n?

[timid silo]

oh n is pointless

{0,1,2,3,4,5,...}

[novel knoll]

Yes

[timid silo]

alright i have a good basic understanding now, ill practice more with the other questions.

again thanks for the help and being patient @novel knoll

.close

[obtuse pebble]

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[fluid sinew]

How do I graph this

[fluid sinew]

<@&286206848099549185>

[compact shadow]

First you draw 2 lines y=4(x-1)+2 and y=-4(x-1)+2. Can you do that?

What is in the cos by the way?

[fluid sinew]

What

[fluid sinew]

It’s the cos function

[valid phoenix]

https://classcalc.com/graphing-calculator

[compact shadow]

(x+2)/5?

[valid phoenix]

you can use this to check your answer

[compact shadow]

I mean what is next to cos? Cos what? Cos(2+x)/5 ?

[fluid sinew]

It’s 2pi/5

I don’t have the character for it on my keyboard

[compact shadow]

It’s a constant then…😂

[fluid sinew]

Yes

[compact shadow]

Then just one line

[fluid sinew]

Do u know how to graph trig functions cuz it’s not a straight line

[compact shadow]

It’s a constant

If it was cos(x), then I draw two lines as I said, and then I draw cos(x) between those two lines

[fluid sinew]

Yeah ur no help

[compact shadow]

Good,Blocked

[fluid sinew]

U don’t know shit buddy

[limpid birch]

equation you wrote write here doesn’t have your cosine as a function of x. It is a constant multiplied by a variable making it part of the slope of the line.

If this isn’t the answer you want, pick a different subject to study. It seems more likely that you wrote your function wrong, if you’re expecting a different answer.

[obtuse pebble]

@fluid sinew Has your question been resolved?

[obtuse pebble]

@fluid sinew Has your question been resolved?

[obtuse pebble]

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[crisp dune]

could someone please tell me the values they get for a,b and c

im just wondering if my textbook solutions are incorrect

[tardy epoch]

You want someone to do all the work?

Post your attempt and someone can help verify

[crisp dune]

ok then

a=1/2

b=1

c=3/2

[tardy epoch]

How'd you get those numbers?

If you have those numbers can't you just plug it in and verify?

[obtuse pebble]

@crisp dune Has your question been resolved?

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[obtuse pebble]

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[calm pollen]

Can somebody explain part B? I don't understand why the range isn't just all real numbers

[obsidian isle]

put g inside of f

like you're making a sandwich

this should explain it

or actually here's a better example. that was unclear

[calm pollen]

I can find the new function, x-4. Wouldn't the range of that just be all real numbers?

[obsidian isle]

does (sqrt(x))^2 = x?

yes it does always. but sqrt(x) itself is not real for negative x

and we run into problems when plugging that in

[calm pollen]

I understand that

but once it's the new function does that matter?

[obsidian isle]

the domain of sqrt(x) is non negative reals. the domain of x^2-4 is all reals

take the intersection of those sets

[obtuse pebble]

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[calm pollen]

Still a bit confused, how does that relate to the range?

[obsidian isle]

sqrt(x)^2 - 4 should have a range corresponding to the minimum and maximum values of x for which the sqrt function is defined

[calm pollen]

That makes sense, why are thinking of sqrt(x)^2 and not just x because we simplified?

Like I understand it, but i dont get the mathematical rule

Is there a rule relating domain/range etc?

I think I get it

thanks

.close

[obtuse pebble]

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[spiral maple]

P(Orange|A)

[pearl rune]

Yeah I'm not sure how to find that

[spiral maple]

Use the definition

[pearl rune]

Sorry could you please explain for me? I don'treally understand 😦

[spiral maple]

what's the definition of conditional probability?

[pearl rune]

the probability of event A occurring, given that event B occurs

[spiral maple]

computational definition

Hint: It's a fraction

[pearl rune]

is it P(A AND B)/P(B)?

[spiral maple]

Yes

P(A|B)=P(AnB)/P(B)

[pearl rune]

I tried doing that and there wasn't an option for the answer

assuming that I did the P(AnB) right which I think i did 😦

[spiral maple]

P(Orange and A)=P(A|Orange)P(Orange)

probability you get an orange marble * probability said orange marble has an A

P(A|Orange)=.92
P(Orange)=.78

[pearl rune]

and then you get .7176

[spiral maple]

,calc .92*.78

[warm shale]

Result:

0.7176