help-36

[eternal lichen]

So have you seen this before:

[crystal mirage]

no 😭 sorry i should probably go watch a super long lesson about probability cause we’ve only went through the basics

[eternal lichen]

Mhmm, basically it means that the probability of drawing two reds = P(RR | R) * P(R)

[crystal mirage]

okay

[eternal lichen]

So if you know the chance of the second red given the first was drawn, the probability of drawing two is just that probability times the probability of drawing the first

So what's the probability of drawing the first red?

[crystal mirage]

12/34

so it’s 12/34 * 11/33

?

[eternal lichen]

Yes

That's P(RR)

[crystal mirage]

ohh

[eternal lichen]

It's not bad if you think about the drawing process. First draw is 12/34. Given that draw, the second is 11/33

And you can use the same idea to come up with the probability of very complex events

[crystal mirage]

okay

so if i want to find out the probability of drawing out two of the same color i’d have to do the probability of the thing you explained but with all the colors and plus them together?

so like as you mentioned probability of drawing two reds + two blues + two whites + yellows = probability of drawing two of the same color?

sooo give me a sec

[eternal lichen]

yes, good

[crystal mirage]

so it’s 140/561

?

[eternal lichen]

Ummm, I didn't calculate it exactly

If you send me your work I can check if it's right

[crystal mirage]

i didn’t write it out properly but i think i did it right?

[eternal lichen]

Yes

This is good

Ah, wait

[crystal mirage]

oh

[eternal lichen]

it should be 33 for the second probability, always

you have 11/34

and 8/34

[crystal mirage]

OOPS i noticed it rn i wrote it wrong

i meant 33

[eternal lichen]

Ok, then it should be correct

[crystal mirage]

that’s why the thingy under i forgot what it’s called in english is still 1122

[eternal lichen]

ah, yeah

the thingy is called the denominator in english

[crystal mirage]

thank you then smm! also there’s a linking task asking what would be the probability of drawing two that are of the opposite color, would it just be the opposite then so like 561-150 which would be 421 so 421/561?

[crystal mirage]

thank you

[eternal lichen]

Mhmm, yes, drawing two that are not the same color is 1 - probability of drawing two that are the same color

[crystal mirage]

okay okay thank you so much actually i was stuck on this and eventually gave up and then went back to it

is there a name to the formula u used?

or if formula is even the right term for that umm

[eternal lichen]

It's called the law of total probability

It's derived from Bayes theorem and P(A or B) = P(A) + P(B) + P(A and B)

[crystal mirage]

okay thank you so much

[eternal lichen]

np

[crystal mirage]

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[uneven bridge]

I was given this question for homework, but I believe we haven’t covered how to solve it… (question 21). Would someone mind explaining how it is supposed to be solved so I can see if I’ve learnt it? There are bunch of questions like this.
The thing I don’t know how to do is calculating trig functions of regular numbers like 2/3. Usually it's 1/sqrt2 or something that works out nicely

[cunning glen]

use double angle formula for sine and draw a triangle, note that sin(x) = opp/hyp and cos(x) = adj/hyp

[uneven bridge]

Oh right was just a simple detail I was missing, of course

Thanks

Wait, but then how do I calculate the exact value of cos^-1(2/3)

[cunning glen]

you dont need to

let x = cos^-1(2/3)

so cos(x) = 2/3

draw a triangle with adjacent side of length 2 and hypotenuse of length 3

use pythagoras theorem to find sin(x)

[uneven bridge]

Got it thank you so much, that’s very helpful to know

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[final saddle]

Please don't occupy multiple help channels.

[vital crag]

!1c

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Please stick to your channel.

[vital crag]

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[scenic junco]

how come i did this wrong

tutor says it should be correct

maybe there was a miscalculation but im not sure

nvm got it

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[prisma edge]

How do i solve this system

[prisma edge]

$x’=-x$, $y’=-y^2$, $x(0)=x_0$, $y(0)=y_0$

[soft zealot]

jsidind810

[prisma edge]

solve the ivp

<@&286206848099549185>

<@&286206848099549185>

[hazy night]

@prisma edge is the ' notation derivative?

[tranquil pine]

the fraction broke

[prisma edge]

yse

equivalent to dot

please help me man

i have to solve the ivp explicitly for x0 in R and y0 in R \ {0}

@hazy night can u help?

[hazy night]

I do not understand what u just typed out

[prisma edge]

Just solve the ivp

[soft zealot]

Ralepsi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[prisma edge]

@tranquil pine is this chatgpt

[tranquil pine]

no

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[tranquil pine]

physics question, how do we know that v = 0 when position is equal to amplitude

[tranquil pine]

wait nevermind

i got it

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[warm hemlock]

I feel like this is super simple but I can’t figure it out

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[warm ether]

for them to have one solution, they can neither be parallel or be the same line

parallel is the main point really
if theyre parallel theres either no solution or infinitely many

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@warm hemlock Has your question been resolved?

[warm hemlock]

Hmmm

So does the y intercept change

[hot depot]

for this

B give infinite solution cuz same line
A and D give zero solution cuz it parrarel

i would ans C

4x-y = 3
y= 4x-3

And C is y = -4x+5

when positive linear and negative linear it got 1 intercept point

@warm hemlock i think this can help

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[hot depot]

r = {(x,y) ∈ R x R I x^2 - y^2 = 2x+4y+39}

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[hot depot]

r = {(x,y) ∈ R x R I x^2 - y^2 = 2x+4y+39}

[hot depot]

ah it midnight

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[humble stream]

Less of a math problem, more of an applied math problem. We know the classic applied trig problems "The viewing angle to the top of a tower is 37°. You walk 10 meters towards the tower. The viewing angle to the top of the tower is now 44°. How tall is the tower?"

If you were to go outside, and see a tower, what would be a simple way with no specialized equipment to easily determine what the angle is to the top of the tower? If I wanted to measure the height of a telephone pole on my street, how could I do that? Not in theory, but actually do it.

[humble stream]

Would the best way be to place a marker on the ground, walk 10 meters, place a second marker, then walk far enough away and just hold up a protractor?

I feel like there might be some easier method that I'm missing.

[sour tendon]

i think a laser pointer would make it easier to measure the angle

[sour tendon]

wouldn't the angle decrease as one walks 10m towards

[humble stream]

How?

[humble stream]

No, it increases. Imagine you barely see a building on the horizon. You're basically looking at it level. The angle to the top is extremely small.

Imagine you walk up to the building, and touch it. The angle to the top is now nearly 90 degrees. Walking closer increases the angle you have to look up to look straight at the top.

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[ancient thistle]

Hello

[ancient thistle]

How do I prove this?

$\lim :{n\to :\infty :}\left(\sum :{i=1}^n:\left(\left(\frac{b-a}{n}\right)i+a\right)\frac{b-a}{n}\right)=\frac{1}{2}\left(b^2-a^2\right)$

[soft zealot]

LE SSERAFIM

[autumn geode]

OMG

wow impressive proof

but just rewrite it is as an integral

$\int _a^bx:dx:$

[soft zealot]

nosqldb

[autumn geode]

and then the proof is immediate

[ancient thistle]

What's the point though

[autumn geode]

WHAT

WDYM WHATS THE POINT?

[ancient thistle]

The question doesn't allow you

[autumn geode]

OHH

lmao

igu

[autumn geode]

okay so

break it up

[ancient thistle]

How?

[autumn geode]

and then calculate the limit

$\lim _{n\to \infty }\left(\left(\frac{\left(b-a\right)^2}{n^2}\frac{n\left(n+1\right)}{2}\right)\right)$

[soft zealot]

nosqldb

[autumn geode]

and the answer is immediate

[ancient thistle]

This is how I did it

[autumn geode]

okay

that's not bad

but uh

recall the summation formula for 1 + ..... + n

[ancient thistle]

How can I implement this?

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[obtuse pagoda]

Part b can someone pls check my answer isn't matching the key

[zinc slate]

,w rotate

[zinc slate]

,w rotate

[soft zealot]

Results provided by WolframAlpha

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

Requested by yomiko787

[obtuse pagoda]

,rotate

[obtuse pagoda]

Oof 😭

I'll just send again

[zinc slate]

lmao

,rotate

[obtuse pagoda]

I used this formula

[zinc slate]

you have to do 2i, 3i, 4i, etc.... on the denominator

[obtuse pagoda]

But I did no .?

2! Is just 2 . 1
And then 3! = 32*1

3 x 2 x 1

[zinc slate]

x^4 term

nvm wait

[obtuse pagoda]

But question said till x^3

[zinc slate]

ahh

you singled out -2x

first and second term are right

3rd, 4th,5th...... term you should have (-2x)^2, (-2x)^3, (-2x)^4 ....

what you did was (-2)x^2, (-2)x^3.....

[obtuse pagoda]

Ahhhh

Tysmmmm

[zinc slate]

np

[obtuse pagoda]

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[vague cargo]

i've been trying to solve this problem all day yet i'm still absolutely stumped. would appreciate any help!

[soft meadow]

a^2022 * (a^2 - 1) + b^2022 * (b^2 - 1) = 0

have you tried contradiction method? I think that can be used

[vague cargo]

oh no i haven't

[soft meadow]

I am not sure entirely confident whether that would be helpful.. but you can try once

[vague cargo]

do you have any idea as to how i would go about it? i don't think i've ever had to use it before so i don't really know what i have to do

[soft meadow]

first thing that you can do is that without loss of generality you can assume a >= b

Are you fine with this statement? Have you seen or heard about it before?

[vague cargo]

i have, yes

what i did was
Set a >=b
Divide everything by a^2022
And without loss of generality, we get (a^2 - 1) + (b^2 - 1) <= 0

but i'm not sure if that is correct

[prime oar]

wot

how

[soft meadow]

how did you go from 3rd line to 4th line exactly? can you show me the steps

[vague cargo]

ah no there were no steps i just tried thinking of what i could do and if it made sense then i would expand on it

i had been up all night yesterday trying to figure it out so i just guessed at random and hoped it would make sense the next morning

[soft meadow]

try out the contradiction part once

you can google contradiction method for detailed understanding
for now the process is as follows - whenever you have to prove something..assume the opposite. Then use this opposite equality/inequality to land up in a situation which is mathematically impossible

[autumn geode]

this is a very easy proof

just assume that $a^2 + b^2 > 1$

[soft zealot]

nosqldb

[soft meadow]

don't give her the answer right away

@autumn geode

[autumn geode]

$a^{2022} (a^2 -1 ) + b^{2022} (b^2 - 1) = 0$

find the contradiction

and ur done

[autumn geode]

no I'm giving them the setup for the contradiction

[soft zealot]

nosqldb

[soft meadow]

ok fine fine..sorry for the interuption

[vague cargo]

thank you both for your help

i'll see what i can do

ah

[vague cargo]

i really have no idea what to do after this step

i don't really know what direction i'm supposed to go in so i just kept dividing and simplifying with no real goal

i did try everything i could think of but in every case i just ended up with lots of numbers that only made me stray further from the actual solution

if you could point me in the right direction it'd be very helpful

because as it stands, i don't really know what i have to do and so i just aimlessly try to extract something from the problem

[autumn geode]

what

do you not want to become a mathematician?

anyway

$a^2 > 2 - b^2$

[soft zealot]

nosqldb

[autumn geode]

$a^{2022}(1 - a^2) + b^{2022}(1 - b^2) > a^{2022}(b^2 - 1) + b^{2022}(1 - b^2)$

[soft zealot]

nosqldb

[autumn geode]

$a^{2022}(1 - a^2) + b^{2022}(1 - b^2) > a^{2022}(1 - (2 - b^2)) + b^{2022}(1 - b^2)$

[soft zealot]

nosqldb

[autumn geode]

$(b^2 - 1)(a^{2022} - b^{2022})$

[soft zealot]

nosqldb

[vague cargo]

how did we get to the right part of this inequation?
i'm not sure i get it

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@vague cargo Has your question been resolved?

[vague cargo]

ah

well

thank you for your help

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[dim karma]

help

confused

hellloooooooooooooo

[vague cargo]

to find the average rate of change, you have to divide the total change by the time taken for that change to occur

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[umbral shuttle]

is everything correct here?

[vestal frigate]

Looks good to me

In line four you might want to change the wording so that '1' is after the negative sign

I think that's what you meant to say in the context of identifying the value of a

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@umbral shuttle Has your question been resolved?

[umbral shuttle]

ty for that

.close

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[violet haven]

The lengths of the corresponding sides of 2 similar right triangles are in the ratio of 4:7. The hypotenuse of the smaller triangle is 20 inches long. How many inches long is the hypotenuse of the larger triangle?

[violet haven]

how would i go about solving this

[little python]

they are similar triangles

thier ratios of sides are equal

[violet haven]

what do i do with the ratios

[violet haven]

i still don't get it

you can change the ratios by multiplying how does that help me find the hypotenuse

[little python]

when 2 triangles are similar thier ratios of sides are equal

just like in this example

similarly for ur question

this would

be

$\frac{4}{7}=\frac{20}{x}$

[soft zealot]

🐱!Yajat! 【Catfan1398】🐱

[violet haven]

so the small triangle would have side lengths of 4 and 7?

[bronze lynx]

No

What is a ratio

[violet haven]

a fraction

i thibk

[bronze lynx]

Yes but in this case what is the ratio representing

[violet haven]

no idea

[bronze lynx]

"The lengths of the corresponding sides of 2 similar right triangles are in the ratio of 4:7."

[violet haven]

so they're like

so you can divide the ratio down to 4/7

[bronze lynx]

The ratio of what

[violet haven]

idk how to say it

but like

it simplifies to 4/7

i think

[bronze lynx]

Ok pretend side a on triangle 1 is 4, what is side A on triangle 2?

[violet haven]

8

idk

[bronze lynx]

Well

If the ratio of the sides is 4 to 7

What does that mean

[violet haven]

so is it 5

[bronze lynx]

How did you get there

[violet haven]

after 4 is 5

[bronze lynx]

As in 4+1?

[violet haven]

the ratio of the sides are 4 thru 7 so i said 5 as the next one

[bronze lynx]

Not through

4 to 7

As in 4/7

Like the fraction you said

Ok wait

What does 2 triangles being similar mean to you

[violet haven]

same angles

[bronze lynx]

Ok same angles and...?

[violet haven]

sides that are like

you can multiply to them

i think

[bronze lynx]

Give me an example

[violet haven]

if a side is like uhh 2 a similar triangle could have that same side be 4

i think

[bronze lynx]

Thats a possibility

But

More specifically, thats only possible if the similar triangles have a ratio of corresponding sides that is 1:2, aka 1/2

Because 2/4 = 1/2

What would that mean if another side on the triangle with side = 2, is equal to say 3?

What would the corresponding side be on the other triangle

[violet haven]

idk

9

or uhh

6 nvm

[bronze lynx]

Yes exactly

And if the last side is lets say 5, what is the corresponding side on the other triangle?

[violet haven]

10

[bronze lynx]

Perfect

So the sides on 1 triangle are (2, 3, 5) and since the ratio of corresponding sides is 1/2, the sides on the corresponding triangle are (4, 6, 10)

Does that make sense?

[violet haven]

yes

[bronze lynx]

Ok so what if the ratio of corresponding side was 1/3 not 1/2

What happens to the corresponding triangle of that same (2, 3, 5) triangle

[violet haven]

multiply by 3,

?*

[bronze lynx]

Yep so

[violet haven]

6 9 and 15

[bronze lynx]

Awesome

Ok so heres a little harder one before we go back to the problem

If triangle 1 has sides (3, 6, 9), and the ratio of corresponding sides is 3/4, then what are the sides of the corresponding triangle?

[violet haven]

do you multiply by 4

[bronze lynx]

Not only that though

Whats different between the ratio being 1/4 and 3/4

[violet haven]

1/4 is .25 and 3/4 is .75

[bronze lynx]

Well yes

Ok so

Back to (2, 3, 5) and (6, 9, 15) for a sec

The ratio is 1 to 3

What does that mean (besides multiply by 3)

[violet haven]

you can divide by 3

[bronze lynx]

Right

More specifically it means that for every 1 side length of triangle 1, triangle 2 is 3 of those side lengths

Make sense?

[violet haven]

no

[bronze lynx]

Ok so

Let me rephrase

For every 1 added to the side length of side a on triangle 1, 3 is added to the side length of side A on triangle 2. So if side a on triangle 1 is as we said 2, then for triangle 2 since we are adding 3 for every 1 added and there are 2 added, it is 3*2 = 6

Is that any better?

[violet haven]

that's worse

i don't understand any of this bro

[bronze lynx]

Ok

[violet haven]

do you add 3 every time to the sides

[bronze lynx]

Basically

Pretend you have 2 piles

Both piles start at 0

If you add 1 to pile 1, then you add 3 to pile 2

[violet haven]

oh ok

[bronze lynx]

So then Pile 1 = 1, and Pile 2 = 3

And then if you add another 1 to pile 1 you add another 3 to pile 2

So then Pile 1 = 2, and Pile 2 = 6

And so on

[violet haven]

i understand that now

[bronze lynx]

But thats for a ratio of 1 to 3

Nice

So instead if we have a ratio of 3 to 4

And both piles start at 0

What happens if you add 3 to pile 1

[violet haven]

you have to add 4 to pile 2

[bronze lynx]

Right

[bronze lynx]

So back to this

If triangle 1 has sides (3, 6, 9), and the ratio of corresponding sides is 3/4, then what are the sides of the corresponding triangle?

[violet haven]

so i have to add 4 to each one?

[bronze lynx]

Each one meaninggg

[violet haven]

7 20 and 13

[bronze lynx]

Not quite

[violet haven]

i mean 10

[bronze lynx]

Still

In our pile case, both started at 0

So in this case, you have to start at 0 too

[violet haven]

so 4,4,4

[bronze lynx]

Treat each side separately

So side a of triangle 1, 3 was added how many times?

[violet haven]

3 times?

i have no idea

[bronze lynx]

Ok let me simplify

Triangle 1:
Side a = 3
Side b = 6
Side c = 9

If we started at 0

How many times was 3 added to Side a?

[violet haven]

once

[bronze lynx]

Yep

And to Side b?

[violet haven]

twice

[bronze lynx]

And to side c?

[violet haven]

3 times

[bronze lynx]

Yep

So then if have the ratio of 3/4, or in other words, if you add 3 to one side, you add 4 to the corresponding side

And triangle 2 starts at 0 as well

What is Side A in triangle 2?

[violet haven]

4

[bronze lynx]

Yup

And Side B?

[violet haven]

4

[bronze lynx]

No

Ok

So for Side b in triangle 1, we added 3 how many times like you said?

[violet haven]

2

times

[bronze lynx]

Yes so how many times do we need to add 4?

[violet haven]

wait so side b doesn't start from 0

[bronze lynx]

It does

We started at triangle 1:
Side a = 0
Side b = 0
Side c = 0
Then we added 3 once to side a, twice to side b and 3 times to side c
So as a result:
Side a = 3
Side b = 6
Side c = 9

[violet haven]

why do we add it twice for side b and three times for side c

[bronze lynx]

Bc you said

One sec

[bronze lynx]

^

[bronze lynx]

^

To get to 6 from 0 you added 3 two times

And to get 9 from 0 you added 3 three times

[violet haven]

yea but why does that happen

why doesn i add 3 three times to side A

[bronze lynx]

Oh thats just because I said that triangle 1 has sides (3, 6, 9)

We were trying to figure out how many times we added 3 to each side

If we started at 0

[violet haven]

oh ok

[bronze lynx]

Anyway, we start now at triangle 2:
Side A = 0
Side B = 0
Side C = 0
Now for every time we added 3 to each side of triangle 1, we need to add 4 to the sides of triangle 2.

So Side A = ?

[violet haven]

so 4 8 and 12

[bronze lynx]

Perfectttt

So to sum it up we started with triangle 1 which had sides of (3, 6, 9) and said it was similar to triangle 2 with a ratio of 3/4. After using that ratio, we got that triangle 2 has sides (4, 8, 12)

That all makes sense now right?

[violet haven]

not rlly

all i know know is to add 4 each time

[bronze lynx]

Well no, you know that operator for triangle 2 is to add 4 each time the other triangle side adds 3.

So for the future if the ratio is 5 to 4, you add 4 each time the other side adds 5

And what if the ratio is 6 to 4?

[violet haven]

you add 4 each time the other side adds 6

[bronze lynx]

Perfect

[violet haven]

but i have no idea what that means

[bronze lynx]

I mean you essentially know how to use a ratio in terms of similar triangles

Which is whats important for this question

Lets try again

If the ratio between corresponding sides of similar triangles is now 2 to 5, describe what happens to side A of triangle 2 if side a of triangle 1 is 2?

[violet haven]

5

[bronze lynx]

What about 5

[violet haven]

you add it

side a is 5

i think

[bronze lynx]

Yep

[violet haven]

so 5 10 and 15

[bronze lynx]

Thats if the sides b and c of triangle 1 are 4 and 6

But its not necessarily always going to be that way

Lets do a practice q

Same question but now

Triangle 1:
Side a = 2
Side b = 6
Side c = 8
Triangle 2:
Side a = 5
Side b = ?
Side c = ?

[violet haven]

15 and 20?

[bronze lynx]

Awesome

You got it

So lets now go back to the original question

The lengths of the corresponding sides of 2 similar right triangles are in the ratio of 4:7.

Actually

Lets start with this

Triangle 1:
Side a = 4

Triangle 2:
Side b = ?

[violet haven]

7

[bronze lynx]

Yep

[violet haven]

wait

[bronze lynx]

Oh

[violet haven]

so it's 35

[bronze lynx]

Wow

Yeah it is

Good job

[violet haven]

45 is 20 75 is 36

wait

discord bru

[bronze lynx]

Yeah lol I know what you mean

[violet haven]

but i get it

[bronze lynx]

Thats great

Any other q's?

[violet haven]

would i be able to find side b of the smaller triangle

[bronze lynx]

Not unless you had side b of the bigger triangle

[violet haven]

so it would be impossible

[bronze lynx]

Yeah

[violet haven]

i have one more question

[bronze lynx]

Yeah?

[violet haven]

how would i figure this out

[bronze lynx]

Ah

Ok so starting with (-a)^n

When is that positive and when is that negative

[violet haven]

i have no clue

[bronze lynx]

Ok

Lets take a step back

What is 2^2

[violet haven]

4

[bronze lynx]

Yep

What is -2^2

[violet haven]

4

[bronze lynx]

Yep

What is 2^3

[violet haven]

8

[bronze lynx]

Yep

What is (-2)^3

[violet haven]

-8

[bronze lynx]

Awesome

Is 2 even or odd

[violet haven]

even

[bronze lynx]

Is 3 even or odd

[violet haven]

odd

[bronze lynx]

Cool

So if (-2)^2 is positive and 2 is even, and
If (-2)^3 is negative and 3 is odd, then

What does that mean about if a number is even or odd in the exponent?

[violet haven]

if it's even then it'll be positive if there's a negative if it's odd it'll be negative

[bronze lynx]

Yes

So

Now, if we go to a^m

If a is positive, what does that say about a^m?

[violet haven]

it's positive

[bronze lynx]

Yes

So if its positive and it is less than (-a)^n, what does that mean about (-a)^n

[violet haven]

n is probably odd

[bronze lynx]

Why so

[violet haven]

because uhhh

idek

[bronze lynx]

Lol

Thats ok

So if I have a positive number lets say 3

And I have x > 3

Can x be negative?

[violet haven]

no

wait so n is even

[bronze lynx]

Yep

That removes which options

[violet haven]

f g and j

[bronze lynx]

Yep

So now all thats left is to figure out if m>n or n>m

So

Lets back up for a sec

If we said (2)^2 = 4 and (-2)^2 = 4

And we said thats for even exponents

And n is an even exponent

Then that means if we have (a)^n it would also be equal to (-a)^n right?

[violet haven]

yea

[bronze lynx]

Ok so lets substitue that in

We need (a)^m < (a)^n now right?

[violet haven]

yes

[bronze lynx]

Cool

Do you know what makes that true?

[violet haven]

i guess whatever n is it's bigger than m

[bronze lynx]

Yeah

Because

If 2^2 = 4

2^3 = 8

8 > 4

So if the exponent is bigger then the result will be bigger

Which is what we want

So n has to be bigger than m

And the answer is ?

[violet haven]

H

[bronze lynx]

Yep

[violet haven]

i might have some more

[bronze lynx]

Alright, I have to go. I'm sure someone else can take over.

[violet haven]

ight bro ty for your help cya

[bronze lynx]

Of course

[violet haven]

.close

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[tranquil pine]

Why does $\frac{0.032b^2}{b^-3}=0.032b^5$

[soft zealot]

Matt

[tranquil pine]

i forgot some of the exponent rules so im tryna understand

bruh

-3 is an exponent

[shut gazelle]

$\frac{1}{b^{-n}} = b^n$

[soft zealot]

CaptainNova22

[shut gazelle]

That's the exponent rule that's getting applied

[tranquil pine]

so when youre dividing by something with a negative exponent

it turns into a positive exponent

and you add with the other exponent

[boreal mica]

Yeah

[tranquil pine]

ok thanks

.close

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[grim imp]

Is this correct

[grim imp]

Idk if anything changes with the plus or minus sign I was just taught how to do principal root

Idk if anything changes

Nothing changes right fr

Ty

.close

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[plush sparrow]

could anyone help me with proof of the first one

[plush sparrow]

so basically

the proof says:

g ◦ f injektiv

then it says

f (x) = f (x′) follows g(f (x)) = g(f (x′))

because g is a function

then he follows :
g ◦ f injective => x = x'

[urban maple]

yup! what are you unsure about?

To show f is injective, you want to say f(x) = f(x') => x = x' right?

[plush sparrow]

jep

[urban maple]

so just apply g to both sides

[plush sparrow]

gf(x) = gf(x')

[urban maple]

and then you get g(f(x)) = g(f(x'))

but we know that g o f is injective

so that means x = x'

[plush sparrow]

jep

[urban maple]

and so you're done!

[plush sparrow]

and how do i know that f(x) is now injective

[urban maple]

Because you showed x = x'

that was the whole point

[urban maple]

You ended up show this is true

i.e. you started with f(x) = f(x') and you ended up at x = x', so f is injective

[plush sparrow]

okay dumb question

but if i says f(x) = f(x')

that g(f(x)) = g(f(x'))

[urban maple]

what's your question?

[plush sparrow]

no i got it sorry

the second one is harder to proof right

if something is surjectiv

i need to show

[urban maple]

should be as easy 🙂 !

[plush sparrow]

that g(y) = Z right

[urban maple]

Well given z, you need to show there is a y such that g(y) = z, yes

[plush sparrow]

to understand it correctly

the image of g must be the whole set Z

[urban maple]

well, that's one way of saying it but it's a little better to break that down so that

Given any z in Z, you can find y such that g(y) = z

same meaning, just easier to work with

[plush sparrow]

can i ask yo another questioon

so i wanna show that this is surjective

so i need to show that

∀y ∈ Y : ∃x ∈ X mit y = f (x)

f(n) = (-1)^n

[urban maple]

yup!

[plush sparrow]

soo

i would have

n = log -1 f(n)

bug log to base -1 isnt defined right?

but logically it must be surjective right?

i mean i can find an x for so that f(x) = -1 and an x so that f(x) = 1

hmh

[urban maple]

You're thinking too hard 🙂

you want to show that (-1)^n = 1 and -1 has a solution

in N

well? what are some numbers in N? and what do you get if you do (-1)^n of them?

so for example try 1 2 3

[plush sparrow]

jes for every

even number i get 1

for every odd number i get -1

but in another example

to test this for surjective

y = 1-2x

1-y/2

[urban maple]

yup!

[plush sparrow]

x= 1-y/2

so for every y i can find a x = 1-y/2

right?

[urban maple]

yup!

[plush sparrow]

but when i do it like thos

with y= (-1)^n

n = log -1 (y)

i cant find an n for every y

because log-1 isnt defined?

[urban maple]

for different functions you show it in different ways

yes it doesn't work because log-1 isnt defined but

why even bother? its such an easy function you were able to tell by inspection

from odd and even numbers

[plush sparrow]

thats true

but how does that make any sense

its obv surjective

but if i want to show it generelly with n = log-1(y) it doesnt work

[urban maple]

what do you mean how does it make sense?

no one said that to show a function is surjective you have to show an inverse

a surjective function doesn't have to have an inverse

consider the function {1,2,3,4.5} -> {1} that just maps everything to 1

no inverse

but its surjective

if you're able to find an inverse its helpful, but its not a given at all

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@plush sparrow Has your question been resolved?

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[tranquil pine]

.close

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[last grove]

What is the result be if 4y+11

[tranquil pine]

what do you mean?

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[mighty elk]

Can anyone check if this proof in QL is correct? I'm struggling with existential elimination

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[final saddle]

Please don't occupy multiple help channels.

@crude nova Has your question been resolved?

[eternal sluice]

Because it's an equilateral triangle each angle is 60 deg, so use trig functions (sin, cos, tan) to find BK

BK is the height so use the triangle area formula (1/2)bh to find the area A

[crude nova]

idk trig im in 7th

grade

[eternal sluice]

I don't remember how to find the height using what's given

[crude nova]

oh rip

whats a

at least

or tell me how to

pls

[eternal sluice]

The problem is I don't know the length tho ima say 0.43 is the area

I'm not sure tho

[crude nova]

its wrong

im on my last try

[final saddle]

@crude nova Has your question been resolved?

[wise oracle]

Is BK not sqrt(a^2-(0.5a)^2)? And then U simplify that

and area would be value of BK * 0.5a simplified

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[next lance]

Idk what i did wrong here but apparently its super close

Like one tiny mistake somewhere

.close

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[jade fable]

It asks for the blue-encircled

Yet I’m not sure how to compute the stuff at the bottom line

Any advice

[autumn geode]

Yes

I can help you

Do you know what i^2 is?

[jade fable]

it is -1

[autumn geode]

Okay so what would z^2 be

[jade fable]

9/10-2 * 3/10 * 2/5 i -4/25

for the Z to be the number mentioned in the question

[autumn geode]

Mhm

Now what is the magnitude of that

[jade fable]

it is 37/25 -12/50 i

I suppose the magnitude of z means the value of z?

after being simplified for sure

[autumn geode]

No

[jade fable]

ohh

I see

that is the distance (origin, Z^2)

[autumn geode]

Mhm

[jade fable]

sqrt[ (37/25)^2 -(12/50 )^2]

a arrow from the tail ot the head of a vector is what i have seen when searching the word on the internet

[autumn geode]

It should be +

[jade fable]

sqrt[ (37/25)^2 + (12/50 )^2]

then what should I do?

[autumn geode]

Add it all up

It’s a sum

Do the same process up to n

Keep track of the previous one Yoo

[jade fable]

u means adding them up one by one

[autumn geode]

Mhm

From n = 1 to n = 10

[jade fable]

wdym

it sounds tiredsome

[autumn geode]

That’s the problem

You might find a pattern

Which could be super nice

[jade fable]

i didnt see it

[autumn geode]

I have a question tho

are you from an asian country

[jade fable]

yes I do

[autumn geode]

how does tutoring work

do ppl get paid a lot

I've heard that's a thing

[jade fable]

do you mean teacher

or ppl in the tutoring industry

[autumn geode]

ppl in the tutoring industry

[jade fable]

cram school is quite popular in my country, so i guess cram school teachers do get a lot of money for their work.

i see the pattern of |z|^r where r go from 1 to 10

but it is pointless, as i had already recongnized it at the very start

and theres no such a formula for the computation

[final saddle]

@jade fable Has your question been resolved?

[autumn geode]

What

[final saddle]

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[latent elk]

please help i dont understand the last part of the working at all

<@&286206848099549185>

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@latent elk Has your question been resolved?

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@latent elk Has your question been resolved?

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[vernal mica]

What is the partial derivative of sin(xy) ?

[strong radish]

with x or with y?

[vernal mica]

with x

and y

i didnt find a sure answer

for either

[strong radish]

for x it would be y*cos(xy)

and for y it would be x*cos(xy)

[final saddle]

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.

[vernal mica]

ok, i wasnt sure because my calculator gave me a 0

idk why

but thanks

[strong radish]

wc

[shut gazelle]

What calculator are you using?

[vernal mica]

geogebra

[shut gazelle]

Because not all calclulators can do partial derivatives

[vernal mica]

it should be able to

but idk, maybe a bug

.close

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[mental roost]

hey

[mental roost]

i have

i have something like this

how can i calculate this?

a friend of mine just squared the entire thing, but i think that doesnt work

i say we would translate into something like a+bi and then take the norm

[worldly vale]

call the thing inside z

then this is equal to $z\cdot \overline{z}$

[soft zealot]

ΣΑC

[mental roost]

ahh nice

so to get z bar, i just swap the minus in the exponent

thank you^^

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[sharp gorge]

Is this a binomial distribution with p = 0.5 and q = 0.5 and n = 4

[royal gust]

11,12,13 are

Well, 14 can be answered with it too

[sharp gorge]

14. f(3) + f(4) yes

Thank you

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[coral bluff]

My answer is 2

But confused with 0
Should I include 0 in non negative numbers?

[strong radish]

yes

0 is included in non negative numbers

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[coral bluff]

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[coral bluff]

.ckose

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[final saddle]

✅

[coral bluff]

So what will be correct answer? Only B

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[ruby shore]

help!

[ruby shore]

can someone walk me through step by step?

[supple jolt]

Do you know what the absolute value does

[ruby shore]

uh

makes everything a real number?

or like

[supple jolt]

No

[ruby shore]

makes numbers non negative

[supple jolt]

Yes

Whats |3|

[ruby shore]

3

[supple jolt]

Whats |-3|

[ruby shore]

3

[supple jolt]

Good

What do you not get in your exercise

Just apply this

[ruby shore]

so 3-4 is -1

-1 something? 6

what’s happening between the absolute value lines and the normal numbers

[supple jolt]

Solve the absolute values first

Then worry about the other terms

[ruby shore]

-3 turns to 3

[crude idol]

this reminds me of when i get pemdas wrong

[ruby shore]

2/-3 is 6

[crude idol]

yep

i mean

[ruby shore]

i never claimed to be smart 🤷‍♀️

[crude idol]

actually yes

[quiet zinc]

what

[ruby shore]

absolute value

[crude idol]

i think its |2(-3)|

[quiet zinc]

oh you mean|-3|

ok.

[ruby shore]

so

[crude idol]

so the answer is -7

[ruby shore]

-1 |6| /3

what happens with the absolute value lines

like

what’s the operation

[quiet zinc]

multiplication

[ruby shore]

between -1 and 6

[crude idol]

multiplication

[ruby shore]

is that an absolute

like

always

[quiet zinc]

if nothing is mentioned yeah we take it as scalar multiplication

[ruby shore]

okie dokie

thank you

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[nova walrus]

help me please

[tranquil pine]

For all x,y in the field R and you excludes 0 x cannot equals to y because it would equals to 0?

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[frozen sparrow]

Hey I am confused on this question if anyone can explain it to me please

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[frozen sparrow]

😭

[frozen sparrow]

I'm not even doing homework this is a revision sheet

This is the solution sheet the teacher sent and this question wasn't even solved

[frozen sparrow]

.

[final saddle]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[frozen sparrow]

I see

How can I change it?

[thorn grotto]

Just post a picture

Screenshot it or take a photo

[thorn grotto]

Have you tried i already?

[frozen sparrow]

Yes

The one I'm confused on is PRS

POS is 180-(42+42) and I think PRS is half of POS

[thorn grotto]

Yes

Its a theorem actually

[frozen sparrow]

Yeah I just been confused as my classmates were saying otherwise

[thorn grotto]

https://images.app.goo.gl/mEPPY5iJKiFb7D5C6

[frozen sparrow]

I basically have zero idea on SPQ and PSQ

[frozen sparrow]

Ooh thanks I'll make use of this!!

I'll try and memorize it

[thorn grotto]

SPQ is the more difficult one

Try looking at the quadrilateral PQRS

And use the theorem on the bottom right