help-38

[bright seal]

-3 not 3

There is a less in front of 3

-1(6/2)=-3

[wintry zealot]

No

[bright seal]

$5+7-3+11=5+4+11=20$

[solid kiln]

Task Bot

[bright seal]

Ok so far?

[wintry zealot]

No

bruh I might as well js give up

i don’t even know ts

[bright seal]

What is not clear

[wintry zealot]

Like everything idk

[bright seal]

From where precisely

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[plain tusk]

im confused

no progress

[lilac flame]

what is the total weight of red bricks

[plain tusk]

total?

hmm

is it like 20kg?

im not sure

[lilac flame]

yes

why ru unsure

[plain tusk]

was confused on how to get total weight from only the mean and amount of objects

[lilac flame]

mean = 5 = sum / number = sum/4

how do u find the mean weight

add up all the weights then divide by the number of bricks

[plain tusk]

mean = add numbers and divide by numb of bricks

[lilac flame]

yes

[plain tusk]

oh ok

[lilac flame]

now multiply both sides by number of bricks

do the same for blue

[plain tusk]

5 blue = 45kg total

green = 6kg total

[lilac flame]

yh now found the mean of all 10 bricks

[plain tusk]

i got 7.1kg

71/10

therefore, donna is incorrect

[carmine mauve]

Isn't Donna wrong here by saying "the mean weight of the 10 bricks is less than 7 kg"?

[plain tusk]

yes i believe so

[silent canyon]

Similar triangles have the same ratio of sides

[carmine mauve]

Oh, I misread this. My bad 😉

[plain tusk]

i dont understand

[carmine mauve]

Take triangle ABC. The ratio of sides is clearly 9 : 15.

Now, imagine I scale it up by a factor of 2. Then the 9 cm side becomes 2 x 9 cm which is 18 cm, and the 15 cm side becomes 2 x 15 cm which is 30 cm.

Now, the ratio of this doubled triangle is 18 : 30, which we can reduce to (2 x 9) : (2 x 15) which is 9 : 15.

[plain tusk]

why would you double it?

[carmine mauve]

because I chose to in that example

[plain tusk]

as in the scale it up part

so could u scale it up by 5?

or like any number

[carmine mauve]

I could

Any number

If I chose a scale factor of 5, then the ratio would be (5 x 9) : (5 x 15) which is still 9 : 15

[plain tusk]

ok i understand that

[carmine mauve]

You need to;
0. know similar triangles have the same ratio of side lengths.

1. work out by how much the second triangle has been scaled up or down by
2. use that scale factor to calculate the length of the other side.

[plain tusk]

ok ye

[plain tusk]

1.5

/1.5

[carmine mauve]

yep

[plain tusk]

pr would be 6

oh yeah

oh so thats just similar shapes

[carmine mauve]

[plain tusk]

why does the question say angle ABC = angle PQR

shouldn't it say shape or triangle

i kinda thought i'd have to do trig

[carmine mauve]

ABC means "the triangle with corners A, B, and C"

[plain tusk]

yeah i get that but why angle

is it just to throw the person off?

[carmine mauve]

∠ABC would mean "the angle between lines AB and BC"

[carmine mauve]

Oh, I see what you're reffering to. I didn't properly it.

[plain tusk]

np

[carmine mauve]

It's because we know they're both right angle triangles, so by telling us they share another common angle, they're telling us the two triaangles are similar

tbh, they could have left that part out.

[plain tusk]

ohok

[carmine mauve]

I guess just extra information?

[plain tusk]

useless info lol

this one is connected to other question

does congruent mean same?

or like similar

[carmine mauve]

So, congruent means they are the exact same triangle, just drawn rotated.

[plain tusk]

so would you draw them out seperately

to understand it better

[carmine mauve]

they're the exact same triangle. you only need to draw it once.

that's what "congruent" means

[plain tusk]

oh

so would i do 10-4 to get GK

?

[carmine mauve]

you forgot point F

[plain tusk]

have i labelled the triangle wrong?

[carmine mauve]

nope, you've got it right

just need to add a point F between E and G

[plain tusk]

like that?

[carmine mauve]

Yyou've correctly identified GK = GE = 6 because the two triangles are congruent. Can you do the same with GH?

What other side is the same length as GH?

[plain tusk]

FG

[carmine mauve]

yep

[plain tusk]

so EF = 2cm?

[carmine mauve]

yep

[plain tusk]

i did 6-4

that question is not that bad tbh

do u have time for this one?

[carmine mauve]

1. knowing it's not obtuse, what's the gratest angle AOB can be?
2. use that to sum the smaller angles equal to it and solve for x

[plain tusk]

90?

89

[carmine mauve]

is 90 obtuse?

[plain tusk]

90 is right angle

[carmine mauve]

yep, so is it obtuse?

[plain tusk]

no

90+ is obtuse right?

[carmine mauve]

👍

90 is not obtuse

90.00000000001 would be obtuse XD

[plain tusk]

oh lol

over 90

and lower than 180

[carmine mauve]

well, as you said, it's a right angle

angles are either

• less than 90 (acute)
• exactly 90 (right)
• more than 90 (obtuse)

now sovle for x

[plain tusk]

ohh

it says not an obtuse

so would i do = 90?

16

[carmine mauve]

[plain tusk]

ohhh

the greatest value of x

i was a bit confused on why it had to be 90

last one

before i get off

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[vale flower]

how do I know which quadrant the angle is in if it’s in radians without converting the radians into degrees?

[vale flower]

like for tan(17π/6), it’s -√3/3 since it’s in quadrant two but like how do u know that it’s in quadrant 2?

[crimson pebble]

Do you know the boundaries of quadrants in degrees?

Convert those boundaries to radians

[vale flower]

what do u mean by boundaries?

[rare aurora]

what angles are in the first quadrant?

[vale flower]

30, 45,60

[rare aurora]

well these are some specific examples

but it's any angle between 0 and 90 degrees, those would be the boundaries CST is referring to

[analog cradle]

What I usually do is convert the fraction into a decimal.
E.g. 17π/6, I do 17÷6 = 2.8333 (I don't include the π)

If the decimal is in between 0 and 0.5, it's in Q1.
If it's in between 0.5 and 1, it's in Q2
If it's in between 1 and 1.5, it's in quadrant 3
If it's between 1.5 and 2, it's in quadrant 4.

In this example, it's 2.83333 (so similar to 0.83, cause it goes past 2). Therefore, it's in Q2

[vale flower]

ohh alr

oh wait that makes so much sense

thank youu!

is there any faster way to do this? cuz im expected to solve the functions in 24 seconds without calculator

should I like memorize all the radians of the unit circle or is that not really necessary?

[analog cradle]

It might not be necessary, cause just like the example you gave earlier, it goes past 2π, so the questions could be from anywhere before or after 2π yk

[analog cradle]

I can't think of a faster way without a calculator, but someone on here might be able to come up with it?

[crimson pebble]

Memorizing the special angles helps yes

Well first coterminal stuff, convert your angle to something between 0 and 2pi by adding or subtracting multiples of 2pi

[vale flower]

Like 30 45 60 angles?

[crimson pebble]

Yes, I’d add 0 and 90 as well

[vale flower]

is that to find the reference angle?

or coterminal

[crimson pebble]

That’s for coterminal angle first

But the next step is reference angle yes

[vale flower]

I don’t really know the difference between the two 😭

actually nvm

[crimson pebble]

So coterminal angles, all the trig functions share the same value

[crimson pebble]

Use this trick to determine the quadrant

Then get the reference angle, which is easy for radians because it’s a matter of looking at the denominator of the simplified fraction

For reference angle, all the magnitudes of the trig functions are equal, but the signs change depending on quadrants

[vale flower]

ohh so like if the fraction can’t be simplified further like 13pi/6, the reference angle would be pi/6?

[crimson pebble]

Well except 13pi/6 has a coterminal of pi/6

But basically yeah

For example, 11pi/6

Or 4pi/6 simplifies to 2pi/3, so we use pi/3 as our ref angle

[vale flower]

got it

thank u!

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[lone basin]

Are you trying to find the equuation of this curve?

[heady robin]

I am giving this function: F(x)=3sin(2(x-C)), I have to find out what C is

[lone basin]

Ok

[heady robin]

Actually the function was F(x)=Asin(B(x-C)) but I found A=3 and B=2

[lone basin]

Do you know about function transformations/translations

[heady robin]

No

[lone basin]

Essentially, f(x - C) will translate the function to the right by C units

[heady robin]

Ok, so is there a way to solve for C?

[lone basin]

Yes

For now, assume C = 0

What is F(0)

[heady robin]

F(0)=3sin(0)

[lone basin]

Which is...?

[heady robin]

0?

[lone basin]

Here, pick an x value such that F(x) = 0

[heady robin]

What is it other than 0?

[lone basin]

Well, you can see that F(0) = -3 based on the graph

So we need to find a different C value other than C = 0

[heady robin]

-pi/4?

[lone basin]

Ok, so youre choosing x = -pi/4

That means we need to move the function left by pi/4 units, or right by -pi/4 units

So what does that tell you about C?

[lone basin]

_ _

[heady robin]

C=pi/4?

[lone basin]

Technically that works, but to conform with the x-coordinate you chose, you should use C = -pi/4

[heady robin]

But that gives me the invert of the graph

[heady robin]

I think I understand now, thank you for your help

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[lone basin]

Oh alr

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[barren sequoia]

Need help with 3 and 4, the question asked for them to be in different orders. I tried drawing the surfaces on a 3D graph and have something written down but for some reason a≠b or 8/15≠1/3 for question 3. Then for question 4 idk how to do 4b in a way that I end up with just a number

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[barren sequoia]

<@&286206848099549185>

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[frank kestrel]

okayy soo im back haha... with my fellow friend @coarse chasm

im pretty sure the answer for the first one is like x = -15 and x=0

[frank kestrel]

but im not rlly paticularly sure

and the rest is more quadratics 💀

but one by one we shall go!!

[exotic pine]

correct

[frank kestrel]

WAHOO

this ione im guessing
x=0 x=8 so similar thingy then?

[exotic pine]

yes

[frank kestrel]

ok okkk thank yeww :3

[exotic pine]

what sthe diffrence between option 1 and 3

[frank kestrel]

i genuinly dont know

its the same thing i think maybe a error?

idk..

i do have one more tho 💔 this one.. now im terrible w word prolems #englishnotmyfirstlangauge

[exotic pine]

use the hint

[frank kestrel]

Ohhhh so like x^2 -15x= 0 then

so then x would be 15?

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[frank kestrel]

uh

🧍

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[kind token]

Find F(x), if n=20

[kind token]

I found the first one to be F(x)=20x-x²/2+C

Is this correct? There are no more steps I can do?

[solemn hound]

Translate please?

[kind token]

.

Find F(x)

[solemn hound]

ah i see

[solemn hound]

This is correct yes

[kind token]

Alright this is really important that I get all of them right so I'll just type here what I got for them)

[solemn hound]

sure

[kind token]

2. F(x)=20x^21/21+x^35/35+C

3. F(x)=20x^-5

[kind token]

Why is this incorrect?

[solemn hound]

second term

[kind token]

After the plus it's 7x^35/35

[solemn hound]

just re do it

[kind token]

35:7

[solemn hound]

okay well you missed the 7 in your message, and 7/35 =?????

[kind token]

The cancel out

Hold on

[solemn hound]

what happend to the 7?

just dissapeared?

[kind token]

Or is the last = incorrect?

[solemn hound]

last equals is incorrect

[solemn hound]

^^^^^^^

[kind token]

So not /35 /5

Ok wait

So

2. F(x)=20x^21/21+x^35/5+C

4. F(x)=-5x^-4+C

[solemn hound]

3 is also wrong

[kind token]

That's for 4 I skipped 3 somehow

[kind token]

Yea I skipped it doing it rn

3. F(x)=10x^-2+C

[solemn hound]

close

[kind token]

Oh

Wait

[solemn hound]

yes

[kind token]

-10

[solemn hound]

i cant tell what 4 is

pciture too blurry can you zoom in?

[kind token]

One sec

[solemn hound]

also instead of writing 10x^-2 you can write 10/x^2, idk if it matters for ur teacher

[kind token]

I'll do that too I think, idk either I'll just provide both

[solemn hound]

can you send a zoomed in picture of the questions?

[kind token]

x^-20/4

The tiny thing

[solemn hound]

yea thats correct

[kind token]

Alr I'm on to 5 then

Can I do more here?

[solemn hound]

why is the exponent -20/2?

[kind token]

Square root

There's always a 2 on the root we don't write right

[solemn hound]

but why is it negative?

[kind token]

Good question wtf am I smoking 😂

Shouldn't be negative

11

Why did I write 9

Holy fuck

[solemn hound]

eh try again

just restart it

[kind token]

x^2•x^11/11+C

Is that incorrect?

[solemn hound]

yea

just do it again youll get it

[kind token]

Ale

Alr

[kind token]

I got this again idk

[solemn hound]

show ur work

[solemn hound]

you cant just integrate like that

simplify f(x) first

[kind token]

2x^11?

Alr

[solemn hound]

thx haha

[kind token]

I can't be bothered to scroll up again)

Can I integrate with this

[solemn hound]

yes

remember that S(a+b) = Sa + Sb

where S is integral sign

[kind token]

Yep alr

I'm lost

-20x^-1 should be correct

But then -20/-2 that's 10

So just +10x^-2?

[solemn hound]

what you wrote is correct

[kind token]

Alr

And if I were to put it into fractions I would write -20•1/x + 10•2/x

20/x

Or

Yea

[solemn hound]

Uh no?

oh wait

yea

[kind token]

+10 2/x

[solemn hound]

2/x?

[kind token]

x^-2

[solemn hound]

yes

1/x^2

[kind token]

Ah shit

Yea didn't look right

So

-20/x+10/x^2

[solemn hound]

yes

[kind token]

-20x+10/x^2

Idk if it's necessary to do that too

[solemn hound]

what? why 20x?

-20/x =/= -20x

[kind token]

I did write -20x

Or wdym

[solemn hound]

=/= is not equal

why does -20/x simplify to -20x?

[kind token]

Same denomination I think it's called?

[solemn hound]

just write it the first way

[kind token]

Ok

[kind token]

So just this

[solemn hound]

that is considered "more" simplified 99% of the time where it is a polynomial

[kind token]

Aito good to know

Ty for bearing with me so far btw sorry I'm kinda slow)

[solemn hound]

youre doing actually really well

[kind token]

So now 7

Do I have to multiply by 1/20?

[solemn hound]

simplify?

[kind token]

So up to this point it's correct?

12/20 cos20x

And 3/5

+C

Ofc

[solemn hound]

always

this one might be a bit tricky to see

[kind token]

Yes I just did it all incorrectly cause I forgot the formula

Well didn't notice it

[solemn hound]

S(sec^2x) = tanx

[kind token]

Moving to another class rn soz give me a bit)

[odd lichen]

you study integral in high school?

[solemn hound]

I did...?

[kind token]

Yes

[solemn hound]

what is stg?

[odd lichen]

we don't study integral but differential in China

[kind token]

1/cos^2

[kind token]

This is incorrect?

[solemn hound]

is that how youre supposed to write it? it is usually written as sec^2

[solemn hound]

well yes you didint even integrate it

[solemn hound]

^^

[kind token]

sec?

[solemn hound]

secant?

1/cosx = secx

[kind token]

These are the formulas I have

[odd lichen]

1/cos^2x

[solemn hound]

ah okay

write it like that then

just a difference of notation i guess, never seen it before

in that case you are still incorerct

[odd lichen]

sorry i remember that tanx's differential

[kind token]

Great 😂

[solemn hound]

chain rule?

i dont know what it is in russian

[kind token]

How come

[kind token]

It's Ukrainian

[solemn hound]

chain rule

[kind token]

8 should stay no?

[solemn hound]

show me your whole sheet i will show you the rule

because i dont know what it is in ukranian but in english it is called chain rule

[kind token]

The formulas?

[solemn hound]

yes

[odd lichen]

f(g(x))'=f'(g(x))*g'(x)

[solemn hound]

hm its not there

okay one sec

[kind token]

Ait

[odd lichen]

is that the chain rule?

[solemn hound]

@kind token is this everything you know?

[kind token]

Ill send the full math formulas one second

Should be somewhere here maybe

This is the file

[solemn hound]

okay wait gimme a second

[kind token]

Nw take Ur time

[solemn hound]

you cant do chain rule on derivatives im stupid lol

do you know what u substitution is? @kind token ?

[kind token]

I believe so

[solemn hound]

youre supposed to use that

[kind token]

I did though no..
I mean we have the formula of 1/cos^2x=tgx+C you see it right

[solemn hound]

yes but notice how we have 20x inside the cos

nnot just x

[kind token]

Ah

Times 1/20

?

[solemn hound]

yes that works

but im currious as to why you know that?

[kind token]

Ahh ok makes sense

Know what

[solemn hound]

that you multiply by 1/20

its correct

but im just wondering why

[kind token]

I was told to multiply the invert whenever there's a number beside x, I got really confused as to when we do it and when we don't so I made up my own philosophy of doing it only when dealing with cos sin tg

[solemn hound]

Hm okay

[kind token]

Sounds like a bunch of bs but it's been working XD

My teacher just couldn't explain it to me

[solemn hound]

it follows from u substitution but idk if you know about what that is

sure well you can always ask for help her

here

[kind token]

I don't think we covered it yet

[solemn hound]

interesting then

[solemn hound]

lol this is a pretty bad rule to follow

[kind token]

Idk how else to get it

I understand it's bad and even dangerous

But I just dk

[solemn hound]

Okay well when you have the time you should ask here

[kind token]

Aito

2/5 tg20x+C

9

-15/2 sin x/20

I have to apply to the power of 9?

Or can I just smack that shit into the integration and ()^10

[solemn hound]

i really think you should have learned u subsitution

there isint much of an easy shortcut for this one

i mean kinda

[kind token]

I agree, I don't think we're taught enough math

Coming from a Math based course into a regular one we are not taught enough

[solemn hound]

when is this due?

[kind token]

Friday

Tomorrow

[solemn hound]

i think you should wait till you go home and studdy u subsitution

[kind token]

Wdym

[solemn hound]

go home, learn u substitution, then do the problems

[kind token]

I think after I do them? I also need to ask about when to multiply by an inverted number and when to not

[solemn hound]

That is precisly what u subsition will tell you

[kind token]

My priority rn is the tasks because they'll raise my grade from 90 to 95

[solemn hound]

yea except theres no easy way to do the problems you posted, you kinda have to learn how to do it

and if you dont have to learn it this week then next week or the week after you will have to

[kind token]

Hmm

[solemn hound]

its a pretty simple, but valuable concept

[kind token]

Is it complicated? u substitution

[solemn hound]

and you really dont seem to be struggling

no, it should be part of your course...

i can explain it now if you want

[kind token]

If you could then yea I want to finish this rn

[solemn hound]

okay

you okay is i use S as the integral symbol?

[kind token]

Yep

[solemn hound]

Do you know what the chain rule for derivatives is?

[kind token]

Let me look it up and I'll tell you

[solemn hound]

df(g(x))/dx = f'(g(x))g'(x)

[kind token]

Yea looks like what we're going to cover tomorrow

[solemn hound]

Thats crazy

anyways

u-subsitution is used when you kinda what to do the reverse of that

so for example if you take Scos(3x+5)dx you might think the answer is sin(3x+5) + C

but it is not because we didint take into account the 3x+5 in the cos function

[kind token]

When it's actually 1/3?

Or is that not

What this is

[solemn hound]

yes... but we will get to why 1/3 in a sec

[kind token]

Ait

[solemn hound]

so when you have a function in a function, to put it simply, you can basically take the inner function and replace it with u

so for cos(3x+5) you would take u=3x+5

then you get cos(u), which is easy to solve

but

Now we have Scos(u)dx, where u=3x+5

but notice how we have dx still there we cant integrate over u

[kind token]

Yep

[solemn hound]

so what you can do is basically write this

u=3x+5

d(u)/dx = d(3x+5)/dx

du/dx = 3

[kind token]

We're dividing?

[solemn hound]

dx = du/3

[solemn hound]

do you know what dy/dx means?

[kind token]

Differentiate

[solemn hound]

yes

[kind token]

I very roughly know but

Not that well

[solemn hound]

so were not diving we are differentianing both sides in respect to x

f'(x) = df(x)/dx

[solemn hound]

understand this?

[kind token]

Uhh

Differentiate the function

[solemn hound]

its okay to say no

[kind token]

And then divide it by

Differentiation of x

[solemn hound]

no im just saying that writing df(x)/dx is the same thing as writing f'(x)

like they mean the exact same thing

[kind token]

Yea idk I'm a bit lost

[solemn hound]

dont think of it as divide

just think as d/dx means take the derivative

[kind token]

Ok ik what f'(x) is

I wasn't taught the df thing though

[solemn hound]

yes and if you write (d/dx) * f(x) that is the same thing as f'(x)

[solemn hound]

it is simply different notation

[kind token]

Alr

I was just only taught f'(x)

[solemn hound]

so if i say (d/dx)(x^2) that is equal to 2x

[kind token]

Yep

[solemn hound]

okay so lets go back

[kind token]

Got that

[solemn hound]

we have Scos(3x+5)dx

[kind token]

Yep

[solemn hound]

we replace the inner function with u such that u=3x+5

so we get Scos(u)dx

but we still have dx there so you cant just solve it

[kind token]

You have to separately integrate them?

Cos and u

[solemn hound]

no we have to replace the dx with something

so now we take u=3x+5

[kind token]

Oh wow

[solemn hound]

u=3x+5

on both sides we will differentiate with respect to x

(d/dx)u = (d/dx)(3x+5)

following?

[kind token]

With respect to x, unfamiliar with what that rly means

[solemn hound]

that just means differentiate the variable x

[kind token]

Alr

[solemn hound]

if you had f(y)=y^2 f'(y) means differentiate with respect to y

[kind token]

I get this yes

[solemn hound]

(d/dx)u = (d/dx)(3x+5)

du/dx = 3

[kind token]

Yep

[solemn hound]

du=3dx

[kind token]

Or wait is it 3?

[solemn hound]

dx=(1/3)*du

[kind token]

Ah yep

Yep yep

I'm slow

[solemn hound]

no ur really not lol

so now going back to our original equation

Scos(u)dx

[kind token]

Wait

[solemn hound]

Scos(u)1/3 * du

(1/3)Scos(u)du

(1/3)sin(u)

(1/3)sin(3x+5)

[kind token]

This seems important
So what you did here was move around u and x and it becomes 1/3
Yea I'm horrible when it comes to that sort of thing

[solemn hound]

i moved around du and dx to solve for dx so we can replace it in our original equation

we can do another example

[kind token]

That's really smart

[solemn hound]

question 8

[kind token]

Yep

[solemn hound]

S(8/cos2(20x))dx

that is the question

[kind token]

8/

[solemn hound]

we will take our inner function, 20x and replace it with u

so u = 20x

so now we have S(8/cos2(u))dx

8S(1/cos2(u))dx

you understand why i moved the 8 outside right?

[kind token]

Well I don't think it changes anything, you can do it but idk why you would
Does it mess with something later on?

[solemn hound]

no no, its just "better" to move numbers outside when you can

[kind token]

Fair enough

[solemn hound]

okay so going back

8*S(1/cos2(u))dx right?

[kind token]

Yea

[solemn hound]

now we need to find what dx is

so u = 20x

du/dx = d/dx * 20x

du/dx = 20

dx = 1/20 * du

[kind token]

This

[solemn hound]

and thats why you multiply by 1/20

[kind token]

du/dx is like u'?

[solemn hound]

yes

exactly

[kind token]

d/dx

Is just x'?

I'm missing something

[solemn hound]

(20x)'

you can think of d/dx as the '

[kind token]

Oh alr

[solemn hound]

Do you still understand?

[kind token]

From here it's really difficult for me to get if to multiply or divide or whatever else

Like ik we need dx

dx=20/du is my initial thoughts but it's actually multiply

[solemn hound]

well yes if you have a/b = 20

its just algebra

a=20b

b=a/20

[solemn hound]

its just algebra

[kind token]

Yep alr

[solemn hound]

so now going back

=8S(1/cos2(u))dx

=8S(1/cos2(u))(1/20)du

[kind token]

And dx=1/20du yea

[solemn hound]

=(8/20)S(1/cos2u)du

=(2/5)(tanu)

=(2/5)(tan20x)

[kind token]

That's rly smart

[solemn hound]

okay so try 10

i will help you

[kind token]

Give me a second I'm gonna write all that down

[solemn hound]

yea so this multiply by 1/20 rule is based off of something, if you can tell already, we are diving by the derivative of the inner function, in this case if you have 20x the derivative is 20

[kind token]

Alright I somewhat understand from writing it down

Practice should help yea

[solemn hound]

try 10 now

[kind token]

So

The ^9 scares me should I not pay it much mind?

[solemn hound]

yea first write it out in S dx form

[solemn hound]

YES

now what is your "inside" part

[kind token]

20x?

[solemn hound]

only 20x?

[kind token]

Or the whole bracket

Ah

Wait

Bracket=u

[solemn hound]

in most cases yes

but you can think of it as a function (20x-4) inside a another function (inside function)^9

for the example befoer the inside function was 20x

and the outside function was 1/cos2(x)

you good?

[kind token]

Yea sry moving classrooms)

[solemn hound]

yes

but write out that u=20x-4

[kind token]

Mmm I haven't done this ' in a while

One sec

20x^19

And I need dx

[solemn hound]

woaw

[solemn hound]

no

[kind token]

🥹

Ok wait

[solemn hound]

20 * x^1 - 4

look at your sheet

[kind token]

From 20 X we just rewrite 20

Ohhh

Fuck

20

Just 20

[solemn hound]

yea

[kind token]

dx would be du/20?

[solemn hound]

yes

[kind token]

du is 20x^2-4x?

[solemn hound]

?

no where did you get that from?

[kind token]

I'm using the wrong

Fuck

I confuse them often

[solemn hound]

you found dx, just replace it in your equation

[solemn hound]

yes but wait

the du/20 is just 1/20 * du

and you can take 1/20 out of the integral

[kind token]

Smart

Ok wait

[solemn hound]

YES

[kind token]

S(20x-4)•20?

5S

This feels wrong XD

[solemn hound]

why did you replace u before integrating?

[kind token]

Ok up to here

Then what

I replace u?

Just not du

[solemn hound]

integrate first

then replace

[kind token]

u10/10

du

[solemn hound]

yes u10/10

[kind token]

Ok thank god

[solemn hound]

5 * u10/10

[kind token]

I plug in u here?

Oh I can shorten

[solemn hound]

yes

and yes

[kind token]

u^10/2

To the power of 90??

Ok hold on

[kind token]

No

10

[solemn hound]

u^10/2

replace u now

[kind token]

This seems like a big ass number idk if that's correct

[solemn hound]

that is correct

[kind token]

Do I need to put it to the power

Or can I leave it

[solemn hound]

nah you can leave it

[kind token]

Thank god

Alr I also want to try it with my old method

So I can write both for my teacher

[solemn hound]

Sure

your old method just involves multiplying by 1/20 which is exactly what you did

[kind token]

Oh damn I don't think I can do it with my old method

Cause it's not like cos sin tg

But it is in brackets

Wtf

Yea idk how to approach it

[solemn hound]

its fine

try 11

first simplify f(x)

[kind token]

Fuck man this is tiring XD

Ok one moment

[solemn hound]

last one you got this

[kind token]

u is brackets

[solemn hound]

ye

[kind token]

why is it u btw

x would just be inconvenient?

[solemn hound]

wdym

[kind token]

Instead of u you can write any letter

I'm used to seeing dx within the integration symbol

Eh just forget it

du/dx=2

dx=du/2?

[solemn hound]

ye

[kind token]

du/2=1/2•du

[solemn hound]

yes

[kind token]

Soz I need to go offline for 10-15 mins

I'll ping you or DM you with №11?

[solemn hound]

sure

[kind token]

It's taking longer than I thought it would)

[trim jolt]

@kind token Has your question been resolved?

[kind token]

.close

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[limpid dawn]

compare it to 1/e^x

[sterile bramble]

problem is I don't understand the idea of comparing

[limpid dawn]

you are trying to find a greater converging integral

by leaving x out of the denominator you make the denominator less, and hence the overall expression greater

[sterile bramble]

and how does this help with me knowing if it will diverge or converge

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[heady mesa]

help please

[dapper swift]

you should be subtracting 19 not subtracting 3

f(3) = 19

,w (3 + h)^3 - 3(3 + h) + 1 - 19 simplify

[solid kiln]

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Requested by sooouth.

[dapper swift]

ah so the rest of your work is correct

[heady mesa]

thank you!

im so confuse

.close

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[dapper swift]

yeah next time you might want to write (f(3 + h) - f(3))/h, as in sub in a = 3

no worries!

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[marsh forum]

Trying to find the arc length here

[marsh forum]

the issue is the integral is rather messy to set up, is there any short cut?

Like the acr length is given by

$

$\int_{-\ln(4)}^{0} \sqrt{ (e^tcos(t)-e^t(\sin(t))^2+(e^t\sin(t) +e^t\cos(t))^2 + e^{2t}} dt$

[ionic pendant]

i have a feeling it will get nicer once you expand everything out

[dapper swift]

in particular take out a sqrt(e^(2t)) = e^t first

[ionic pendant]

not sure how the last term escaped from the square root there

[glad wren]

wow

[solid kiln]

What a wonderful world it is !

[marsh forum]

hmm

[dapper swift]

wait sorry

it is e^t, got distracted and thought e^t could be negative

[dapper swift]

apologies

[marsh forum]

I think taking out an e^{2t} should work

[dapper swift]

it's hard multihelping is my excuse

[marsh forum]

$\int_{-\ln(4)}^{0} e^{t} \sqrt{3}$?

[solid kiln]

What a wonderful world it is !

[dapper swift]

yep!

[marsh forum]

hmm

okie

so $5\sqrt{3}$

[ionic pendant]

e^0?

and e^(- ln 4)?

[marsh forum]

that's 1

oops

[solid kiln]

What a wonderful world it is !

[dapper swift]

this is (e^(ln 4))^(-1)

[marsh forum]

oh right

-ln(4)

which is 1/4

so \sqrt{3} (1+1/4)?

so $\frac{5 \sqrt{3}}{4}$

[solid kiln]

What a wonderful world it is !

[ionic pendant]

adding?

[marsh forum]

f*

no

what's wrong with me

[dapper swift]

it's okay I'm sleepy too

[marsh forum]

$\frac{3 \sqrt{3}}{4}$

[solid kiln]

What a wonderful world it is !

[marsh forum]

Is this fine ?

[ionic pendant]

,w arc length of (e^t cos t, e^t sin t, e^t) from -ln 4 to 0

[solid kiln]

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Requested by cloudedhorizons

[marsh forum]

Thanks

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[frank bough]

Ppl help me with this

[round mango]

have you tried anything

[frank bough]

I am not sure how to do with percentage

[naive otter]

Start with considering the length x, and form eqns

[round mango]

do you get what it means to increase by 10%

[frank bough]

Can u explain in detail

[round mango]

say the length is 100

[frank bough]

No thats the thing

[round mango]

what will be the new length if i increase it by 10%

[frank bough]

110

[round mango]

yes, howd u get it

[frank bough]

Bcz i have lenght

In question it isnt there

[round mango]

no what i mean is

how did u go from 100 to 110

use the same logic

this time, with just a variable l

[frank bough]

What

[round mango]

you did 100 + (10% of 100) to get 110

am i right

[frank bough]

Yes

[round mango]

so

just replace

100 with the variable l

[frank bough]

Ok

Now what

[round mango]

do the same for breadth

b- (20% of b)

and write what theyve given you in the form of a mathematical eqn

[round mango]

you know that 10% of l just means 10/100 * l right?

[frank bough]

Yes

[round mango]

so write that

[frank bough]

Oh

[round mango]

and then they have said that the perimeter remains the same

[frank bough]

Can u writw how equ comes

[round mango]

no i wont

do it yourself

[frank bough]

Indid not understand

[round mango]

Okay lets see

[frank bough]

Ok

[round mango]

percent or 'per cent'

its like saying if i divided the thing into 'cent' i.e. 100 parts

[frank bough]

Hmm

[round mango]

how many parts will this occupy

so like

10 per cent of 50

is 10 / 100 * 50

so if i have l

10 per cent of l

just means

10/100 * l

[frank bough]

Ok

Next

[round mango]

rewrite these

and use them

in the perimeter formula

[frank bough]

Can u do it like this ig

[round mango]

that is literally what i told you to do on your own

[frank bough]

I couldn’t understand

How is it 1.1 l cm and 0.8 b cm

[round mango]

what is l + 10/100 * l

you know fractions?

[frank bough]

Yes

[round mango]

so what is it

[frank bough]

l+l/10

[round mango]

yes and what is 1/10

[frank bough]

This is the thing i am not understanding

[round mango]

what are you not understanding

l+l/10 is the same thing as l + l * 1/10

[frank bough]

Thwn next

[round mango]

or you can look at it like l(1+1/10)

[round mango]

what is 1/10

[frank bough]

Idk

What r u trying to say

How 1.1 l cm

Anyone help

[round mango]

do you get this

[frank bough]

No

[round mango]

ok then what about this

do you get this

[frank bough]

No

Is it right

[round mango]

yes

1/10 is just 0.1

so l +0.1l=1.1l

[frank bough]

Ok

How 1

[round mango]

what is x+2x for example

[frank bough]

2x+x

[round mango]

?

yes and what is that

if you cant do that i suggest you review your materials

[frank bough]

Just tell me how 1.1 came

[round mango]

i literally did

[frank bough]

See
l + 0.1l = ?

[harsh vessel]

That 1.1 is an error it's supposed to be 0.1

[frank bough]

No its 1.1

[round mango]

.

on how to collect like terms

[frank bough]

Yes i ll check them thxx

[round mango]

one time something plus 2 times that thing is 3 times that thing

one time soething plus 0.1 times that thing is 1.1 times that thing

[frank bough]

Ok ill check

Thank u

.close

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[harsh vessel]

Okay you are correct

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[worldly wing]

If we can remove both nullspaces from this diagram (i.e. from the domain and codomain) to get a bijective mapping from the row space to the column space, does that mean that we can get an rxr invertible matrix by removing certain rows and columns of an mxn matrix A?

[worldly wing]

and is this the largest possible invertible matrix we could get?

[amber python]

yes

[worldly wing]

that's pretty cool

[amber python]

yes

you can find those columns and rows using rref as usual

[worldly wing]

oh it's just the pivot rows and columns

so it's unique?

[amber python]

i think the rows won't just be the pivots

the columns will be

you'll either have to backtrack or you could just do column reduction after you kill the columns you don't need

so should be unique

wait no that sounds sus

i don't think it's unique because you might have different choices of columns that span the image

[worldly wing]

yeah

you can have different sets of r columns that span the whole column space right

[amber python]

yes

[worldly wing]

and also different sets of r rows that span the row space

[amber python]

yes

a related cool result is that you can always choose bases of the domain and codomain so that the matrix is an rxr identity matrix in the corner and 0s elsewhere

[worldly wing]

yeah I think that was a question/fact mentioned in the book

[amber python]

so rank is the only invariant of a matrix under base change

[worldly wing]

the only invariant?

[amber python]

yes