math-help

[latent siren]

Yep

[atomic elm]

0

then we good

ok

awsome

[latent siren]

hell yeah

[atomic elm]

thx

thank you

[latent siren]

you just gotta power through that computation though.

[atomic elm]

yeah

[latent siren]

I just checked it, and it is indeed 0.

[atomic elm]

ok

thanks

i understand it now

thank you 😆

[latent siren]

This is a nice progression of questions because you can use (a) to figure (b) out.

[atomic elm]

ya

thanks ever so much

[latent siren]

no problem

[atomic elm]

hi again lol

this is confusing me aswell

[fierce totem]

Can someone help me with my math homework?

[atomic elm]

what kinda math we talking about

[latent siren]

I think this is just an algebra problem? The kth term of seq. A is k/(14k+30), and the kth term of seq. B is 2/k. So if the kth term of A is equal to kth term of B, we just equate them, i.e. k/(14k+30)=2/k. Solve for k.

This is equivalent to solving for the equation k^2 = 28k+60.

[foggy cosmos]

so basically k^2 -28k -60 = 0

so (k-30)(k+2) = 0

k = 30 or -2

but because you cant have a negative term in a sequence k = 30

[potent pewter]

Hi so

I’m pretty sure I’m correct but idk

[foggy cosmos]

yea that's right

[potent pewter]

Ok thanks bro 🙂

[foggy cosmos]

yup of course

[potent pewter]

😄

[left knoll]

Can someone help me with this please!

[bleak tree]

C-120

The area of the triangle is: (b×h)/2 => (10×8)/2=40

And the area of the rectangle is: L×l=20×8

So the area of the shaded part is 160-40=120

C

[bleak tree]

I hope that was helpful 😊

[left knoll]

Ayee thank you so much

Smartie

🥰

I appreciate itttt

[bleak tree]

Your welcome 💜

[left knoll]

Sorry I can't figure this out either

[wicked carbon]

does it tell you if your answer is right right after?

i believe it is 32 if that's correct i can explain how i got it

actually i have a quiz to take in a second but this is how i got my answer:
the key thing is that the vertices on the small square are located at the center of the circles & the diameters of the circles span the entire big square (lmk if you need me to explain that in more detail)
the area of square: s^2 (s = side length) so 8 = s^2 --> s = sqrt(8)
this means the radius of the circles are = sqrt(8)
length of BIG square = 2* diameter_of_circle --> 2 * sqrt(8) = 4sqrt(2)
again area of square = s^2 --> [4sqrt(2)] ^2 = 32

[vestal minnow]

Ya I think its correct.

[potent pewter]

I believe I am correct, but just to make sure I am please let me know. (:

[earnest axle]

u are

[potent pewter]

Ok! Thanks a lot, have a good night! 😁

[earnest axle]

u too!

[severe cairn]

Hi, im russian, lets go solve math problems

Who interested?

Average(x, y) /G(x, y) =24/25, x/y?

G(x, y) =sqrt(x*y)

[severe cairn]

Who solve?

[rugged imp]

Is the answer complex?

[bronze torrent]

x+y/2√xy=24/25
Squaring both sides
(x+y)²/4xy=576/625
x²+y²+2xy/xy=4(576/625)
x/y+y/x+2=2304/625
Let x/y=t
Therefore t + 1/t = 2304-1330/625
t+1/t=994/625
It's coming out complex

[rugged imp]

Yeah

[frozen holly]

I got 576/625

[left knoll]

A ball is dropped from top of tower 300 m high.After 1 sec another ball is dropped with 20m/sec from top of tower. Where and when they meet?

[supple island]

describe x for both and put them equal

do you know how to do that?

[left knoll]

i did yuss

i even got the ans but i dodnt understand what the initial reference point is

don't*

[supple island]

can you rephrase? i didn't quite understand what's the problem

[rugged imp]

I think you just need to set t=t-1 for the second problem and set u=20 and equate the displacements

[supple island]

what do you mean?

[left knoll]

can you try to do it

i got the ans as 11.25 from the bottom

but the ans is 11.25 from the top

[supple island]

of course it's from the top

[left knoll]

i dont understand the ans

[left knoll]

but how?

[supple island]

they aren't dropped from the bottom of the tower

[severe cairn]

So answer in my problem is 16/9 or 9/16 lts True

[supple island]

x=0 is when they are on top of the tower

[left knoll]

can you solve it and send the process

I would be greatful

[supple island]

it won't be any different then what you've found, just think about this:
where are the balls dropped? so where are the balls at the start of the problem? so where do i start counting?

[frozen holly]

What you got for speed 1 and speed2

[supple island]

what does it matter?

[rugged imp]

Even I don't understand his question tbh. I just sent a solution

[left knoll]

i got the same

but i dont understand what it represent

[supple island]

can you answer these questions @left knoll

[rugged imp]

Dist from top of the tower

[left knoll]

they are dropped from the top

one with initial velocity 0 and anothe one with initial velocity of 20

[supple island]

ok so at the start of the problem is their x=0 or the height of the tower?

[rugged imp]

See if I took initial position to y=300 my eqn of motion would be diff

But I took top of tower as reference

[left knoll]

height of tower ofcourse

[supple island]

do you know that height?

[left knoll]

yuss

300 m

[supple island]

well then you did a bad job descibing x

[rugged imp]

Then you eqn of motion will be 300-y=1/2gt2 for first ball

Wait

Ami wrong

[supple island]

x=300-1/2gt^2

you're not wrong

[rugged imp]

Yeah

[left knoll]

since the body is falling you have to take - displacement right?

[rugged imp]

Yes

But from where?

The original position

That is y=300

[left knoll]

and equating the two equations and getting t

[rugged imp]

Yes

[left knoll]

and putting it in eqn 1

[rugged imp]

I don't think you quite understand the physics but you do understand the formula

What you are telling me is the maths behind it

[left knoll]

i get that part my problem is with the displacement what is the initial refrence point the ground or top and why

thats what i dont understand

[supple island]

imagine this: 2 balls are launched in a horizontal plane, the first has v=0 but accelaration=g, then after a 1 second a second ball is launched with the same accelaration but v=20, when wll they meet?

[left knoll]

yeah exactly

[rugged imp]

You know what I'll send a solution taking the bottom of the tower as the origin

[supple island]

it's literally the same problem

[rugged imp]

Yeah

[supple island]

but you don't start counting from the bottom of the plane

cuz you don't know where it is

[left knoll]

got it

thanks @rugged imp @supple island for making me understand the concept

[supple island]

here the height of the tower is to determine whether or not the balls will actually meet

for if x of meeting was greater than 300m the balls wouldn't meet at all

[left knoll]

wait @supple island

i have another question

[supple island]

sure

[left knoll]

one object is dropped from top and another one is lunched from bottom

[supple island]

at the same time?

[left knoll]

yuss

[rugged imp]

Then you have to set a reference and describe y according to that refernce

Be careful in that

[left knoll]

i will send the question

[rugged imp]

Kk

[left knoll]

i got the correct ans but dont know what it represent

[rugged imp]

Ahh

[left knoll]

An object is dropped from the top of the tower of heigh 156.8m.and at the same time another object is thrown vertically upward with the velocity of 78.1ms-¹ from the foot of the tower when and where the object meet?

[supple island]

describe the equation of motion for both objects from the same reference point (from top or bottom)

[rugged imp]

Guys imma head out now

[supple island]

kk

[left knoll]

okay

[supple island]

and then equate them

[left knoll]

then i will get the time

[supple island]

yup

[left knoll]

and if i put the time at the equation for the object thrown vertically i get distance in respect to bottom right?

[supple island]

depends on the ref point you've taken

how do you describe the equations of motion?

[left knoll]

the object is thrown vertically form bottom

s=ut+1/2 at^2 in this condition a=g

[supple island]

for example if i take the ref point at the bottom the dropped item would be
xdroppped=h-1/2gt^2 and the thrown would be xthrown=vt-1/2gt^2

[left knoll]

okay got it

[supple island]

but if i take ref point from the top
xdropped=1/2gt^2
xthrown=h-vt+1/2gt^2

because now g has the sam direction as x

and v has the opposite

[left knoll]

yeah got it

[supple island]

👍

[left knoll]

thanks man

really appriciate it

[supple island]

np, have a good one

[left knoll]

you majoring in physics ?

[supple island]

yup

[left knoll]

okay nice

[brave wing]

Can anyone help me with this,?

Topic - signum function

[urban berry]

I need help(

[somber hemlock]

Is it 3?

[inland marten]

Photo from Kam Keng Yang

Can someone help me

[somber hemlock]

X^-2 = y?

[inland marten]

Answer is y= 1/x^2 but idk the working

[low orchid]

in polynomials

do powers be 1

always

[inland marten]

omg thank you so much

[brave wing]

Is it ? It's a hw so idk the answer, do u have it's working?? 🥺 I keep getting answer a

[somber hemlock]

Signum function can only take 3 values.. 1 when x>0, 0 when x=0 and -1 when x<0. That way (2x-1) can take these three values only

[brave wing]

Yh but that quadratic equation gives 2 values which is +ve ,ie..signum function would be 1 know ? = 1 sol

[somber hemlock]

Yeah but the whole quadratic’s value can be positive, negative or zero ryt

Sgn is on the whole quadratic

[brave wing]

But The solutions are +ve (x-2) and (x-1)

So 2 positive solutions , ie..1 in sgn right?

[somber hemlock]

You can put x=1.5, then the signum(-ve) will give -1

Or pur x=2 or 1 and get sgn(0)=0

[brave pendant]

how do u add checkilists in the to do lists
[6:18 PM]
???

[hollow dust]

I need to calculate an average but the 1st calculation is 0/0, do I need to consider this ?

[hollow mauve]

Never

This is Undefined Value

[hollow dust]

Yeah I know

[hollow mauve]

Send me the ques?

[hollow dust]

But it is more complicated than that

It's in french so you may won't understand

But I can translate

Let's hop in dms

[brave wing]

Use ◻️

:white_medium_square :

[brave pendant]

and can you put a timer in chat??

timer 3:00:00

???

[brave pendant]

add this

[brave wing]

I found this ,idk much about commands
Ask in

#general-chat

[fringe cargo]

Can someone help me with these?

[meager spruce]

Could someone help me with this math problem step by step?

For the area of the square, I got 144, but I’m not sure with the circle

Since I got 144, that eliminates 2 answer choices, but idk how to get the pi with area of a circle

[silk quiver]

144 + 3/4 of the area of the circle

[hoary knoll]

the area of a circle is pi*radius²

[silk quiver]

which is 108pi

[hoary knoll]

here you only have 3/4 of a circle

[meager spruce]

It’s not 144 pi is it?

[hollow escarp]

No

[silk quiver]

144 +108pi

[hollow escarp]

Convert area of square in terms of pi

[silk quiver]

no you dont need to

[hollow escarp]

144/3.14

[meager spruce]

12 is the radius, but how’d I get the 108? I don’t know where that came from.

[silk quiver]

144 is the area of the square then just add the 3/4 area of the circle which is 108pi

[hoary knoll]

you do 3/4 * pi*radius²

[meager spruce]

Oh, I think I get it now. Thanks y’all!

[hollow escarp]

You can’t add 108 pi and 144 and get the total answer in terms of pi

[silk quiver]

why tho that's the answer

[hollow escarp]

Check question in pic

It’s to find area of figure in terms of pi

[hoary knoll]

check the answers tho

[silk quiver]

isn't 144+ 108pi in terms of pi?

[hollow escarp]

Oh, I didn’t see

I didn’t notice the choices

My bad

[potent pewter]

Am I correct, I think I am but not too sure..

[hoary knoll]

yes, that's correct

[potent pewter]

Thanks so much! 😄

Have a good day!

[hoary knoll]

you too 🙂

[severe cairn]

Who would like watch russian mathematic?

In english)

Write me

[severe cairn]

I would tell about olimpiad math, english books. Please dont ignor, write me

[fringe cargo]

How would I approach this question?

Q6)

[scenic garnet]

Can anyone help to find out if this series is convergent or divergent?

[latent siren]

Hint, let u=ln(k), du=(1/k)dk

[foggy cosmos]

im not entirely sure, but i think you would do a chi square test, or possibly a linear regressions test

[hidden forge]

Extra hint: use the integral test

[latent siren]

Be sure to check that the series satisfies the hypotheses of integral test

[tame frost]

Anyone able to help me out?

[celest topaz]

get common denominator and then solve for x

7x/42 - 3x/42 = 84/42
7x-3x=84, and u can solve it from there

[tame frost]

Got it, 🙏

[fringe cargo]

Would this be a suitable method for part 2ii)

I assumed by finding the probability that you win in under 6 trials, multiplied by two to account for the 2 initial successes, then multiplying my the probability of success would give me the probability that the 3rd success occurs on the 6th trial.

Please can someone help me as I am not sure if it is right

[nimble jackal]

hey guys can somebody pls explain this for me: 7z+5-4z=

[latent siren]

7z+5-4z = 3z+5, you can only add (or subtract) terms that has the same variable.

[random flame]

Eyo can someone help me with Q6? Ping if you do and thank you!!

[left knoll]

Yes it is 32!

[left knoll]

Thank you so much for taking the time I appreciate it

Thank you!

[jagged dune]

please if ans is correct

length is 8.48 or 6rt2

[random flame]

Yeah it's supposed to be 6rt2

But idk how to get it

[jagged dune]

did u get the intersection points?

[random flame]

You mean points A and B?

[jagged dune]

between the curve and line

yes

a and b

[random flame]

Yeah I did

[jagged dune]

ok

so use the formula

[random flame]

Is it the one that goes
(x1-x2/2 , y1-y2/2)?

[jagged dune]

nah

[random flame]

I'm not sure what formula to use -^-"""

[random flame]

I- oh-

[jagged dune]

use this formula

[random flame]

What does d stand for?

[jagged dune]

distance

[random flame]

Ah aight thank you so much!!

[jagged dune]

👍

[random flame]

Ayo it’s me again 😂
I need help with Q7a, the book and is weird ;-;
Ping if you do and thanks again!!

[jagged dune]

did u solve any of the 3 questions

a,b,c,d?

[random flame]

No

Not at all

[jagged dune]

ok

[random flame]

I got stuck at part a

[jagged dune]

check if the ans are correct

a. 18-(x-3)^2

[random flame]

Yeah it's correct

h o w

[jagged dune]

w8 ill send the ans first ill explain next

[random flame]

Aight

[jagged dune]

b.(3,18)

c.3+3rt2

[random flame]

Wait b is supposed to be a number not a coordinate

[jagged dune]

ooohh

[random flame]

Yee

It's asking for a value

[jagged dune]

so 3 maybe

[random flame]

No it's actually 18

[random flame]

For this one supposed to be in coordinate form

[jagged dune]

(3+3rt2, 0)

as its on y axis

[random flame]

Yup

There's like two ans for part c

But anyways

[jagged dune]

the maximum was supposed be on yaxis its supposed to be 18

my bad

[random flame]

Yee issokay

[jagged dune]

3+3rt2 and 3-3rt3

2*

but they have asked for a+b

rt2 for

form

[random flame]

Ima just send the book ans in

Hold on

Just look at Q7

[jagged dune]

ok w8 ill write down a solution for u

[random flame]

Aight

Thanks a lot man

Rly appreciate it

[jagged dune]

This is for question c

[random flame]

I still can't find question a tho

[jagged dune]

ok a is simple

its given over there use (a+b)^2 form

so break the equation down

into

-(x^2 - 6x -9)

-(x

-(x^2 - 2*3 + 9 ) to make it (x+3)^2 and since u taken +9 to balance u have to take -9 outside the brackets which makes it -9-9 so -18

-{(x+3)^2 - 18}

18-(x+3)^2

i made an error while typing

its not x+3 its x-3

did u get it

?

[burnt cloud]

can someone help me out on this

[random flame]

Oh oop srysry I'm currently having online school

Thanks a lot man

[random flame]

Do you have to solve it or simplify?

[burnt cloud]

I have to simplify it.

[supple island]

find the common denominator and then solve the quadratic equation

[random flame]

Ah kk lemme see if I can do it or not

I got x^3-3x^2+30x+350=0

Not sure if it's correct or not

[burnt cloud]

okay thank you so much!

[left knoll]

Can someone help me? Whether it's easy or not - I don't understand how to workout probabilities

[jagged dune]

thats the whole question ?

looks kinda incomplete

[left knoll]

Nevermind! I was very confused why it was incomplete. Litterally for every question I have to scroll all the way up to the first question. It's really confusing

[jagged dune]

oh ok ok

[left knoll]

It doesn't hint at all that they're giving the information from the first

thank you!

[jagged dune]

👍

[glass tide]

Its not correct

@burnt cloud the simplified equation is x^2-8x+70

[left knoll]

For this i got x^2-8x+70=0 but idk if it’s right or not

[glass tide]

@left knoll yes

its right

[left knoll]

Yep i think that’s right

[glass tide]

@burnt cloud When u have to solve an equation of any sort, remember to find where the equation = 0. Meaning when the X variable cant read a Y variable on the graph. in this case, for every fraction on the face of earth X cant read a Y whenever the denominator is equal 0.

for ur equation the denominateur would eqaul 0 whenever x= 5 , -4

[neat trail]

uhmm this is calculus like finding the area between curves

[glass tide]

@neat trail not really its more basic than calculus

what part U cant do ?

[neat trail]

this is our lesson rn :< and i dont really get it

[glass tide]

ok

what the question again

[neat trail]

the pic i sent above

to find the area between curves

[glass tide]

ok

wait a sec

[neat trail]

thank youu

[glass tide]

im sorry if you get confused

i study math in french

not english

ill do my best

[neat trail]

ohh it's really okay

much appreciated 😊

[glass tide]

first u need to be able to see a few things about ur equation

the sign of the 'highest' x will tell you what side the parable faces

10x-x^2

the highest x is negative

[neat trail]

so downward?

[glass tide]

like a upside down bowl

yess

then you can find where the equation touchs the axes

[neat trail]

how about the area?

[glass tide]

yes but there are steps to this

its not just a formula you apply

can you draw 10x-x¨2

[neat trail]

omg sorry i cant rn

im having classes lol

[glass tide]

ok fine good luck

its not hard really

very simple

[neat trail]

ohh okay

[severe cairn]

x(1/6 - 1/14)=2 x=2/(1/6 - 1/14)=2/8=0.25

[severe cairn]

Sorry, 1/6 - 1/14= 8/84=2/21 x=2//2/21=2*21/2=21

Why this problem so strange, how old are you?

[nimble jackal]

oh ok thank you so much

[stark karma]

anyone know how to do this? i have forgotten

[peak eagle]

it's been some years since I worked with Taylor polynomial. But I think you just need to differentiate 3 times and put in x = 0.
than you should be able to see it

[jagged dune]

-30??

ans

[latent siren]

Hey, if P(x) is the fifth degree Taylor polynomial for f expanded at 0, then the coefficient of x^3 is equal to f'''(0)/3!. What does this mean? The coefficient of x^3 in P(x) above is -5, therefore -5=f'''(0)/3!, so f'''(0)=-5(3!)=-30.

So yes, the answer should be 30.

-30, I mean.

[stark karma]

Thanks!

[left knoll]

guys

i am having a question

[placid coral]

Hey there, does anyone here use RStudio?

[faint thistle]

I forgot to say thanks lol ty

[nova coral]

hi can someone help me solve this equation? ik the answer but idk the steps to it
2^3x=1/4

x = -2/3

[celest crow]

3x=-2 so x=-2/3

[nova coral]

Ah ok, thank you

i was overcomplicating in my head when the answer was right there (2^-2 then continue from there) 😓

[true nexus]

hey could someone please help with this, i'm a little lost on where to start

[supple island]

think of it as 2(sinx/x)^2

i'm sure you have done the limit for x->0 of sinx/x

[true nexus]

o wait

i got it

p sure the answer is 2

[silk quiver]

use lhopital's rule

[true nexus]

ohh rightt

tyy

[supple island]

it is

[true nexus]

oki cool thxx

[left knoll]

yo

is anyone good at complex analysis

im trying to find the residue values to calculate this integral

[bronze torrent]

Idk what residue values are but I can solve this integral

[left knoll]

could you please? i have my exam tomorrow and i'm kinda freaking out

[bronze torrent]

Ok

[broken field]

can someone show me how to draw the geometric shapes for the f(x) line? i don’t need the final answer for the problem i just wanna know where to draw the shapes cus it’s throwing me off

[bronze torrent]

Sorry but I'm stuck in between

[bronze torrent]

Just satisfy any two points for equation and join them

[left knoll]

yeah its hard it's to do with isolated singularities

[bronze torrent]

I'm a highschool student I don't know that much 😅

[green summit]

You can even calculate the area under the graph by isolating each term

[broken field]

well no that’s not how to solve it. i have to find the area between y=f(x) and the x-axis from x=0 to x=2. the worked out solution has 4 areas. i’m just confused on where to draw the shapes to find these areas.

[left knoll]

find the areas of triangles

Allocate +ve for above the xaxis and -ve for below

Sum them up

[broken field]

ty !

[left knoll]

How can i calculate the height of a square pyramid?

[peak eagle]

baseline(?)*height /2 don't know if it's called baseline of the triangle in english

do you know what it would be if you put in the numbers in your case?

[left knoll]

?

[peak eagle]

whats the height of your triangle?

[green summit]

i guess this should do it

if this is the square pyramid that you are talking about

[peak eagle]

ahh sry I didn't read the question right

[left knoll]

yeah this way is true thanks

[peak eagle]

use Pythagoras

[green summit]

yup

[lunar rover]

a way for find height. From non-eng chat @left knoll

[meager spruce]

Could someone help with this problem?

“Mr. Tran has 2 bags of 26 cards for each letter of the alphabet. He removed a card from each bags. What is the probability he will get a consonant AND a vowel?” (Y isn’t considered a vowel here)

Do I do it 1/52 x 1/51?

[left knoll]

@meager spruce 21/26 x 5/26

the probability of a consonant x the probability of a vowel

[left knoll]

Hi! ,How can I solve this problem ?
"People from a random city are interviewed regarding their perception of the future of the national economy.
If only 30% of the people in the city are women, how many interviews would you expect to have to do to interview 250 women?"

[minor sluice]

I think 30% of total = 250 so you would do a proportion of 30/250 = 100/x. I got 833.

[left knoll]

Thanks!

[prime coral]

Guys i have my last math exam tomorrow i am so scared any tips?

[wide idol]

Do some practise papers

[latent siren]

If you have already studied for as much as you can, I think you're better off taking a rest.

[icy knot]

Please give me a hand :3

[prime coral]

@latent siren @wide idol ok thank you guyss

[white condor]

did you mean sec(x)?

[icy knot]

No, sen(x)

[white condor]

ohh i see, sen(x) = sin(x)

[icy knot]

*Find the sum of values of "K"

[icy knot]

Sorry :c

[royal marsh]

oh you call it different things?

always used sin(x). got confused

[minor sluice]

same...

[minor sluice]

be scared but prepared

Nervous energy helps and if you are 100% on the material you will do good

Like I am somehow passing my math and if I am, you can too

[latent siren]

Yeah, I find that a certain level of tension is good during exams.

Not too much, of course. But not too little that you don't care about it. I'm just glad that I'm doing with written exams though lol.

[meager spruce]

Hey guys, I’m kind of familiar with how to solve this problem, but I also forgot some steps. Help?

I understand 4’10, is 4.83 - but I forgot the steps to solve it

[left knoll]

You should use the triangle resemblance

[upper juniper]

Yeah

I'd use proportion. The ratio of heights is equal to the ratio of the shadows

[minor sluice]

Yea proportion is best

[meager spruce]

How do I do proportions again?

What’s the formula and steps to do?

[upper juniper]

Look~

I found a similar example

[proper sail]

im kinda young, so I SUCK at answering these stuff fyi, but I need help.

if x+y=3 and xy=4, what is x^2+y^2

[upper juniper]

can u check if you wrote it correctly? I tried doing it but I feel like something's missing~

[grand blade]

how you solve this type of questions is by manipulating it! taking (x+y)^2 = 9, we get x^2 + y^2 + 2xy from expanding the (x + y)^2. then, we can minus the 2xy by -2(4). thus we are left with 9-8=1 ! hope i answered your question @proper sail

[upper juniper]

Yess, I came to the same conclusion, but if x^2 + y^2 = 1
Then x+y couldn't be 3

[left knoll]

This may be possible if you have been told that it is an irregular number

[supple island]

idk what an irregular number is, but it is possible with complex numbers, if you simply solve the system x+y=3 xy=4 you'll find a quadratic equation with determinant<0

[left knoll]

Is it 1?

[proper sail]

Well, the options were 1, 2, 3 and 4

Im just guessing this question is wrong

[burnt shoal]

I agree with PhysStudent.

[proper sail]

I didnt really understand what PhysStudent said

cuz Im Korean, dont really understand that far interms of math stuff

so ur saying the answer should be smaller than 0?

at this point im just guessing my teacher was wrong

[grand blade]

Complex numbers are numbers that dont exist/imaginary (?) is the way i would explain it. sqrt(-1) is an example of one. a little rusty on the topic so correct me if im wrong

[proper sail]

sqrt(-1) is the only complex number we learnt

like i = sqrt(-1) if I aint wrong

[grand blade]

well, to be more accurate a complex number can have a real part along with an imaginary part, which is sqrt(-1). as long as there is a sqrt(-1) it would be considered a complex number.

as to your question i think someone else is probably more qualified than me to answer it, so sorry :( but i rather not explain further when im not 100% sure

[hollow escarp]

most probably the case. Your teacher might have made a question up from the back of their head. and since the answer we got is among the options , we don't need to worry too much about how the question is wrong .

[burnt shoal]

Yes, it is something like that. I don't remember much about that topic, but this is what PhysStudent was talking about:

You get a negative number inside a square root, which means you can't solve that with real numbers.

[prime coral]

Does anyine know how to find K

[left knoll]

?

[peak eagle]

try putting in your roots (x-c) than +c is your root. if you put in your roots than you should know what happens P(x) (should be zero) than you could read what b is

just a tip for how to get b. you could maybe also use polynom division

if you still don't know how to solve it dm me

[left knoll]

thanks will try that

[peak eagle]

try to change the formula so you have k^(-1,154) on one side than take the (-1,154)root
if you still don't know what I mean I can show you on another example

[prime coral]

Can u show the example?

[peak eagle]

on your calculator there should be a sign like this . the x is the exponent of k

[prime coral]

Ah yes i see

Thanks alot

[faint thistle]

[left knoll]

is that meant to be y = 3sin(2t) not r

[edgy crag]

Does anyone know this?

[left knoll]

3x^3

[edgy crag]

Omgg thank you so muchh

[maiden fog]

Can anyone answer this for me please?

[ashen laurel]

made a mistake but i think the answer is legible

[maiden fog]

Thank you🥰

[green summit]

did you get an answer for this?

[green summit]

sorry for the mess😅

[faint thistle]

Nope

@green summitAppreciate it man

I SEE okay cool

i missed a step

:(

[green summit]

no problem

[serene ginkgo]

how do you express 3^(2-i) in cartesian form?

[peak eagle]

3 or e as in exp?

[serene ginkgo]

3 but its under the chapter on complex exponents

[peak eagle]

ok than I can't help you, I am hearing this semester a similiar course didn't have that yet sry

[serene ginkgo]

its ok:)

the answer is 9cos(ln3)-9isin(ln3) im just not sure how to get there

[peak eagle]

maybe the last one is more helpful 🤔 you do both the exp and the log since they nullify each other.

and from there you can just use the euler formula

[serene ginkgo]

alright thanks that makes sense:)

[green summit]

you have to apply base change theorem on 3^-i and change it to e as the base

you can do that by assuming e^t = 3^-i ,
take ln on both sides and substitute the value of t back in e^t and replace 3^-i

then you can apply the eulers theorem

[serene ginkgo]

thats so smart thank youuu

[green summit]

do you want a pic?

[serene ginkgo]

i think i got it thanks:))))

[green summit]

yup

[loud nymph]

Does anyone know some graph coloring websites or calculator?

[cold kestrel]

Need math help (Calculus)!

Need math help (Calculus)!

[candid hatch]

For graphing calculator, I use Desmos

[green summit]

i guess D is the correct option for this i used approximate method so im not sure

[main hornet]

wasssup

[meager spruce]

I think it’s gonna be on the left side of the graph?

[main hornet]

is anyone here a member of james' patreon?

[cold kestrel]

yeah thats right

[main hornet]

wrong channel. sorry

[cold kestrel]

process?

[green summit]

let me send a pic

[green summit]

this has to be C in my opinion coz it has only 3 cases
f(x)>g(x) => 2(f(x)-g(x))
rest are 0 as f(x)<g(x) will not be max and equality will be same as 0

[cold kestrel]

ok thats good explanation, thank you

[green summit]

on second thoughts ill explain the process,

[5sinx] + [cosx] = -6
so 5sinx should be in range of [-5,4), similiarly cosx will be[-1,0)
after this multiply cosx by root(3) and add sinx's range to it
im not sure abt this tho it will give you an approximate andwer and then eliminate the options

[cold kestrel]

can send me a pic tho im not able to undertand lol

[green summit]

you wont understand the pic too XD ill try to write it neatly

[cold kestrel]

🤣

[green summit]

if this helps XD

try solving it using graphs to visualize it better

[sage cobalt]

Could any one help me with question 2. Greatly appreciated

[cold kestrel]

thank youu

[green summit]

@odd oak

[sage cobalt]

damn you're a beast, THANK YOU

[sage cobalt]

just to check, when v = S/T, doesnt that turn out to be s = -11.3?

[narrow hill]

is s the distance?

[sage cobalt]

s is the displacement

[modest ice]

Yall can someone solve this for me pweasssss?

[narrow hill]

i was wondering when finding B-C velocity, is 10.5sec the time sprinter went from B to C? it seems to be that it should be something like V = (100-S)/(10.5-T), where T is the time of A-B;

because from B to C, running 10.5 sec with velocity of 10.6 makes it total distance of 113.3m which seems totally absurd as the Total distance of A to B and B to C combined should be 100m

[sage cobalt]

I think that 10.5 might be the total time taken

The question is quite vague, my group of friends all had different interpretation of the The questions haha

[narrow hill]

mm so then V = (100-S)/(10.5) is wrong? since 100-S is the distance of B to C and the time spent when travelling B to C is not 10.5? But answer seems to be right? hek, i don't know

[sage cobalt]

But with 100-s/10.5 = 10.6 you get S =-11.3 tho

Which is impossible as this guy is running in a straight line

[narrow hill]

hah yea that's why i was advocating (100-s)/(10.5-t) = 10.6.

is the total distance 100m or 100m is just B to C distance?

[left knoll]

O had the same

Uh

It was a long time ago tho

[narrow hill]

Hey dud, this might be helpful

[meager spruce]

What formula do I use to solve?

[cinder ibex]

Maybe the perimeter 2 pi × 0.07m is to 360°, 88° - x

That is what i would try but i cnt fully explain cause im not very used to math terms in english

@meager spruce

[gentle zinc]

2πr (θ/360)

You should get in the habit of using google instead of asking here

Anytime it's a formula that you're looking for, information is more readily availble using a search engine than asking others.

[queen thistle]

Hello, can someone please assist me on this problem.

[noble jacinth]

Can someone help me the find proof for 7b) ? Would be very much appreciated

[latent siren]

at the top of my head, this is what I'd do: substitute cos(2x)=cos^2(x)-sin^2(x), and 1 = sin^2(x)+cos^2(x)

[left knoll]

can anyone help me with these?

[noble jacinth]

Ah THank you! I was wandering how you could convert the 1

[fading ingot]

can anybody help me how to solve q1 and q2 in this system

[latent siren]

substitute q_2 below in the expression for q_1 above, then solve for q_1

[left knoll]

May I get some help if that's okay?

[hoary knoll]

determine B (sum of the angle of a triangle is 180°) then use basic algebra formula (cos sin tan) to determine a and b

[hoary knoll]

express q2 with q1 in the first expression (it's just sums, you can do it)

then replace it in the second expression

and boom

[latent siren]

I'm actually doing research right now, so now might not be the best time (I'm procrastinating). You can post your question here, maybe somebody else will answer.

[left knoll]

Can you dm me the steps? I want to see if it's similar to what my teacher does it if that's okay

[river marten]

I am having trouble understanding what my medium temperature should be, as the thermometer passes through two separate "mediums". Anyone knows how one would go about solving this problem?

[weary arrow]

I think the 56° reading is from inside, and it's just as it is placed outside that it has this reading (so assuming not affected by the temperature change yet).

I'm not sure if that made sense, but I think you're supposed to find the "speed" of the thermometer and use that to calculate how much colder it reads after 2 minutes

[river marten]

Thank you for this, I am going to try something based on what you said

Ok I solved it 🙂

thank you so much!

if anyone needs the solution let me know I can post

[weary arrow]

Fantastic!😄

[random flame]

Hi can someone help me with this? Ping if you do and thanks!!

[weary arrow]

First find the third angle (total is 180 degrees, so this is 94), then use the sinus rule to find x (a/sinA = b/sin B)

So x/sin46 = 20cm/sin94

[random flame]

Ooo aight thank you so much!!

Eyo it’s me again 😅
Can someone help me with part b? Ping if you do and thanks!!

[left knoll]

can someone tell me how to find the least speed

[random flame]

Thank you!!

[left knoll]

hii, can someone help me with this question please , it's about series

[left knoll]

thanks man

[dense steeple]

is the answer correct??

[left knoll]

yuss

its correct

[proper sail]

@upper juniper @grand blade @left knoll @supple island @left knoll @burnt shoal Update to this: a^2+b^2=(a+b)^2-2ab, so the answer is 1

[silk quiver]

an = (9^n - 8^n)/9^n

[left knoll]

A stone is projected horizontally with 20m/s from top of a building . Calculate its position and velocity after 3 seconds neglecting air resistance

can someone have a look into it

Pls

[left knoll]

thank you

[left knoll]

Thank you so much

[upper moth]

Does anyone know how to prove this? I'm having some trouble with this problem

[stuck pewter]

Can anyone help me with math?

[left knoll]

Is it 5 ?

[left knoll]

Hey guys! Can someone help me?

I found m^2+2k^2+n^2=2 but I dont know how continue

[dense steeple]

is it m.n in the question??

[left knoll]

No, that's all there is.

[green summit]

Is it m1n or mn!?

If its mn then ans is 0

[dense steeple]

yess i also got zero

[fading ingot]

can you help me, what is true for this function in point [0,0]?

[dense steeple]

can u translate it ??

[fading ingot]

yes, i did 😄 i mean what is true for point [0,0]

[dense steeple]

ohhh

[fading ingot]

the last one means "none of them"

[left knoll]

mn

[green summit]

Yup then its 0

[left knoll]

Thank you so much @dense steeple and @opaque escarp

What will be the velocity and direction of projection of an object which passes in a horizontal direction over the top of a building which is 50 m away and 25 m high?

can yoy guys just check the angle and tell me what you got

[covert anchor]

How do i find the value of log63

[worthy slate]

same as how u found log_5 (7)

just do log(63)/log(5) which is 2.57

[covert anchor]

I dont understand why tho

[worthy slate]

thats just how u compute logs on a calculator

like a formula sorta

[covert anchor]

oh ok

what if it was log_5(0.84)

[worthy slate]

then it would be log.84/log5=-.10833

[green summit]

Well you don't need to do that you can simply write it as log_5(7x9)=>
log_5(7)+2log_5(3) and the values are given just substitute

[worthy slate]

^that works too

[covert anchor]

log_5(7)+2log_5(3)
I dont understand why 2log_5(3)

[worthy slate]

its also another rule. if there is an exponent, u can move the exponent to the front of the log. in this case, 3^2=9

[covert anchor]

ok nice forgot abt it

thks guys

any tips on being good at math ?

[worthy slate]

https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/

check that website for the general log rules

[worthy slate]

practice practice practice

[covert anchor]

14 and failing at this lol

[worthy slate]

meh ur fine, u still got alot of time to mess up. just make sure u understand these materials well so that when u get to the harder stuff, u wont fall behind

[lime junco]

hi guys, can u guys help me with question c, d , e and f please

[covert anchor]

factorise out the x

as in placing the x outside of the expressions

[worthy slate]

@lime junco

[covert anchor]

what do i do for c and d

[lime junco]

Thank you so much!

[round orbit]

if a + b =5 then solve 1/a +1/b

i khow the anser but i don't get the concept applied here. would love if you could give some source to learn about the concept used here

[frail yarrow]

you can substitute the values to find the answer in variable

like you could solve using a= 5- b

[round orbit]

you mean subsitution method?

[frail yarrow]

1/5-b + 1/b

this way

[round orbit]

just a sec lemme see

[frail yarrow]

okay

or you can substitute a as well

[ruby tinsel]

Hi guys, I have a question on 3D vectors sphere. I had figured out part a and the point that line passes through the point on the sphere in b but I do not understand the direction bit. Could anyone please explain?? Thank youu!

[worthy slate]

Uhhh I think this is right? Idk I'm rusty on the rules

[covert anchor]

The ans is wrong but its fine

[worthy slate]

welp

[round orbit]

i did that but didn't got the right anser. it must sometihng else

[frail yarrow]

what is the right answer

it must be an expression right

[round orbit]

If α and β are the zeros of the quadratic polynomial f(x) = x
2 – 5x + 4, find the value of 1/α + 1/β
– 2αβ.
Solution:
From the question, it’s given that:
α and β are the roots of the quadratic polynomial f(x) where a = 1, b = -5 and c = 4
So, we can find
Sum of the roots = α+β = -b/a = - (-5)/1 = -5
Product of the roots = αβ = c/a = 4/1 = 4
To find, 1/α +1/β – 2αβ
⇒ [(α +β)/ αβ] – 2αβ
⇒ (-5)/ 4 – 2(4) = -5/4 – 8 = -27/

maybe this will help ya understand it

[frail yarrow]

ahhhh you gave me an incomplete question mate

[round orbit]

yeah but the calculation is the same i think

maybe

[frail yarrow]

it is similar

[random flame]

Eyo just a question
How do I change 3/2 into log base 8 smtg? If ya get what I mean-
Ping if you answered and thanks!!

[ruby tinsel]

If anyone has an explanation, please just ping mee thxx

[worthy slate]

@random flame its just 8^3/2 (that is if ur asking what x is for the eq log base x=3/2)

[random flame]

I'm asking log base 8 x = 3/2

Is that possible?

[worthy slate]

@random flame ya so 8^3/2 is the answer for that

[silk quiver]

log base 8 8^3/2

[random flame]

Ohhh

Okie I get it now

Thankiew!! ^w^

[round orbit]

got it.

[left knoll]

Guys! Can someone help me?

[peak eagle]

don't just learn formulas. try to understand what it means and how it's connected with others
I was in 8th grade when math made sense to me and now I am studying it in uni

as tip: ask your teacher, believe it or not they want you to understand it as well so ask, ask, ask, 🙂

[left knoll]

@silk quiver @green summit ı think u re so good at math plz can u help me? It is important for me

[peak eagle]

as tip: what is your neutral element in addition? and what does it mean to have a reversible element?

[left knoll]

Oh sorry the original version of this question is in Turkish

So there must be an error caused by translation

I'll send original question

[peak eagle]

I can't read it, try to put in the question in deepL (translation program), and put the translation here, I don't have the turkish symbols on my keyboard, so I can't do that

[left knoll]

Oh okay whatever thanks for ur helps

[covert anchor]

I need to simplify
10^lg43

[silk quiver]

43

[covert anchor]

is there a rule for solving that ?

[silk quiver]

no just set the value equal to x then transform it to log

[covert anchor]

too helpfull today thanks

[green summit]

i dont understand this question im sorry

[left knoll]

Okay Thank you, though.

[green summit]

im sorry again.

[silk quiver]

where's that derivative question?

[silk quiver]

i got 0 as answer

[glad smelt]

that's correct

[silk quiver]

i just set values for alpha, beta and gamma

is that ok?

[glad smelt]

ummm

ig that should work

[glad smelt]

gotcha , thanks

I don't know if there's another way to do this apart from putting values

[green summit]

you can give alpha = beta = gamma = 0

[green summit]

there is just do it as it is

the alpha beta and gamma cancel out each other

[glad smelt]

that will make x=1 then

[green summit]

as you can see from the equation itself

[glad smelt]

only constants will be left

[green summit]

yes you want dy/dx

which is 0

[glad smelt]

ahhah

nice way

lol

[green summit]

dont do this in written exam tho XD

[glad smelt]

XD

[covert anchor]

e and f idgi

[weary pagoda]

for e, apply ln on both sides
so it becomes---> ln(5^x-1)=ln(2^x)
in logarithmic form you can send the powers in front
----> (x-1)ln5=xln2

expanding bracket--->xln5-ln5-xln2=0
---->x(ln5-ln2)=ln5
x=ln5/(ln5-ln2)

applying the same rules and logic, you can solve the other equations

note that ln(e)=1

[covert anchor]

thks

recently not able to cope with this tuition work

[meager spruce]

40?

[lethal crown]

Hi everyone, can somebody help me with this please

[peak eagle]

if you have that option yes

[left knoll]

Is there circle center in there

If you randomly pick two numbers between -2 and 2, what is the probability that the sum of their squares will less than or equal to 3

had this in my math test today and completely fucking froze even though thats probably an easy ass question

[solid anvil]

anyone knows the formulae for crude death rate

[silk quiver]

A

[silk quiver]

is the answer 9/20

[mental dragon]

I'm not sure but this is what I'm thinking
[-sqrt(3), sqrt(3)] is the range of numbers with squares <=3
[-2, 2] is the total range
so the answer is (sqrt(3) + sqrt(3)) / (2 + 2) = sqrt(3)/2

[left knoll]

Hey sorry for interrupting everyone, but could someone explain why he does "+" between E1 and E2 in the second exercise and not a subtraction like in the first exercise

[mental dragon]

Seems like the question is asking you to find a way of combining E1 and E2 so that the x's and y's cancel out.
There is no hard rule to use subtraction or addition. It just so happens that in the second problem, 8E1 + 4E2=0.

[left knoll]

Ohhhh so you basically choose wich one is better to cancel x and y ?

[mental dragon]

A hint is that the multiplier for E1's x is negative (-4) and the multiplier for E2's x is positive (8). So it makes sense that you don't need to change the sign (subtract) to get to 0. If that seems too complicated, you can just try different combinations and see what works.

yes ^

[left knoll]

okay i got it thanks a lot

[last sentinel]

help

please

[left knoll]

@left knoll @neat roost

[left knoll]

2 semicircle becomes one whole
30.2.3,14=188,4
And 80+80=160
160+188,4=384,4

[left knoll]

Anyone know hw to do 1?

how*

[candid rivet]

I think you can use the fact that sin²(x)+cos²(x)=1

and once you know the value of sin(x) and cos(x) you should be able to get all the other values

[left knoll]

Do you mind helpin in dms?

im just a tiny bit confused ngl.

[candid rivet]

yes no problem

[left knoll]

Ty so much.

[left knoll]

Tysm.

[icy knot]

Help

[brave wing]

A basic one-
Is there any prob on writing 8/√2 as 2√2/√2 ? If not when am I supposed to split like this?

[paper mortar]

"Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red. Explain what this probability means."

Anyone able to help me out

Please

[robust prism]

can anyone tell me where is the height please

thank you

[silk quiver]

there a re three heights for any triangle

[analog kettle]

[robust prism]

if i nid to find the area

[analog kettle]

use cos formula to find the longest side

and then sine formulae

to find the angles

and from there the heights

[robust prism]

hmmm

ok thanks

[silk quiver]

if you need the area you dont need the height

get the other side using the cosine law then perform heron's formula to find the are

[robust prism]

wow i haven't learn that

[silk quiver]

yeah they don't teach that in high school

this formula is so useful in trigonometry. always remember this

[shut portal]

@robust prism 1/2 ×8 × 6 ×sin 135

[robust prism]

which one is the length of height

wait

i mean 6 ×sin 135 is height or 8 ×sin 135

[shut portal]

That's not height, there's a formula of area, where angle b/w 2 sides and 2 sides are given

[robust prism]

hmm

ok thanks

[shut portal]

Then you can find height by comparing it

If you need to

[robust prism]

😃

[red spruce]

Is there a simple way to solve those AP PROVING QUESTIONS like if a b c are in ap then prove this and that

There's Follow a certain steps in books but isn't math supposed to be free thinking

[merry sentinel]

Math is free thinking

[frail nova]

Help i cant solve it

I always get x1 right but x2 wrong

X1 should be -2
And X2 should be 3.5
But i keep getting
X1 = -2
X2 = -1 and 0 and 1

[frail nova]

Still wrong

[near acorn]

x1=-2 and x2=3.5

[frail nova]

No you did x1 =3.5
X2 = -2

Even tho its right

Aaaa my brain hurts

يا محمد متأكد من حلك

[near acorn]

doesn't matter really, but if you want to precise then yes x1=3.5 and x2=-2 since there is a plus minus

[frail nova]

لأنو أنلخمت انا

[near acorn]

put x1 and x2 back in the original equation and see if both sides are equal

[near acorn]

متأكد

[frail nova]

طيب يسلمو

لأنو عندي أمتحان الأثنين و قاعد بضغط نفسي في وسط أمتحانات آخر السنة

[near acorn]

بالتوفيق

[covert anchor]

3b what on earth shuld i do

I just learnt longarithms and I a dumbfounded

[near acorn]

4^(x+1) = 5 e => log(4^(x+1)) = log(5e) => {log property} => (x+1)log(4) = log(5e) => x+1= log(5e)/log(4) => x = log(5e)/log(4) -1

[covert anchor]

i need to solve for x i think

[near acorn]

x = log(5e)/log(4) - 1 which is the last term I wrote, I can write on paper if you want🙂

[covert anchor]

yes please

I got handed all this questions without learning it

[near acorn]

I suggest you have a look at the logarithmic properties, they are helpful when solving problems like this one.

[covert anchor]

the answer is o.882

any idea how to get there ?

[near acorn]

Are you allowed to use a calculator?

[covert anchor]

yes ofc

[near acorn]

on a calculator, use ln(5e)/ln(4) - 1, since the base is Euler's number e

[covert anchor]

(5e) how do i type that in calc

[near acorn]

you can also use log(), you get the same answer

[near acorn]

5*e^1

[covert anchor]

ok its fine now thks

[ashen laurel]

is my answer to part c right?

[peak eagle]

yes and no
you formed the equation right but this > sign indicates you that t is really bigger than 24 but if you but your right side in the calculator it says 23.0259.... so 24 whole hours. so if you put this > it should be 23 because than that sign indicates you that t is bigger. which means that you need to put an t >= 24 from the beginning or say t > 23

your population is bigger already than 1 000 000 after 24 hours.

[ashen laurel]

ahh i get it, thanks a lot!

[steady spear]

this is the solution for finding the sum of all 3 digit values that are a multiple of 14 but not 21

I understand everything apart from why they used 42 instead of 21?

they say Well we only have even multiples of 21 so these are the multiples of 42. 900/42 =~ 21 of theses.

id dont get what they mean by that

[left knoll]

anyone here

i need help

[dense steeple]

send question i will try

[dense steeple]

btw u preparing for ??jee

[left knoll]

yeah

send quick

dont ask questions

pls

[dense steeple]

ok

[left knoll]

i just came in 11

these questions are fucking my brain

[dense steeple]

z>y>x

[left knoll]

send how

[dense steeple]

put c=2 and calculate

[left knoll]

ok

[wanton bolt]

second is right

[dense steeple]

i guess you are sending these during an exam so i wouldn't help you cheat

[left knoll]

are selection test

for the sake of my reputation

[dense steeple]

these aren't that hard, you can solve if you try them

sorry mate cant help you there 😫

[left knoll]

.

ok only one last

im 14 what do you expect from a kid

[dense steeple]

sorry bro didnt knew that

ok which one you want to know the most

[left knoll]

its ok

[left knoll]

last one

[dense steeple]

ok trying

[left knoll]

i have no clue what im doing

[dense steeple]

15

[left knoll]

5 , 4 , 3 , 6 options

btw value of cos1 cos2 cos3 till cos 179 is 0 did i get it right

[dense steeple]

yes

[left knoll]

not in option

[dense steeple]

trying it once more wait

[left knoll]

if sin theta minus cos theta = 1 then sin theta into cos theta is 0 right??

im doing the normal questions

[dense steeple]

yup

[green summit]

even if your reputation is at stake don't cheat, your are just fooling yourself, give your best and complete the test no matter what your age is.

[left knoll]

https://tenor.com/view/boht-hard-hard-work-harden-eminem-yes-gif-13473620

i submitted

[left knoll]

whats the answer

is this answer 3

i somehow tried a bit

yo

anyone

[peak eagle]

put your right side in the calculator and put for the variable a what is written left. 🙂
you should be able to do that 🙂

[sullen musk]

guys help

anyone?

[alpine escarp]

it's a PRMO question. Having qualified PRMO in both 9th and 10th, I can tell you that the exam is pretty hard for a highschooler. It's equally hard in grade 11 and 12 when you dont have much time for olympiads. Don't COPY. You're studying for yourself not to gain reputation at school/coaching. Get that outta your mind first.

All you need is to get about 10 questions right during the final exam. In my time (2-3 years ago) it was about 8-9 questions

[left knoll]

i got 2 questions right

or 3

[covert anchor]

I think many of us here are 14 , Im 14 and im gonna ask a few qs later too

[covert anchor]

Math is really hard for me

[left knoll]

samee

[alpine escarp]

Good. I'm proud of you for getting 2 questions right. But don't cheat.

Practice more and more.